On simulating quantum erasure

Presenting Author: Mohammad Alhejji, University of Colorado JILA
Contributing Author(s): Emanuel Knill

Quantum erasure is one of the most well-understood error models for quantum information processing. However, comparatively little is known about it in the high noise regime, i.e. where the erasure probability exceeds a half and the quantum capacity vanishes. We study the problem of exact simulation of erasure using a fixed resource channel (to be used as many times as needed). We characterize the set of channels that can positively contribute to a convex decomposition of erasure. We point out a connection between simulating erasure and conditional quantum error correction. For the particular case of simulating erasure channels with other erasure channels, we show that stabilizer codes do not improve erasure channels with zero quantum capacity.

Non-Markovian decay of two excited atoms coupled via waveguide

Presenting Author: William Alvarez-Giron, Universidad Nacional Autónoma de México
Contributing Author(s): Pablo Barberis-Blostein, Pablo Solano, Kanupriya Sinha

Synchronization is a universal phenomenon that pervades physical systems ranging from fireflies to planetary motion. When multiple atoms are excited by a laser, the light emitted by them is synchronized in lockstep, an effect commonly known as superfluorescence. In this work, we explore the dependence of this synchrony on the interatomic separation, considering two excited atoms with separations being very close to very far, where the radiation that synchronizes their emission can exhibit significant delays. Such delays can build correlations between the atoms inducing superradiance and subradiance emissions, even non-decay single-excitation states, a phenomenon we refer to as `subflourescence'.

An adaptive algorithm for ansatz construction with condensed quantum circuits

Presenting Author: Panagiotis Anastasiou, Virginia Tech
Contributing Author(s): Yanzhu Chen, Sophia E. Economou, Edwin Barnes, Nicholas J. Mayhall

Quantum simulation of strongly correlated systems is expected to be the “killer” application of quantum computing on noisy intermediate scale quantum (NISQ) devices. One of the most promising NISQ algorithms, the variational quantum eigensolver (VQE), brings down the quantum resource requirements by leveraging the power of classical optimization, yet the gap between the most compact and accurate known ansätze and the coherence properties of our best quantum hardware is still too wide for the VQE to offer a quantum advantage. Recent progress on the theoretical side has reduced the resource requirements with an adaptive algorithm for problem-tailored ansatz construction called ADAPT-VQE. The algorithm uses local energy gradient information to iteratively construct a VQE ansatz specific to the problem at hand, one unitary at a time. In this work, we introduce a variation of the algorithm, which modifies the way the ansatz is created by adding multiple unitaries at a time. Our algorithm results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared to the original ADAPT-VQE. These improvements can contribute to the challenging goal of demonstrating useful quantum advantage with NISQ hardware.

Flag gadgets based on classical codes

Presenting Author: Benjamin Anker, University of New Mexico CQuIC
Contributing Author(s): Milad Marvian

Fault-tolerant quantum error correction is essential for full-scale quantum computing due to high noise levels; however, fault-tolerance in general requires many expensive resources, particularly qubits. Recently it has been shown that by using flag gadgets it is possible to perform fault-tolerant syndrome extraction, a key subroutine of quantum error correction, using fewer resources than conventional methods. Although flag gadgets have already been used in several experiments, a framework that applies to general quantum codes and does not require fast physical operations to achieve a resource reduction has been missing. We develop a framework to design flag gadgets using classical codes, which is applicable to all stabilizer codes. Using this framework we show how to perform fault-tolerant syndrome extraction using exponentially fewer qubits than conventional methods. We also show how to fault-tolerantly measure multiple stabilizers using a single gadget. Using the developed framework we perform numerical simulations to find several small examples where our constructions reduce the number of qubits required. These small examples may be relevant to near-term experiments on small-scale quantum computers.

Local quantum overlapping tomography

Presenting Author: Bruna Araujo, University of New Mexico
Contributing Author(s): Marcio M. Taddei, Daniel Cavalcanti, and Antonio Acın.

Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size. Nevertheless, there are situations in which one is only interested in a subset of these parameters and a full reconstruction is not needed. A paradigmatic example is a scenario where one aims at determining all the reduced states only up to a given size. Overlapping tomography provides constructions to address this problem with a number of product measurements much smaller than what is obtained when performing independent tomography of each reduced state. There are however many relevant physical systems with a natural notion of the locality where one is mostly interested in the reduced states of neighboring particles. In this work, we study this form of local overlapping tomography. First of all, we show that, contrary to its full version, the number of product measurements needed for local overlapping tomography does not grow with system size. Then, we present strategies for qubit and fermionic systems in selected lattice geometries. The developed methods find a natural application in the estimation of many-body systems prepared in current quantum simulators or quantum computing devices, where interactions are often local.

Read this article online: https://arxiv.org/abs/2112.03924

Multi-mode Gaussian State Analysis with Total Photon Counting

Presenting Author: Arik Avagyan, National Institute of Standards and Technology, Boulder
Contributing Author(s): Emanuel Knill, Scott Glancy

The continuing improvement in the qualities of photon-number-resolving detectors opens new possibilities for measuring quantum states of light. In this work we consider the question of what properties of an arbitrary multimode Gaussian state are determined by a single photon-number-resolving detector that measures total photon number. We find an answer to this question in the ideal case where the exact photon-number probabilities are known. We show that the quantities determined by the total photon number distribution are the spectrum of the covariance matrix, the absolute displacement along each eigenspace of the covariance matrix, and nothing else. In the case of pure Gaussian states, the spectrum determines the squeezing parameters. For mixed states we investigate the set of admissible covariance matrices with a given spectrum. In particular, we derive conditions under which the squeezing and temperature parameters are determined by the spectrum.

Extrinsic geometry of Quantum states

Presenting Author: Alexander Avdoshkin, University of California Berkeley
Contributing Author(s): Fedor Popov, NYU

Consider a set of quantum states |ψ(x)⟩ parameterized by x taken from some parameter space M. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann invariant P⁽³⁾(x₁,x₂,x₃) = tr[P(x₁)P(x₂)P(x₃)], where P(x) = |ψ(x)⟩⟨ψ(x)|. Mathematically, P(x) defines a map from M to the complex projective space CPⁿ and this map is uniquely determined by P⁽³⁾(x₁,x₂,x₃) up to a symmetry transformation. The phase arg P⁽³⁾(x₁,x₂,x₃) can be used to compute the Berry phase for any closed loop in M, however, as we prove, it contains other information that cannot be determined from any Berry phase. When the arguments xᵢ of P⁽³⁾(x₁,x₂,x₃) are taken close to each other, to the leading order, it reduces to the familiar Berry curvature ω and quantum metric g. We show that higher orders in this expansion are functionally independent of ω and g and are related to the extrinsic properties of the map of M into CPⁿ giving rise to new local gauge-invariant objects, such as the fully symmetric 3-tensor T. Finally, we show how our results have immediate applications to the modern theory of polarization, calculation of electrical response to a modulated field and physics of flat bands.

Read this article online: https://arxiv.org/abs/2205.15353

Numerical evidence for exponential speed-up of QAOA over unstructured search for approximate constrained optimization

Presenting Author: Andreas Bärtschi, Los Alamos National Laboratory
Contributing Author(s): John Golden, Stephan Eidenbenz, Daniel O'Malley

We present numerical evidence for an exponential speed-up of a Quantum Alternation Operator Ansatz (QAOA) over Grover-style unstructured search in finding approximate solutions to constrained optimization problems. To this end, we conduct a comprehensive numerical study on several Hamming-weight constrained optimization problems (Max-k-VertexCover, Densest-k-Subgraph, Max-Bisection) for which we include combinations of all standardly studied mixer and phase separator Hamiltonians (Ring mixer, Clique mixer, Objective Value phase separator) as well as quantum minimum-finding inspired Hamiltonians (Grover mixer, Threshold-based phase separator). We identify Clique-ObjValue-QAOA with an exponential speedup over Grover-Threshold-QAOA in terms of the number of rounds necessary to reach an approximation ratio of 99%, with all other QAOA combinations coming in at a distant third. For Max-k-VertexCover and Densest-k-Subgraph we also give an efficient gradient descent based angle finding strategy. For comparison, we tie Grover-Threshold-QAOA's scaling in terms of the number of rounds necessary to sample high-value solutions to the same asymptotic behavior as that of unstructured search. Our result suggests that maximizing QAOA performance requires a judicious choice of mixer and phase separator, and should trigger further research into other QAOA variations.

Read this article online: https://arxiv.org/abs/2202.00648

Simulating NISQ dynamics using quantum trajectories with few jumps

Presenting Author: Philip Blocher, University of New Mexico CQuIC
Contributing Author(s): Anupam Mitra, Tameem Albash, Akimasa Miyake, Ivan Deutsch

In this poster we present results on the efficiency of classically simulating the dynamics of open quantum many-body systems using a combination of quantum trajectories and 1D tensor network methods. Using quantum Monte-Carlo wavefunctions, the unraveling of the master equation gives rise to an ensemble of stochastic quantum trajectories conditioned on potential measurement outcomes (jumps). These trajectories must then be averaged over with appropriate jump statistics to obtain the system’s density operator. The averaging is usually done in a stochastic manner until a sufficient threshold for the sampling error is reached. Here we instead propose a deterministic method of sampling trajectories that avoids the computational overhead of stochastic trajectory sampling, is suitable for simulations of noisy intermediate-scale quantum (NISQ) devices, and has an easily computable sampling error. The usual object of interest in simulations of NISQ many-body dynamics is expectation values of local observables – e.g., one- or two-body correlation functions. These expectation values of local observables are regarded as being more robust to decoherence than other quantities less accessible to NISQ devices, and we conjecture that this robustness to decoherence implies the existence of a model solvable with classical efficiency. We apply our trajectory sampling method to demonstrate the efficiency of classical simulations of open quantum many-body dynamics, in support of this conjecture.

Simultaneous stoquasticity

Presenting Author: Jacob Bringewatt, University of Maryland Joint Quantum Institute
Contributing Author(s): Lucas T. Brady

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

Read this article online: https://doi.org/10.1103/PhysRevA.105.062601, https://arxiv.org/abs/2202.08863

Optimizing the Tradeoff Between Trotter Error and Gate Error in Three- and Four-Wave Plasma Problems

Presenting Author: Amy Brown, University of Southern California
Contributing Author(s): Yuan Shi, Vinay Tripathi, Bram Evert, Yujin Cho, Max Porter, Xian Wu, Vasily Geyko, Alexander Hill, Christina Young, Eyob Sete, Ilon Joseph, Jonathan DuBois, Matthew Reagor, Daniel Lidar

Simulations on near-term quantum hardware are limited by hardware error, from gate infidelity and decoherence, and by algorithmic error introduced by approximations, such as the Trotter-Suzuki expansion. Using compilation techniques and an optimal Trotter step size, the algorithmic error incurred by the Trotter- Suzuki expansion, referred to as the “Trotter error,” can be mitigated, and the simulation depth can be improved. In this paper, we explore the tradeoff between Trotter error and gate error in pursuit of the optimal Trotter step size. In particular, we simulate the three-wave and four-wave interaction Hamiltonian, describing a nonlinear optical process, on quantum hardware using a single compiled gate, which we repeatedly apply in a series of Trotterized steps to reach a desired simulation period. We evaluate expectation values of occupation numbers to assess the quality of simulations and use these results to evaluate an optimal Trotter step size. These results serve to facilitate the plasma community’s interest and investment in quantum simulations by demonstrating successful simulation of nonlinear dynamics using product formulas and Trotter expansions to simulate the three-wave and four-wave unitary of interest

Test of Causal Non-Linear Quantum Mechanics by Ramsey Interferometry on the Vibrational Mode of a Trapped Ion

Presenting Author: Joseph Broz, University of California Berkeley
Contributing Author(s): Bingran You, Sumanta Khan, Hartmut Haeffner, David E. Kaplan, Surjeet Rajendran

Kaplan and Rajendran have recently demonstrated that non-linear and state-dependent terms can be consistently added to quantum field theory to yield causal non-linear time evolution in quantum mechanics. Causal non-linear theories have the unavoidable feature that their quantum effects are dramatically sensitive to the full physical spread of the quantum state of the system. As a result, such theories are not well tested by conventional atomic and nuclear spectroscopy. By using a well-controlled superposition of vibrational modes of a 40Ca+ ion trapped in a harmonic potential, we set a stringent limit of 5.4×10−12 on the magnitude of the unitless scaling factor ϵ̃γ for the predicted causal, non-linear perturbation.

Read this article online: https://doi.org/10.48550/arXiv.2206.12976

Two-qubit Quantum Logic Gates for Neutral Atoms Based on the Spin-Flip Blockade

Presenting Author: Vikas Buchemmavari, University of New Mexico CQuIC
Contributing Author(s): Sivaprasad Omanakuttan, Yuan-Yu Jau, Ivan Deutsch

The “spin-flip blockade” was first demonstrated in 2016 by Jau et al. [1]. Analogous to the “Rydberg blockade” for optical excitations, here the spin of one neutral alkali atom in its ground state can be induced to flip between hyperfine manifolds through absorption of a microwave photon, while the two-spins are blockaded from flipping simultaneously. The blockade is caused by the additional energy imparted by a light-shift resulting from Rydberg dressing in the presence of Van der Waals forces. This effect was used to demonstrate the generation of Bell states with fidelity >81% (>90% after SPAM correction). We describe here how to extend this to generate universal two-qubit quantum logic gates. We show that many protocols designed for the optical regime can be translated into the microwave regime and analyze their potential for high-fidelity operation. In comparison to the optical protocols, the ultra-precise control is more easily achieved in the microwave regime, which results in the potential for fast quantum logic gates with reduced noise and low decoherence. We also consider various dressing schemes with different advantages. Finally, we use robust control techniques to make our gates robust against perturbations in hard-to-control parameters. Sandia National Labs is managed and operated by NTESS LLC, a subsidiary of Honeywell Intl., Inc., for the US DOE's NNSA under contract DE-NA0003525. [1] Y.-Y. Jau, A. Hankin, T. Keating, I. Deutsch, and G. Biedermann, Entangl

Quantum circuit debugging and sensitivity analysis via local inversions

Presenting Author: Fernando Calderon-Vargas, Sandia National Laboratories
Contributing Author(s): Timothy Proctor, Kenneth Rudinger, Mohan Sarovar

As the width and depth of quantum circuits implemented by state-of-the-art quantum processors rapidly increase, circuit analysis and assessment via classical simulation is becoming unfeasible. Thus, it is crucial to develop new methods to identify significant error sources in large and complex quantum circuits. In this work, we present a technique that identifies the layers of a circuit that affect the circuit output the most, and thus helps to identify the most significant sources of error. The technique requires no classical verification of circuit output and is thus a scalable tool for debugging large quantum programs in the form of circuits. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.

Read this article online: https://doi.org/10.48550/arXiv.2204.06056

Spontaneous emission in entangling gates for trapped ions at high magnetic fields

Presenting Author: Allison Carter, National Institute of Standards and Technology, Boulder
Contributing Author(s): Sean Muleady, Athreya Shankar, Jennifer Lilieholm, Bryce Bullock, Matthew Affolter, Ana Maria Rey, John Bollinger

Trapped ion systems have achieved some of the highest entangling gate fidelities, often limited by spontaneous emission from off-resonant lasers. Many previous treatments of spontaneous emission assume that the only contribution from elastic off-resonant light scatter to decoherence is through the recoil of the ions. This statement generally applies only to clock qubits. At the high magnetic fields required for Penning traps, however, clock qubits are often not an option. Here we consider the impact of spontaneous emission on Zeeman qubits for different types of entangling gates. In the NIST Penning trap, we have performed quantum simulations and sensing experiments on two-dimensional crystals of hundreds of beryllium ions at 4.5 T with a light-shift gate. A common alternative is the Mølmer-Sørensen gate. One advantage of the Mølmer-Sørensen gate is that it can be configured such that the driven ion motional state is less sensitive to optical phase fluctuations between the driving laser beams. This can be used to improve sensing applications and drive gates in 3-D crystals of up to tens of thousands of ions. We show that in the high-field regime, the light-shift and Mølmer-Sørensen gates perform comparably. We explore a wide variety of operating configurations for both types of gates. We also present a novel treatment of the spontaneous emission for carrier transitions for Pauli X gates, which are closely related to the Mølmer-Sørensen gate.

Magnetic solitons in spinor Bose-Einstein condensates

Presenting Author: Xiao Chai, Georgia Institute of Technology
Contributing Author(s): Di Lao, Sara Sloman, Kazuya Fujimoto, Chandra Raman

Vector solitons are solitary waves occurring in multi-component nonlinear media. In spin-1 Bose-Einstein condensates (BECs), magnetic solitons, a novel type of vector solitons, have drawn considerable attention recently. Their existence relies crucially on the imbalance between intra- and interspecies nonlinear strengths, which stems from the spin-dependent contact interaction. Here we report on the first observation of magnetic solitons in an antiferromagnetic spin-1 BEC [1], where the solitons manifest themselves as a localized spin excitation propagating upon a balanced two-component condensate. By harnessing the underlying SO(3) symmetry of the spin-1 manifold, we derive a class of magnetic soliton solutions with three components and provide experimental evidence of them as well [2]. Moreover, we extend the study of magnetic solitons to the ferromagnetic case, where the solitons behave as a local spin-flip propagating on top of a spin-polarized background [3]. References [1] X. Chai, D. Lao, K. Fujimoto, R. Hamazaki, M. Ueda, and C. Raman, Magnetic Solitons in a Spin-1 Bose-Einstein Condensate, Phys. Rev. Lett., 125 (2020), 030402. [2] X. Chai, D. Lao, K. Fujimoto, and C. Raman, Magnetic Soliton: From Two to Three Components with SO(3) Symmetry, Phys. Rev. Res., 3 (2021), L012003. [3] X. Chai, L. You, and C. Raman, Magnetic Solitons in an Immiscible Two-Component Bose-Einstein Condensate Phys. Rev. A, 105 (2022), 013313.

Read this article online: https://doi.org/10.1103/PhysRevLett.125.030402, https://doi.org/10.1103/PhysRevResearch.3.L012003, https://doi.org/10.1103/PhysRevA.105.013313

A quantum trajectory picture of single photon absorption and energy transport in photosystem II

Presenting Author: Robert Cook, University of California Berkeley
Contributing Author(s): Liwen Ko, K. Birgitta Whaley

We study the first step in photosynthesis for the limiting case of a single photon interacting with a specific photosynthetic molecular complex, photosystem II (PSII) of green plants. In this talk, we present theoretical results that show how the absorption of a single photon evolves over time given individual realizations of idealized measurements of the outgoing photon fields. This describes a single quantum trajectory whose evolution can be far from equilibrium. Our results show how the (null) detection of the outgoing photon confirms that the system must be in the electronic (excited) ground state, which we show is an effect unique to a single photon input. Our theory includes phonon degrees of freedom and non-radiative channels, which allow us to obtain a microscopic estimate of the uniquely high quantum efficiency of plants to convert absorbed photons into electron-hole pairs. We obtain an average efficiency of 92% under realistic ambient conditions, consistent with bulk experimental measurements. We will also discuss what role the greater molecular environment has on the coherence of the single photon absorption, how this affects the net probability of excitation, and what information could be recovered by continuously measuring the phononic environment.

Read this article online: https://arxiv.org/abs/2110.13811

Verification and validation of characterization methods for quantum computers

Presenting Author: Megan Dahlhauser, Sandia National Laboratories
Contributing Author(s): Robin Blume-Kohout, Timothy Proctor, Kevin Young

Characterizing low-level components of quantum computers is critical to understand quantum systems, identify errors, and pursue opportunities for engineering improvements. Tantamount to these characterization tasks is the expectation that an effective and useful characterization should provide accurate predictions of circuit outcomes. Success in accurately predicting circuit outcomes validates our characterization and understanding of our quantum system, whereas a failure to accurately predict circuit outcomes indicates either a poor, inappropriate, or obsolete characterization. While evaluating the performance of a characterization methodology is vital, this performance is not a binary metric and determining when a characterization is performing well or at least satisfactorily can be difficult. We present a generalized process of verification and validation of characterization protocols. We show how to determine and report characterization performance on circuit prediction tasks using statistical tests and simulation. We demonstrate this process in experiment using gate set tomography and randomized benchmarking and evaluate performance on several distinct circuit prediction tasks. We find that our validation process is an effective tool in identifying characterization shortcomings and upgrading methodologies to create more accurate characterizations of quantum devices.

Quantum search by the nonlinear Schrodinger equation with a generalized cubic-quintic nonlinearity

Presenting Author: Benjamin DalFavero, Creighton University
Contributing Author(s): Alexander Meill, David A. Meyer, Thomas G. Wong, Jonathan Wrubel

Continuous-time quantum walks, a quantum analog to the continuous time Markov chain, allow the efficient solution to spatial search problems. At low temperatures and a high number of atoms, two- and three-body interactions cause Bose-Einstein condensates to evolve according to an effective, non-linear Schrodinger equation. These effective nonlinearities can be exploited to accelerate the propagation of the walk, reaching a solution to the search problem faster than the linear case. This acceleration comes at the cost of increased precision needed in the timing of the search. We will present our work analyzing the computational speedups afforded by continuous-time quantum walks with effective nonlinearities for search problems with multiple correct answers.

Quantum Resources Required to Block-Encode a Matrix of Classical Data

Presenting Author: Alexander Dalzell, Amazon Web Services
Contributing Author(s): B. David Clader, Nikitas Stamatopoulos, Grant Salton, Mario Berta, William J. Zeng

We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense N×N matrix of classical data to precision ϵ; the minimal-depth method achieves a T-depth of O(log(N/ϵ)), while the minimal-count method achieves a T-count of O(Nlog(1/ϵ)). We examine resource tradeoffs between the different approaches, and we explore implementations of two separate models of quantum random access memory (QRAM). As part of this analysis, we provide a novel state preparation routine with T-depth O(log(N/ϵ)), improving on previous constructions with scaling O(log^2(N/ϵ)). Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.

Read this article online: https://arxiv.org/abs/2206.03505

Recovery with incomplete knowledge: fundamental bounds on real-time quantum memories

Presenting Author: Arshag Danageozian, Louisiana State University

The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely on the prior knowledge of the environment noise parameter to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates the use of a "spectator" system, which makes an estimate of the noise parameter in real time, then feeds the outcome back to the recovery protocol as a classical side-information. In this article, I present information-theoretic bounds on the performance of such a spectator-based recovery. I show that there is a fundamental bound in the performance of any recovery operation, as a function of the entanglement fidelity of the overall dynamics. The lower bound for the diamond distance has a simple form, and a potentially broader range of applicability in quantum information. I provide information-theoretic characterizations of the incomplete knowledge of the noise parameter to the lower bound, using both diamond distance and quantum Fisher information. Finally, I provide fundamental bounds for multi-cycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge could be an advantage, as errors from various cycles can cohere. Results are illustrated for the amplitude-damping noise.

Read this article online: https://arxiv.org/abs/2208.04427

Quantum and Classical Bayesian agents

Presenting Author: John DeBrota, University of New Mexico CQuIC
Contributing Author(s): Peter Love

We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which the properties of one agent may influence another, we arrive at a flexible framework for treating multiple interacting quantum and classical Bayesian agents. We present simulations in several settings to illustrate our construction: quantum and classical agents receiving signals from an exogenous source, two interacting classical agents, two interacting quantum agents, and interactions between classical and quantum agents. A consistent treatment of multiple interacting users of quantum theory may allow us to properly interpret existing multi-agent protocols and could suggest new approaches in other areas such as quantum algorithm design.

Read this article online: https://quantum-journal.org/papers/q-2022-05-16-713/

Effects of reservoir correlations in non-Markovian atomic collective decay

Presenting Author: Alberto Del Angel Medina, Universidad Nacional Autonoma de Mexico
Contributing Author(s): Pablo Solano, Pablo Barberis Blostein

The Born and Markov approximations play a central role when deriving the master equations of interacting emitters coupled with waveguides. In this work, we calculate the zero-temperature correlation functions of the fundamental guided mode of an optical nanofiber, which acts as the reservoir of one and two interacting atoms. By numerically solving the atomic evolution equations in the non-Markovian regime, we study how its collective behavior establishes when separated at distances close to their resonant wavelength. We find a significant delay between the onset of the atom-atom interaction and a complete super(sub)radiant decay. We observe slight deviations in these decay rates compared to the predictions given by the Markov approximation. Our results also allow us to identify the regimes for which it's valid to regard the correlation functions as displaced delta distributions, an approximation commonly used in waveguide QED. Our work provides a deeper understanding of the collective interaction mechanism in this platform and the approximations used in its description.

Infinite quantum signal processing

Presenting Author: Yulong Dong, University of California Berkeley
Contributing Author(s): Lin Lin Hongkang Ni Jiasu Wang

The quantum singular value transformation (QSVT) [Gilyen, Su, Low, Wiebe, STOC 2019] provides a unified viewpoint of a large class of practically useful quantum algorithms. At the heart of QSVT is a new polynomial representation, called quantum signal processing (QSP). QSP represents a degree-d polynomial using products of matrices in SU(2), parameterized by (d+1) real numbers called the phase factors. When the polynomial of interest is obtained by truncating an infinite polynomial series, a natural question is whether the phase factors have a well defined limit as $d \to \infty$. In this talk, we will show that there exists a consistent choice of the parameterization so that the limit is well defined. This generalizes QSP to represent a large class of non-polynomial functions, and this construction is referred to as infinite QSP (iQSP). We present a very simple algorithm for finding such infinitely long phase factors with provable performance guarantees. We will also show a surprising connection between the regularity of the target function and the structural properties of the phase factors.

Constructing gate cycles with predictable stochastic error rates in the quantum approximate optimization algorithm

Presenting Author: Bram Evert, Rigetti Computing
Contributing Author(s): Mark Hodson, Dennis Feng, Stephen Jeffrey, Ian Hincks, Zhihui Wang, James Sud, Shon Grabbe, Nicolas Didier, Eleanor Rieffel, Davide Venturelli, Joel Wallman, Matt Reagor

Theoretical frameworks for studying quantum algorithms typically assume a well-behaved error model, where average gate fidelities, estimated for instance via randomized benchmarking, are representative and errors are uncorrelated. Experimental quantum hardware routinely breaks these assumptions due to coherent errors and crosstalk. Here, we show how the use of random compilation and cycle calibration strategies can recover a well-behaved error model. These strategies are demonstrated in a large-scale QAOA ansatz.

Rapid exchange cooling with calcium ions

Presenting Author: Spencer Fallek, Georgia Tech Research Institute
Contributing Author(s): Vikram Sandhu, Ryan McGill, Holly Tinkey, Craig Clark, Kenton Brown

In trapped ion quantum information, maintaining low ion temperature of computational ions is key to performing high fidelity gates. However, sympathetic cooling, the current standard in the field, is both slow and experimentally complex. In this work, we experimentally study the technique of exchange cooling. The protocol utilizes a bank of cold ions to cool the hotter computational ions. Both the coolant and computational ions are of the same atomic species. The Coulomb interaction mediates an energy exchange between a coolant ion and a computational ion. However, the rate of exchange depends strongly on the distance between the two ions. Here, we execute the scheme, targeting an exchange rate which achieves cooling times on the order of gate execution times. Additionally, we investigate the concept of cooling through a merge, whereby the ions are brought into the same harmonic potential well and then split apart.

IonSim: A lightweight Julia package for simulating trapped-ion dynamics

Presenting Author: Neil Glikin, University of California Berkeley
Contributing Author(s): Joseph Broz, Kunal Marwaha, Kristian D. Barajas, Thomas Dellaert

We present IonSim.jl, an open-source computational software package in the Julia programming language for simulating the dynamics of trapped ions interacting with laser light. IonSim allows the user to define their system of interest in terms of concrete experimental parameters rather than abstract ones, from which it can efficiently construct the system's Hamiltonian and solve for its time dynamics. User-configurable parameters include motional modes, laser properties and geometry, ion chain length and constituent species, and relevant energy levels and sublevels. The IonSim.jl project is actively expanding its capabilities and robustness, and aims to provide to the trapped-ion community a user-friendly and quantitatively reliable numerical simulation tool.

High-Fidelity Qutrit Entangling Gates for Superconducting Circuits

Presenting Author: Noah Goss, University of California Berkeley
Contributing Author(s): Alexis Morvan, Brian Marinelli, Bradley K. Mitchell, Long B. Nguyen, Ravi K. Naik, Larry Chen, Christian Jünger, John Mark Kreikebaum, David I. Santiago, Joel J. Wallman, Irfan Siddiqi

Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the ZZ interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ† and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device.

Read this article online: https://arxiv.org/abs/2206.07216

Composite Quantum Simulation

Presenting Author: Matthew Hagan, University of Toronto
Contributing Author(s): Nathan Wiebe

We provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single composite channel that builds upon older coalescing ideas for reducing gate counts. The central idea behind our approach is to use a partitioning scheme that allocates a Hamiltonian term to the Trotter or QDrift part of a channel within the simulation. This allows us to simulate small but numerous terms using QDrift while simulating the larger terms using a high-order Trotter-Suzuki formula. We prove rigorous bounds on the diamond distance between the composite channel and the ideal simulation channel and show under what conditions the cost of implementing the composite channel is asymptotically upper bounded by the methods that comprise it for both probabilistic partitioning of terms and deterministic partitioning. Finally, we discuss strategies for determining partitioning schemes as well as methods for incorporating different simulation methods within the same framework.

Read this article online: https://arxiv.org/pdf/2206.06409.pdf

Adaptive entanglement witnessing with limited local measurement

Presenting Author: Ben Hartley, Harvey Mudd College
Contributing Author(s): Becca Verghese, Eritas Yang, Theresa W. Lynn

We derive and experimentally verify the efficacy of an adaptive entanglement witnessing procedure on two qubits that utilizes local measurements in fewer bases than would be necessary for full state tomography. We begin with six classes of witnesses, {W}, formulated by Riccardi et al (Phys. Rev. A 101, 062319, 2020), and construct 3 additional triplet sets of optimal entanglement witnesses, {W’}, that each require local measurements in two further bases. When applied to computationally generated random two-qubit states, our adaptive procedure is able to witness a significantly more complete set of entangled states than the static {W} witnesses alone. The entangled states which remain undetected have a low concurrence. Using polarization-entangled photons generated via spontaneous parametric down conversion, we demonstrate the behavior of {W} discussed in (reference) and also create and measure two-qubit entangled states that cannot be witnessed by the static method but are detected by our adaptive method. Finally, we discuss future experimental implementations and possible directions to improve our procedure.

An efficient scalable benchmarking protocol for analog quantum computers

Presenting Author: Bharath Hebbe Madhusudhana, Max Planck Institute for Quantum Optics

Accurate and precise control of large quantum systems is paramount to achieve practical advantages on quantum devices. Therefore, benchmarking the hardware errors in quantum computers has drawn significant attention lately.Existing benchmarks for digital quantum computers involve averaging the global fidelity over a large set of quantum circuits and are therefore unsuitable for specific many-body control operations used in analog quantum devices. Moreover, average global fidelity is not the optimal figure-of-merit for the applications specific to analog devices, which often use local observables. Here, we develop a new figure-of-merit suitable for analog devices based on the reduced Choi matrix of the quantum operation. We develop an efficient, scalable protocol to completely characterize the reduced Choi matrix. We construct a set of multi-qubit mixed states that can be prepared with a high fidelity and scalability. We then use them as initial states to construct a local process tomography protocol that extracts the reduced Choi matrix. Further, we show how to classically compute the ideal reduced Choi matrix, in order to obtain the local process fidelity – our figure-of-merit. Focussing on the local process fidelities corresponding to a one and two qubit subsystems of an N-qubit system, we perform a numerical experiment, simulating common noise models to illustrate our protocol. Finally, we propose an implementation of our protocol using rydberg atoms in a tweezer array.

Adiabatically implemented quantum imaginary time evolution

Presenting Author: Kasra Hejazi, California Institute of Technology
Contributing Author(s): Garnet Kin-Lic Chan

An adiabatic state preparation method is introduced which implements quantum imaginary time evolution under the Hamiltonian of a system. This method, unlike the conventional quantum imaginary time algorithm, does not require quantum state tomography during its runtime. The adiabatic Hamiltonian for this purpose, that is used to implement the adiabatic time evolution, is found by solving a differential equation. Some numerical results regarding the procedure in one dimension are presented. It is, in particular, shown numerically that it is possible to have a polynomially scaling adiabatic runtime with the system size.

Read this article online: N/A

Fast non-destructive cavity readout of single atoms within a coherent atom array

Presenting Author: Jacquelyn Ho, University of California Berkeley
Contributing Author(s): Emma Deist, Leon Lu, Mary Kate Pasha, Johannes Zeiher, Zhenjie Yan, Dan M. Stamper-Kurn

The ability to measure a subset of a quantum system without perturbing the rest paves the way for quantum error correction, quantum teleportation, and other real-time feedback processes. Here, we demonstrate rapid, localized, and lossless state measurement of single 87Rb atoms in an optical tweezer array adjacent to a high-finesse optical cavity. This extends the capabilities of atomic array experiments by offering an alternative to global detection relying on state-selective atom loss and fluorescence imaging. In our work, single atoms are moved into the cavity for fast fluorescence- or transmission-based readout that differentiates among the ground state hyperfine levels and empty cavity. We achieve measurement fidelities exceeding 99% in timescales of tens of microseconds. To establish the local nature of this measurement, we initialize a two-atom array and perform a microwave Ramsey experiment, with a cavity measurement of the first atom between Ramsey pulses on the second atom. The second atom’s coherence is unperturbed by the first atom measurement.

Read this article online: https://arxiv.org/pdf/2205.14138.pdf

Fast Transport of a Trapped Bose-Einstein Condensate Using Counterdiabatic Driving

Presenting Author: John Holt, Miami University
Contributing Author(s): Chris Larson, Edward Carlo Samson

We present an analysis of fast, coherent transport of a trapped interacting Bose-Einstein condensate (BEC) through three-dimensional (3D) numerical simulations by solving the time-dependent Gross Pitaevskii equation (GPE). A counterdiabatic driving (CD) protocol was used in order to achieve fast transport with a high quantum fidelity outcome. The trapping and CD potentials in the simulations were modeled as painted potentials, and the effects of the optical intensity of the painting beam was studied. By varying the transport time, our results show that a decrease in quantum fidelity is due primarily to either atom loss or center-of-mass (COM) oscillations. At longer (shorter) transport times, COM oscillations (atom loss) is the primary mechanism for decoherence, and the boundary between these two regimes is affected by the optical intensity of the painting beam. We also present comparisons to a constant acceleration protocol, and the robustness of CD driving from other decoherence mechanisms related to the trap depth.

Predicting the success rates of quantum circuits with artificial neural networks

Presenting Author: Daniel Hothem, Sandia National Laboratories
Contributing Author(s): Tommie Catanach, Timothy Proctor, Kevin Young

Current quantum computers are noisy and error-prone. As devices grow in size, we need scalable methods for predicting the performance of a given device. In this work, we explore the potential of neural networks to play this role. We demonstrate a convolutional neural network’s ability to predict circuit success rates under both simulated and experimental error models; in each case outperforming non-neural network models that are based on per gate error rates. We also experimentally investigate how a convolutional network’s ability to predict success rates varies as a function of dataset size and measurement accuracy, achieving exponential improvements in performance on simulated data as measurement precision increases. Finally, we present proof-of-concept work detailing a convolutional neural network’s ability to handle non-Markovian noise on wide circuits (greater than 30 qubits), a regime in which traditional techniques become inaccurate and highly expensive. This work was supported by the LDRD program at Sandia National Labs. Sandia National Labs is a multimission laboratory managed and operated by NTESS, LLC, a wholly owned subsidiary of Honeywell International Inc., for DOE’s NNSA under contract DE-NA0003525.

Entropy fluctuation formulas of fermionic Gaussian states

Presenting Author: Youyi Huang, Texas Tech University
Contributing Author(s): Lu Wei

We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states as measured by von Neumann entropy. The average von Neumann entropy formulas of fermionic Gaussian states with and without particle number constrain have been recently derived in the literature, whereas the main results of this work are the exact yet explicit formulas of the corresponding variance. Different than the previous computation of exact moments in other models of generic states, the key ingredient in proving the results of this work relies on a new simplification framework. The new framework involvs a set of novel tools of dummy summations and resummation techniques. As a byproduct, the proposed framework leads to various new transformation formulas of special functions.

Variational quantum simulation of valence-bond solids

Presenting Author: Daniel Huerga, University of British Columbia

We present a hybrid algorithm to simulate two-dimensional frustrated quantum magnets in the thermodynamic limit. Built upon a cluster-Gutzwiller ansatz, a shallow U(1) symmetric parameterized quantum circuit provides the wave function of the cluster, while information of the infinite lattice is provided through a self-consistent mean-field embedding. We benchmark the algorithm on the J1-J2 Heisenberg anti-ferromagnet on the square lattice and uncover its phase diagram, which hosts long-range ordered phases, as well as an intermediate valence-bond solid (VBS) phase characterized by a periodic pattern of strongly-correlated 2x2 plaquettes. Our results show that the mean-fields guide its convergence avoiding the so-called barren-plateaux, large flat regions in the optimization landscape that generically impede scalability of variational quantum algorithms. The plaquette-VBS phase is accessed by smoothly driving the system from the Neel phase through a quantum phase transition, opening the route for its quantum simulation with current superconducting circuit technology.

Read this article online: https://arxiv.org/abs/2201.02545

Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values

Presenting Author: William Huggins, Google
Contributing Author(s): Kianna Wan, Jarrod McClean, Thomas E. O'Brien, Nathan Wiebe, Ryan Babbush

Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error ε as ε^−1. In this paper we address the task of estimating the expectation values of M different observables, each to within additive error ε, with the same ε^−1 dependence. We describe an approach that leverages Gilyén et al.'s quantum gradient estimation algorithm to achieve M^(1/2) ε^−1 scaling up to logarithmic factors, regardless of the commutation properties of the M observables. We prove that this scaling is worst-case optimal in the high-precision regime if the state preparation is treated as a black box, even when the operators are mutually commuting. We highlight the flexibility of our approach by presenting several generalizations, including a strategy for accelerating the estimation of a collection of dynamic correlation functions.

Read this article online: https://arxiv.org/abs/2111.09283

Coherent Measuring Processes, Standard and Generalized

Presenting Author: Chris Jackson, Sandia National Laboratories
Contributing Author(s): Carlton M. Caves

The Measuring Process is a topic fundamental to Quantum Theory. Yet, the idea of measurement still isn’t understood much beyond the usual idea of single Hermitian observables, often called von Neumann measurements. Most important beyond von Neumann are the measurements associated with the laboriously named Generalized-Coherent-State (GCS) Positive Operator-Valued Measures (POVMs), a.k.a. overcomplete bases. Despite significant application to many fundamental topics such as tomography, phase space, and condensed matter theory, an understanding of the process by which the GCS POVMs can be realized is still widely underdeveloped. The overarching exception to this is the heterodyne measurement of optics, a measuring process understood mostly via the Leaky Cavity model. More recently discovered is the isotropic measuring process, a realization of the spin-coherent-state POVMs that has yet to be performed. [See link] In this talk I’ll share my understanding of Coherent Measuring Processes (CMPs)—that is, non-adaptive measuring processes which culminate into GCS POVMs—with what I call the Principle Instrument Program. How the Kraus operators of a CMP culminate into a GCS POVM is actually independent of the Hilbert space—that is, CMPs have actually nothing to do with the eigenstates of the observables being measured and thus are very different from von Neumann measurement. This departure from the Hilbert space is made by considering what I call the Kraus-operator density.

Read this article online: https://arxiv.org/abs/2107.12396, https://arxiv.org/abs/1805.01012

Doppler cooling of trapped ions under micromotion

Presenting Author: Alexander Kato, University of Washington
Contributing Author(s): Andrei Nomerotski, Boris Blinov

Extending ion traps into two dimensions is desirable to scale up the number of qubits for quantum computation and simulation. However, in radiofrequency (RF) traps, this can be difficult because of ion micromotion. Micromotion in trapped ions is a driven motion that is a consequence of the RF voltage that is used to create the confining potential. This motion inhibits efficient cooling by causing time dependent Doppler shifts and distorting the atomic absorption spectrum. As a consequence, cooling large arrays of ions can be difficult. We discuss two methods for improving cooling in the presence of significant micromotion. The first method is to power broaden and detune the cooling beams, reducing the distorting effects. The second method is to use pulses of Doppler cooling light synchronized with the trap RF, narrowing the range of velocities that must be addressed by the cooling beams.

The landscape of QAOA max-cut Lie algebras

Presenting Author: Sujay Kazi, Los Alamos National Laboratory
Contributing Author(s): Martin Larocca, Robert Zeier, Marco Farinati, Marco Cerezo, Patrick Coles

It is conjectured that the existence of barren plateaus in the cost function for deep variational quantum algorithms is closely tied to the dimension of the dynamical Lie algebra (DLA) obtained from the set of generators of the ansatz. To this end, given a simple graph $G=(V,E)$

. We investigate a variety of salient features of these DLAs, such as their linear symmetries, quadratic symmetries, decomposition into simple Lie algebras, and irreducible representation structure. We find that there are many cases of symmetries that cannot be explained by parity and automorphisms alone, and there are additionally many cases of failure of subspace controllability. However, we also present numerical evidence that these effects, while quite complex, become proportionally less frequent as the graph size increases, even for fairly small graphs, making it very likely that the vast majority of graphs have Max-Cut DLA dimensions that scale exponentially with the number of vertices.

Finite efficiency measurements and quantum back-action control of chaos

Presenting Author: Maya Khesin, Carleton College
Contributing Author(s): Yusuf Ismail (Carleton College), Sacha Greenfield (USC), and Arjendu K. Pattanayak (Carleton College)

Quantum backaction from weak measurement affects the dynamics of nonlinear quantum systems in intriguing and useful ways. Previous simulations showed that for an optical cavity based implementation of the driven Duffing oscillator, the phase setting ϕ for a laser used for measurement changes quantum dissipation. This can considerably alter the energy absorbed, enabling significant control including changing the quantum trajectory dynamics from regular to chaotic and vice-versa. We present new results on the effect of measurement information being discarded, in particular by tracing over trajectories with different stochastic realizations to recover a density matrix. Disparities between dynamics at different ϕ vanish when sufficiently large numbers of trajectories are sampled. We also report on how results interpolate between these for finite efficiency measurements, which requires a different formalism.

Improved quantum query algorithms on non-worst-case inputs

Presenting Author: Shelby Kimmel, Middlebury College
Contributing Author(s): Noel Anderson Jay-U Chung Da-Yeon Koh Chloe Ye

Quantum span program algorithms for function evaluation sometimes have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these improvements persist even without a promise ahead of time, and we extend this approach to the more general problem of state conversion. For example, there is a span program algorithm that decides whether two vertices are connected in an $n$

in advance.

Read this article online: https://arxiv.org/abs/2012.01276

Digital state preparation error in the adiabatic regime

Presenting Author: Lucas Kocia, Sandia National Laboratories
Contributing Author(s): Fernando A. Calderon-Vargas, Matthew D. Grace, Alicia B. Magann, James B. Larsen, Andrew D. Baczewski, Mohan Sarovar

Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize. The digitization of such an evolution introduces an additional structured contribution. We prove that the first-order Trotterization of an adiabatic evolution produces cumulative infidelity that scales as O(δt^2/T^2) instead of O(Tδt) expected from general Trotter bounds, where δt is the timestep and T is the total time. This greatly reduces the required circuit depth for adiabatic digital quantum simulation algorithms and explains why, despite increasing T, infidelities for constant-timestep digitized evolutions still decrease for a wide variety of Hamiltonians. As a consequence, this result resolves an open problem relating these evolutions to the quantum approximate optimization algorithm.

Choosing sequence lengths for single-shot-randomized Clifford benchmarking

Presenting Author: Alex Kwiatkowski, University of Colorado
Contributing Author(s): Scott Glancy, Emanuel Knill

We analyze randomized benchmarking of Clifford gates when a new random gate sequence is drawn for each single shot of the experiment, where a single shot consists of a state preparation followed by a gate sequence and then a measurement. We present calculations of Fisher-efficient choices of sequence lengths for n-qubit experiments that minimize the total experiment time needed to achieve a fixed statistical uncertainty while taking into account the different time-costs of shots with different sequence lengths. We provide comparison to past randomized benchmarking experiments and demonstrate that improvements in signal-to-noise are possible. We also describe models of Clifford randomized benchmarking with possible time-dependent or gate-dependent errors and discuss strategies for choosing sequence lengths in this case.

Designing quantum networks of optically connected microwave systems limited by transduction

Presenting Author: Akira Kyle, University of Colorado
Contributing Author(s): Curtis L. Rau, Alex Kwiatkowski, Ezad Shojaee, John D. Teufel, Konrad W. Lehnert, Tasshi Dennis

Transduction will likely be the bottleneck in quantum networks of optically connected microwave systems, and so these networks will need to leverage the resources which are more readily available in the optical and microwave domains. We begin by characterizing the set of networks involving doubly parametric transducers, such as electro-opto-mechanical devices, when only allowing for optical Gaussian states and operations, but no measurements. We find that even under these constraints, there is no optimal network with respect to the transducer's experimentally limited parameters. For example, the optimal network for a transducer with large quantum cooperativities but limited efficiencies is different than the optimal network for a transducer operating in the opposite limit. We then explore what states, operations, and measurements would be required for a network to only be limited by the transducers. For the doubly parametric transducer's two-mode Gaussian channel, we conjecture that this requires access to optical non-Gaussian resources in order for the network to never be separable across the microwave domains.

Group Invariant Quantum Machine Learning

Presenting Author: Martin Larocca, Los Alamos National Laboratory
Contributing Author(s): Frederic Sauvage, Marco Cerezo, Guillaume Verdon, Faris Sbahi, Patrick Coles, Marco Cerezo

Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data and task are used to build QML models that, by construction, respect those symmetries. Specifically, these group-invariant models produce outputs that remain fixed under the action of some symmetry group $\mathfrak{G}$ associated with the learning task. We first present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and then exemplify their application through several paradigmatic QML classification tasks. Notably, our framework allows us to recover, in an elegant way, several well known algorithms for the literature, as well as to discover new ones. Taken together, our results pave the way towards a more effective QML model design.

Read this article online: https://arxiv.org/abs/2205.02261

Lyapunov control-inspired quantum algorithms for ground state preparation

Presenting Author: James Larsen, Sandia National Laboratories
Contributing Author(s): Matthew Grace, Andrew Baczewski, Alicia Magann

The Feedback-based Algorithm for Quantum OptimizatioN (FALQON) was recently proposed as a new strategy for performing combinatorial optimization on quantum computers. The key feature of this approach is that it does not require any classical optimization, which differentiates it from QAOA and other variational quantum algorithms. Instead, quantum circuit parameter values are set using a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. In this poster, we explore how this framework can be adapted to applications beyond combinatorial optimization. To this end, we introduce a generalized formulation of feedback-based quantum algorithms for preparing ground states of quantum systems in a manner that is optimization-free. A variety of numerical analyses will be presented that investigate its performance for finding ground states of the Fermi-Hubbard model for strongly correlated quantum systems. Sandia National Labs is managed and operated by NTESS under DOE NNSA contract DENA0003525. SAND2022-10728 A.

A multi-qubit quantum gate using the Zeno effect

Presenting Author: Philippe Lewalle, University of California Berkeley
Contributing Author(s): Leigh S. Martin, Emmanuel Flurin, Song Zhang, Eliya Blumenthal, Shay Hacohen-Gourgy, Daniel Burgarth, K. Birgitta Whaley

The Zeno effect, in which repeated observation freezes the dynamics of a quantum system, stands as an iconic oddity of quantum mechanics. When a measurement is unable to distinguish between states in a subspace, the dynamics within that subspace can be profoundly altered, leading to non-trivial behavior. Here we show that such a measurement can turn a non-interacting system with only single-qubit control into a two- or multi-qubit entangling gate, which we call a Zeno gate. We derive simple closed-form expressions for the gate fidelity under a number of non-idealities and show that the gate is viable for implementation in circuit and cavity QED systems.

Two qubit gates for the 0-π qubit

Presenting Author: Zhenxing Liu, University of Colorado Boulder
Contributing Author(s): Joshua Combes, Andras Gyenis

The transmon is the most successful superconducting qubit to date. The next generation of superconducting qubits, also known as protected qubits, are more complicated than the transmon but are expected to have longer coherence times relative to the transmon. By engineering more complicated circuits qubits are “protected” from noise by the laws of physics. The 0−π qubit is one of the most attractive candidates for a protected superconducting qubit. Since the 0−π qubit was proposed [1], it has been thoroughly investigated [2] and even experimentally realized [3]. However, a practical two-qubit gate for 0−π qubit has not yet been proposed. Here we will present the design of several two qubit gates for the 0−π qubit. Specifically, we show how to couple any degrees of freedom in one 0−π to any degrees of freedom in another 0−π circuit. References: [1] P. Brooks et al. Phys. Rev. A 87, 052306 (2013) [2] A. D. Paolo et al. New J. Phys. 21, 043002 (2019). [3] A. Gyenis et al. PRX Quantum 2, 010339 (2021).

A completely non-classical treatment of homodyne measurements

Presenting Author: Noah Lordi, University of Colorado
Contributing Author(s): Eugene Tsao, Scott Diddams, Austin Lund, Josh Combes

Homodyne measurements are popular in both classical and quantum contexts. Traditional homodyne measurements use a strong coherent local oscillator and limit to a field quadrature measurement. The same apparatus can be utilized with various local oscillator states to produce unique and useful measurements. We consider injecting coherent state superpositions, photon number states, and more nonclassical states. Using these novel local oscillators we can construct measurements of logical operators and stabilizers for GKP qubits among other unique measurements. We are able to analyze the resulting measurements through their Kraus representations. This gives a complete picture of the measurement outcomes and post-measurement states.

Obtaining Fastest Known Solution of Chromatic Number With Quantum Search and Quantum Counting

Presenting Author: David Lutze, California Polytechnic State University
Contributing Author(s): Katharina Gillen

Graphs consist of vertices connected by edges. Graphs can be used to model a variety of real world problems such as scheduling, route planning, and data transformation. K-Coloring is a graph problem where the solution is coloring all vertices such that no adjacent vertex is the same color. Chromatic Number’s solution is the smallest possible number of colors that can solve K-Coloring. This work presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2^(n/2)n^2(log2n)^2). This is an improvement over the best known algorithm, with a run time of 2^nn^O(1) [1]. This algorithm uses the Quantum Search algorithm, and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, and is an optimization variant of the NP-Complete problem K-Coloring. NP-Hard and NP-Complete problems are computationally expensive to solve. Any NP-Complete problem can be transformed into any other NP-Complete problem. The solution of Chromatic Number builds off a solution of the K-Coloring. As many NP-Hard problems are optimization variants of NP-Complete problems, this solution of Chromatic Number suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can be framed as NP-Hard problems, so any speed-up in the solution of these problems is widely beneficial. [1] DOI. 10.1137/070683933

Read this article online: https://digitalcommons.calpoly.edu/theses/2342

Spin squeezing and closed-loop magnetometry with magnetic field-sensitive states

Presenting Author: Ian Marsh, University of Arizona
Contributing Author(s): David Melchior, Poul Jessen

Measurements with quantum limited resolution have important applications in metrology and sensing, including atomic clocks, atom interferometry, and magnetometry. In our work we perform a quantum-non-demolition measurement on the collective angular momentum of a million spin-4 Cs atoms. Through quantum backaction this measurement generates upwards of 5 dB of metrologically relevant spin-squeezing. By introducing real-time feedback, we can use the collective spin to perform precision magnetometry with resolution below the standard quantum limit. In the past our ability to leverage squeezing and quantum feedback has been limited by a noisy field environment. We have reduced these background fields by a factor >10,000 at frequencies up to tens of kHz by rebuilding our experiment inside a multi-layered magnetic shield of mu-metal and aluminum. In this quiet field environment, we use radio-frequency (RF) composite pulse sequences to correct remaining classical control errors such as noisy rotations of the collective spin, allowing us to reliably prepare the atoms in the desired initial states. We report progress in implementing closed-loop RF feedback control to generate deterministic squeezing and use the atomic ensemble as an RF magnetometer.

Quantum control in the presence of symmetry and locality

Presenting Author: Iman Marvian, Duke University
Contributing Author(s): Austin Hulse, Hanqing Liu

According to a fundamental result in quantum control, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time. In this talk, I show that this universality does not hold in the presence of conservation laws and global continuous symmetries: generic symmetric unitaries on a composite system cannot be implemented, even approximately, using local symmetric unitaries on the subsystems. In the context of quantum thermodynamics this no-go theorem implies that generic energy-conserving unitaries cannot be realized using local energy-conserving unitaries. I also argue that in some cases this no-go theorem can be circumvented using ancilla qubits. For instance, any rotationally-invariant unitary on qubits can be realized using the Heisenberg exchange interaction, which is 2-local and rotationally-invariant, provided that the qubits in the system interact with a pair of ancilla qubits. Finally, I briefly present some results on qudit systems with SU(d) symmetry, which reveal a surprising distinction between the case of d=2 and d>2.

Read this article online: https://www.nature.com/articles/s41567-021-01464-0, https://arxiv.org/abs/2202.01963, https://arxiv.org/abs/2105.12877

Richardson extrapolation for small diatomic molecules on the QSCOUT device

Presenting Author: Oliver Maupin, Tufts University
Contributing Author(s): Ashlyn D. Burch, Chrisopher G. Yale, Brandon Ruzic, Andrew J. Landahl, Peter J. Love, Kenneth M. Rudinger, Antonio Russo, Ryan Shaffer

Current noisy intermediate-scale quantum (NISQ) ion-trap devices are subject to gate errors around 0.1% for two qubit gates. These errors significantly impact the accuracy of calculations if left unchecked. Error mitigation techniques such as Richardson extrapolation can reduce these errors without incurring a qubit overhead. We demonstrate and optimize this extrapolation on Sandia's QSCOUT device in order to calculate the ground state energy of the HeH+ molecule using VQE. This work uses two methods of scaling our noise: time-stretching our gates and unitary folding. Using simulations, we study how to best integrate Richardson extrapolation into an optimization procedure. We further study the effects of the order of extrapolation on the accuracy and precision of the final energy estimate in order to maximize its effectiveness given a limited sampling budget. Experimental results show that such extrapolation methods can be effective in a vacuum, but may require a large sampling overhead and are sensitive to coherent errors in the circuit.

Improved fidelity of quantum subroutines using parametrized entangling gates

Presenting Author: Karl Mayer, Quantinuum
Contributing Author(s): Charlie Baldwin, Nathaniel Burdick, Jonathan Sedlacek

Continuously parametrized entangling gates allow for reduced gate counts in a variety of quantum circuits. We implement a native Pauli ZZ interaction with arbitrary rotation angle in a trapped ion quantum computer with a QCCD architecture. Using cycle benchmarking, we obtain partial estimates of the stochastic Pauli error channel associated with the gate as a function of rotation angle. We then compile two quantum subroutines, namely the quantum Fourier transform (QFT) and the multi-qubit controlled-Z gate, into circuits with and without the use of parametrized two-qubit gates. We run these circuits with up to 12 qubits and estimate lower bounds on the process fidelity of the circuits in each case. We compare the results with simulations using the error models obtained from cycle benchmarking.

Metastable qubit operations in ${\text{Yb}}^{+}$

-type hyperfine clock states at zero field.

Read this article online: https://doi.org/10.1103/PhysRevA.104.L060402

Robustness and complexity of estimating local observables in quench dynamics of 1D Ising models

Presenting Author: Anupam Mitra, University of New Mexico CQuIC

In non-equilibrium dynamics of quantum many-body problems, a common objective is estimating expectation values of local (few-body) observables associated with dynamical order parameters. It is hoped that these quantities are more robust to implementation errors and decoherence and yet still inaccessible by classical simulation, making them suitable for quantum simulators in the noisy intermediate scale quantum (NISQ) era. Here we demonstrate that this hope is not always justified by focusing on the case of quench dynamics of Ising spin chains in 1D in the presence of decoherence. We first show that the Hilbert-Schmidt distance between the ideal and realized reduced density matrix upper-bounds the error in estimating the expectation values of local observables. This allows us to focus on how accurately we can approximate the reduced density matrix. We show that the few-body reduced density matrices of Ising spin chains are less sensitive to approximation via truncated tensor network representations and decoherence through evolution under a unital Lindblad master equation involving single-spin Lindblad operators. Our results suggests that expectation values of local observables in Ising spin chains are classically tractable and robust against experimental imperfections in NISQ devices. [1] Preskill, Quantum 2, 79 (2018) [2] Zhou et. al., Phys. Rev. X 10, 041038 (2020) [3] Noh et. al., Quantum 4, 318 (2020) [4] Cheng et. al., Phys. Rev. Research 3, 023005 (2021)

Raman scattering errors in metastable 40Ca+ trapped-ion qubits and implementation of Raman gates

Presenting Author: Isam Moore, University of Oregon
Contributing Author(s): Jeremy Metzner, Alexander Quinn, Sean Brudney, Gabe Gregory, Wes Campbell, Eric Hudson, David Wineland, David Allcock

Trapped-ion qubits encoded in metastable states (m qubits) are of interest for their use in the omg qubit scheme, which allows multi-species functionality with a single ion species (See Allcock et al., Appl. Phys. Lett., 119 (2021)). We present an implementation of m qubits in the D5/2 manifold of 40Ca+. Single-qubit stimulated-Raman gates in m qubits are demonstrated and characterized. We use 976 nm laser beams (detuned 44 THz red of the 854 nm P3/2 ↔ D5/2 transition) in order to achieve low spontaneous Raman scattering errors. We compare these observed scattering errors to theory, accounting for effects relevant at large detunings. We also consider these effects in models for scattering in stimulated-Raman driven qubits in the S1/2 manifold (g qubits) and predict markedly different scattering behavior in the far-detuned regime than previous models. Finally, we present experimental progress towards implementing a two-qubit light-shift gate on m qubits using far-detuned Raman beams. Support from ARO.

Logical Majorana fermions for fault-tolerant quantum simulation

Presenting Author: Benjamin Morrison, Sandia National Laboratories
Contributing Author(s): Andrew Landahl

We show how to absorb fermionic quantum simulation's expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key idea is to process information in surface-code twist defects, which behave like logical Majorana fermions. Our approach encodes Dirac fermions, a key data type for simulation applications, directly into logical Majorana fermions rather than atop a logical qubit layer in the architecture. Using the 2D Fermi-Hubbard model as an exemplar, we show two applications of our approach that yield improvements in algorithms. First, by preserving the locality of fundamental fermionic operations, we can reduce the asymptotic circuit depth of a Trotter-Suzuki expansion of the time evolution operator. Second, by working in the paradigm of the Majorana fermion data type, we were able to obtain a $T$-count reduction for the block-encoding SELECT oracle that can be applied even without the use of the twist-defect/logical Majorana architecture described here. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

Quantum Heisenberg interaction between Floquet qubits

Presenting Author: Long Nguyen, University of California Berkeley
Contributing Author(s): Yosep Kim, Akel Hashim, Noah Goss, Brian Marinelli, Ravi Naik, John Mark Kreikebaum, David Santiago, Irfan Siddiqi

Our work displays a solution to engineer the XXZ quantum Heisenberg model in fixed-frequency qubits via the concept of Floquet engineering. We show that by applying off-resonant photon drives, we can adiabatically connect fixed-frequency qubits' eigenstates in the lab frame to the corresponding Floquet states which are tunable in the dressed frame. Subsequently, simultaneous controls of the transverse XX and longitudinal ZZ interactions between the Floquet qubits can be achieved by varying the pulses' amplitudes, relative phases, and durations. We demonstrate the robustness and practicality of this protocol by calibrating and characterizing two-qubit iSWAP, CZ, SWAP, and three-qubit CCZ gate with fidelities of 99.32%, 99.7%, 98.93%, and 92.4%, respectively. Our results illustrate the viability of tailoring qubit frequencies in the dressed frames via application of periodic drives, provides a reliable avenue to engineer the XXZ Heisenberg interaction in quantum systems with fixed frequencies, and adds crucial quantum gates to the toolbox of current state-of-the-art superconducting devices.

Colloidal Cadmium Selenide Quantum Dots Doped with Manganese (Mn:CdSe) as a Tool for Quantum Sensing

Presenting Author: Tommy Nguyen, University of Washington

Quantum point defects in crystals are promising nanoscale sensors for a wide range of applications from magnetism in condensed matter systems to single molecule NMR. One outstanding challenge for defects in single crystal samples is controlling the sensor-sample distance. Here we present a defect-based sensing system based on transition-metal-doped colloidal quantum dots. Colloidal doped quantum dots provide a mechanism to control the dopant spin via the spin exchange coupling between the dopant and quantum dot exciton. Here we outline initialization, control and readout mechanisms for the Mn:CdSe quantum system and present initial results toward single Mn:CdSe isolation in quantum dots which exhibit exchange splittings large enough to optically resolve the Mn spin state.

Implementing a universal gate set for qudits via optimal control

Presenting Author: Sivaprasad Omanakuttan, University of New Mexico CQuIC
Contributing Author(s): Anupam Mitra Michael J. Martin Ivan H Deutsch

Qudits, the multi-level d>2 generalization of qubits, are considered as one of the potential candidates for universal quantum computation given the potential of storing more information in fewer physical systems and improved threshold for fault tolerance. In this work we design protocols to implement a universal set of qudits with high fidelity. As a physical system, we consider encoding a d=10 dimensional qudit in the I=9/2 nuclear spin of 87Sr atoms, a platform under considerable exploration for quantum information processing. As the generators of SU(d) unitary matrices are not natural physical interactions, we use the well-known techniques of quantum optimal control order to implement these gates. Using rf-control Larmor precession with a time-dependent phase and a tensor light-shift interaction we designed waveforms to create an arbitrary Haar-random SU(10) map with average fidelity = 0.9923, under reasonable experimental conditions including decoherence effects. To complete the universal gate set we also require a two-qudit entangling gate. We augment our toolkit with an entangling Hamiltonian arising from the Van der Waals interaction of two atoms in Rydberg states. In particular, we employ “Rydberg dressing,” which allows us to implement a magneto-Rydberg interaction that can be used to generate any symmetric entangling two-qudit gate such as CPhase. Our techniques can be used to implement entanglers for qudits from d=2 to d=10 encoded in the nuclear spin.

Read this article online: https://arxiv.org/abs/2106.13705, https://arxiv.org/abs/2205.12866

Resource-efficient experiment designs for multi-qubit gate set tomography

Presenting Author: Corey Ostrove, Sandia National Laboratories
Contributing Author(s): Stefan Seritan, Matthew Grace, Kenneth Rudinger, Erik Nielsen, Kevin Young,Robin Blume-Kohout

Among the most powerful tools available for characterizing the performance of an entire quantum processor is gate set tomography (GST). GST provides high-precision estimates of all of the parameter values associated with a gate set, the set of all gates, state preparations and measurements available on a device. The experimental cost of performing full-fledged traditional GST can be out-of-reach on many platforms, however, especially when scaling to two or more qubits. High-quality GST experiments need not be as expensive as traditionally presented, however. We demonstrate this by introducing protocols for taking a traditional GST experiment design and producing heavily reduced experiment designs which achieve comparable performance using significantly fewer circuits. The first protocol, germ reduction (GR), significantly reduces the overall number of germ sequences that need to be evaluated. The second, fiducial-pair reduction (FPR), reduces the number of state preparation-measurement pairs which need to be considered. For FPR we will present two approaches, a structured approach which leverages the algebraic structure of each of the germs, and a simpler but unstructured approach where we sample a random fraction of the state preparation-measurement pairs. The efficacy of these heavily-reduced experiment designs is demonstrated analytically based on an analysis and comparison of the Fisher information matrices of these designs, as well as through direct numerical simu

Directed propagation of cold atoms in a weakly modulated optical lattice – a consequence of simple mechanical resonance or highly selective velocity matching?

Presenting Author: Krishna Pandey, Miami University
Contributing Author(s): : Alexander Staron, Kefeng Jiang, Ian Dilyard, Casey Scoggins, Jordan Churi, Daniel Wingert, Ajitha Dharmasiri, Anthony Rapp, David Cubero, Samir Bali

Atoms confined in a dissipative optical lattice randomly diffuse in all directions, however illumination by a weak probe modulates the lattice leading to directed motion, or ratcheting, of some atoms in a direction perpendicular to the probe propagation. Does this directed ratcheting arise from a mechanical resonance between the probe modulation frequency and the oscillation frequency of the atoms confined in the lattice wells? Or, does it arise from a far more selective velocity matching condition, where the speed at which the probe modulation ripples through the lattice matches the average speed at which the atoms oscillate inside the wells? A probe beam that is propagating along a symmetry axis of the lattice is unable to resolve the issue, because in this case the conditions for mechanical resonance and velocity matching are simultaneously satisfied. We show that a slight misalignment of the probe with respect to the lattice symmetry axis is necessary to create a situation where the condition for velocity matching is satisfied, but not for mechanical resonance. By measuring the probe transmission spectrum we observe that directed propagation still occurs in this situation, proving that velocity matching is the origin for this form of cold atom ratchet. The spectral signature for unidirectional propagation is investigated as a function of off-axis angle and lattice well-depth. The data are found to agree well with theory, using no fitting parameters.

Towards absolute calibration of single photon detectors with high accuracy

Presenting Author: Sujeet Pani, University of New Mexico CQuIC
Contributing Author(s): Duncan Earl, Francisco Elohim Becerra

Single photon detectors (SPD) are ubiquitous in many protocols for quantum communications and quantum information processing. Many of these applications critically depend on precise knowledge of the detection efficiency of these detectors. Different methods for determining the efficiency of SPDs have been pursued including the use of transfer standard detectors and different sources of light. A method based on the use of a source of quantum correlated photon pairs provides means for realizing the absolute calibration of SPDs with high accuracy [1]. Given the nature of the generation process in the sources of photon pairs, every time a photon is detected, in principle there is absolute certainty that a second photon exists. This information provides a natural way for measuring the detection efficiency of a SPD in absolute terms [2]. We investigate the potential for implementing this calibration method based on a commercial source of quantum correlated photons for on-site calibration of SPDs without requiring any standard. We compare this calibration method with the method based on transfer standard detectors using stable laser sources. We observe that since efficiency of the source is important in this calibration method, accurate characterization of the source could be a viable way for realizing on-site absolute detector calibration. [1] D. N. Klyshko, Sov. J. Quant. Elect. 10, 1112–1116 (1980) [2] S. V. Polyakov, et al., Opt. Express 15(4), 1390–1407 (2007)

Investigation of inversion interferometry for superresolving point sources in optical microscopy

Presenting Author: Sujeet Pani, University of New Mexico CQuIC
Contributing Author(s): Sajjad A. Khan, Diane S. Lidke, Keith A. Lidke, Francisco Elohim Becerra

Modal imaging can provide unprecedented resolution for imaging point sources, such as single-molecule fluorescent tags used to study biological samples. Theoretical work show that modal imaging can approach quantum limits of optical resolution of thermal point sources as quantified by Quantum Cramer Rao Bound [1], albeit assuming highly idealized measurements described by complex quantum operators. To utilize the potential of quantum measurements for superresolution microscopy it is imperative to understand the critical parameters in optical systems for realizing such quantum measurements under realistic conditions. Our efforts focus on understanding these critical parameters and developing an optical system for superresolving two incoherent point sources (i.e. fluorophore tags) for studying biological samples. We use a Mach-Zehnder interferometer with optical field inversion to realize image inversion interferometry, in principle allowing for near quantum-optimal measurement for imaging point sources. In our work, we combine inversion interferometry with florescence microscope to image fluorescent beads acting as point sources. We investigate the performance of this technique and characterize the effects of aberrations and source bandwidth in the interference visibility. We plan to use this setup to realize superresolved measurements of single-molecule fluorescence and finally, protein dynamics in biological samples. [1] M. Tsang, et al., Phys. Rev. X 6, 031033 (2016)

When is better ground state preparation worthwhile on a quantum computer?When is better ground state preparation worthwhile on a quantum computer?

Presenting Author: Shivesh Pathak, Sandia National Laboratories
Contributing Author(s): Antonio Russo, Stefan Seritan, Andrew Baczewski

An important application for quantum simulation is the accurate and efficient evaluation of ground state energies. One approach is to construct an approximate ground state wave function, and then repeatedly apply quantum phase estimation (QPE) to sample from the energy eigenspectrum of the associated Hamiltonian. The number of repetitions required to observe the ground state eigenvalue will be inversely proportional to the overlap with the exact ground state. As such, higher quality ground state approximations will require fewer applications of QPE. This suggests a tradeoff between improving state preparation and simply repeating QPE. So, when is it worthwhile to invest in better state preparation to increase the efficiency of computing ground state energies? To answer this question, we provide resource estimates for accurately computing ground state energies with and without a layer of sophisticated state preparation. To this end, we analyze the filter-based state preparation technique proposed in Lin and Tong’s “Near-optimal ground state preparation,” providing a new error analysis and additional implementation details. Our asymptotic analysis, as well as explicit T-counts for the transverse field Ising and first-quantized electronic structure Hamiltonians, indicate that state preparation yields a consistent near-quadratic improvement for large system sizes and high target accuracies. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Measurement-Based Quantum Computing as a Tangram Puzzle using Stabilizer formalism

Presenting Author: Ashlesha Patil, University of Arizona

Stabilizer formalism is an important tool to simulate Clifford operations & Pauli measurements. We have extended the stabilizer formalism by (1) incorporating multi-qubit stabilizer measurements (e.g. BSM), (2) providing an explicit procedure using Karnaugh maps from Boolean algebra for converting any stabilizer gate into stabilizer tableau operations (3) designing a new canonicalization algorithm for stabilizer tableaus that first minimizes the number of stabilizer generators with X or Y operators & then those with only Z operators. We use the extended stabilizer formalism to design a Tangram-like game to teach Measurement-Based Quantum Computing (MBQC). The player is given a quantum circuit which they have to map to MBQC using polyominos. Polyominos, consist of square tiles joined edge-to-edge to form different shapes. Each tile denotes one of the three Pauli measurements, differentiated by its color. Polyominos rest on a square-grid playing board, signifying a cluster state. Mapping a quantum circuit to MBQC is equivalent to arranging a set of polyominos, each corresponding to a quantum gate, on the playing board, subject to certain rules. We use the stabilizer formalism & the canonicalization algorithm to evaluate a solution. Higher-scoring correct solution fills up less space on the board, resulting in a lower-overhead embedding of the circuit in MBQC, a challenging research problem.

Quantum Telecloning on NISQ Computers

Presenting Author: Elijah Pelofske, Los Alamos National Laboratory
Contributing Author(s): Andreas Bärtschi, Bryan Garcia, Boris Kiefer, Stephan Eidenbenz

Due to the no-cloning theorem, generating perfect quantum clones of an arbitrary unknown quantum state is not possible, however approximate quantum clones can be constructed. Quantum telecloning is a protocol that originates from a combination of quantum teleportation and quantum cloning. Here we present $1\to 2$

).

Read this article online: https://arxiv.org/abs/2205.00125

A novel non-Gaussianity measure based on the Wigner relative entropy

Presenting Author: Andrew Pizzimenti, College of Optical Sciences, University of Arizona
Contributing Author(s): Andrew Pizzimenti, Prajit Dhara, Sijie Cheng, Zacharie Van Herstraeten, Christos Gagatsos

The enhanced phase-space characteristics of non-Gaussian states of light, albeit necessary for universal quantum computing, render their understanding and production challenging. In attempts to circumvent these difficulties, several works have introduced non-Gaussianity measures, i.e., quantities that assign a real number to states depending on their non-Gaussian content (Genoni et al., 2007, 2008). Based on the Wigner entropy (Van Herstraeten & Cerf, 2021), we introduce a new measure μ[W], which is the Wigner relative entropy between an arbitrary N-mode state and its Gaussian associate defined as μ[W]= ∫ dNq dNp W(q, p) [ln W(q, p) - lnWG(q, p)]. Here, W(q, p) and WG(q, p) are the Wigner functions of the state and its Gaussian associate respectively. Our measure can be complex-valued, and we interpret its imaginary part as the negative volume of the Wigner quasi-probability distribution, while its real part provides information on other intrinsic properties of the state. We provide evidence that μ[W] is a valid non-Gaussianity measure, demonstrate its usefulness in representing states more perceptibly, and discuss its relevance to non-Gaussian state generation.

Measuring operator scrambling without OTOCs

Presenting Author: Pablo Poggi, University of New Mexico
Contributing Author(s): Sivaprasad Omanakuttan, Karthik Chinni, Philip Blocher

Scrambling in many-body systems refers to the spreading of initially localized information to the entire system and has become a key concept in the study of chaos in quantum systems. Most studies so far have focused on characterizing scrambling using out-of-time-ordered correlation functions (OTOCs), particularly through its early-time decay. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires accessing more refined information about the operator dynamics at several timescales. Moreover, OTOCs are intrinsically hard to access experimentally, typically requiring time reversal of the dynamics or the use of auxiliary systems. In this work we study operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a probability distribution in the space of operators. We propose a novel approach that allows us to obtain information about scrambling without time reversal nor ancillas, while also avoiding the arduous task of reconstructing the expansion coefficients directly. This is done by using the dynamics of random mixed states and only local measurements together with randomized sampling. We demonstrate our protocol for the tilted field Ising model undergoing both regular and chaotic dynamics, as well as explore our proposed protocol in the context of circuit models with varying non-Cliffordness.

Demonstration of algorithmic quantum speedup

Presenting Author: Bibek Pokharel, University of Southern California
Contributing Author(s): Daniel A. Lidar

Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum computers (QCs), an experimental demonstration of a provable algorithmic quantum speedup employing today's non-fault-tolerant, noisy intermediate-scale quantum (NISQ) devices has remained elusive. Here, we unequivocally demonstrate such a speedup, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, utilizing two different 27-qubit IBM Quantum (IBMQ) superconducting processors. The speedup is observed on only one of the two QCs (ibmq_montreal) when the quantum computation is protected by dynamical decoupling (DD) -- a carefully designed sequence of pulses applied to the QC that suppresses its interaction with the environment, but not without DD. In contrast to recent quantum supremacy demonstrations, the quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem, in the setting of a game with an oracle and a verifier.

Read this article online: https://arxiv.org/abs/2207.07647

Symmetries, states, and measurements: decoherence and complexity in a single mode evolving under a nonlinear Kerr interaction

Presenting Author: Tzula Propp, University of New Mexico CQuIC
Contributing Author(s): Ivan Deutsch, Tameem Albash, Sayonee Ray

Decoherence limits quantum complexity and thus the quantum advantage that can be achieved on NISQ devices.  As a toy model, we study this in a single mode evolving under the nonlinear Kerr interaction. For the closed quantum system, the Kerr interaction is a structure generating process: the Wigner function develops both sub-Planckian structure and negativity over time as an initial coherent state evolves into a superposition of many coherent states (the kitten states, which are the higher order generalization of the Schrödinger cat state). However, only certain expectation values are sensitive to the coherence and structure of the kitten states, with the expectation values and states connected by the shared symmetry of the cyclic group Z_n. In the presence of weak decoherence, we find that even these expectation values are increasingly described by the Truncated Wigner Approximation in the large-alpha limit, and observe an accompanying general trend of decreased computational cost to numerically predict the measurement outcomes. Lastly, we revisit the question of decoherence more broadly, and explore less conventional, state-independent frameworks for studying decoherence in NISQ-era devices.

Hybridized methods for quantum simulation in the interaction picture

Presenting Author: Abhishek Rajput, University of Washington
Contributing Author(s): Alessandro Roggero, Nathan Wiebe

Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic advantages for some Hamiltonians but incurs prohibitive constant factors and is incompatible with methods like qubitization. We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations over known algorithms. These approaches show asymptotic improvements over the individual methods that comprise them and further make interaction picture simulation methods practical in the near term. Physical applications of these hybridized methods yield a gate complexity scaling as $\log^2 \Lambda$ in the electric cutoff $\Lambda$ for the Schwinger Model and independent of the electron density for collective neutrino oscillations, outperforming the scaling for all current algorithms with these parameters. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $\lambda$ used to impose an energy cost on time-evolution into an unphysical subspace.

Read this article online: https://arxiv.org/abs/2109.03308

Quantum state transfer using input-output theory with time-reversal

Presenting Author: Kevin Randles, University of Oregon
Contributing Author(s): Steven van Enk

Achieving quantum state transfer between separate nodes of a quantum network is a topical problem in developing quantum computing and quantum communication systems. Input-output theory can be used to manage a wide class of field states driving cascaded quantum systems to achieve quantum state transfer. We show how the standard input-output theory is non-trivially modified if the photon is manipulated while propagating between two nodes, from system 1 to system 2. We present a unitary transformation, U, that time-reverses, frequency translates, and stretches the photon wave packet emitted by system 1. U can be tuned to match the different resonance frequencies and decay rates of the systems so that the wave packet is absorbed by system 2. We find that system 2 effectively responds to the time-reversed dynamics of system 1, which can be understood in terms of a change to the state's time argument, rho(t) = rho_1(t') tensor rho_2(t), where t' is a fictitious time for system 1 that runs backwards. For three-level Lambda-systems we numerically illustrate that performing a faultless unitary transformation results in ideal quantum state transfer and analyze the impact of imperfect transformations.

Read this article online: https://arxiv.org/abs/2204.11377

Transition Network Method for Stoquastic Heisenberg Hamiltonians

Presenting Author: Chaithanya Rayudu, University of New Mexico CQuIC
Contributing Author(s): Jun Takahashi, Cunlu Zhou

We consider the problem of finding the ground state energy of a Stoquastic Heisenberg Hamiltonian of the form $H={\sum }_{(i,j)\in E}-X_i{X}_j-Y_i{Y}_j+Z_i{Z}_j$

. Stoquastic Hamiltonians are Hamiltonians with non-positive off diagonal elements in a particular known basis. The exact complexity of this problem is still unknown other than that it is in Stoq-MA. We present a rewriting of the problem as finding the highest eigen energy of a transition network which can yield insights into the structure of the problem, especially when symmetries are considered. We discuss the possibility of using this rewriting to develop a new Monto Carlo algorithm for (approximately) finding the ground state energy of classes of stoquastic Hamiltonians.

Tunable frequency comb for identifying vibrational overtones in a trapped molecular ion

Presenting Author: April Reisenfeld, National Institute of Standards and Technology, Boulder
Contributing Author(s): Yu Liu, Peter Chang, Scott Diddams, David Leibrandt, Dietrich Leibfried, and Chin-wen Chou

Efficient transduction of quantum information stored in stationary qubits to photons at telecom wavelengths will enable low-loss transmission of quantum information (QI) in optical fibers and facilitate the realization of a long-distance quantum network. While atomic ions mostly emit photons at wavelengths below 1 m, molecular ions offer transitions in the telecom wavelength range that can be used for efficient transfer of QI between an atomic ion and a molecular ion [Lin, Y. et al. Nature 581, 273–277 (2020)]. Theoretical frequency predictions of such transitions typically have uncertainties of a few-terahertz, making experimental searches for them challenging. Here, we report our effort toward a light source to search for telecom-range transitions in trapped molecular ions or other narrow-band emitters. A highly nonlinear fiber (HNLF) broadens the spectrum of an amplified Er-doped fiber frequency comb, resulting in a frequency comb with 90 nm 3 dB bandwidth. An acousto-optic modulator can shift the center frequency of the comb by more than one free spectral range of the comb, which effectively probes transitions over the entire spectral width in parallel. We first aim to search for the v = 0 to v = 5 vibrational overtone transition in CaH+, which is predicted to lie in the range between 1440 and 1470 nm by ab inito calculations [Abe et al., CPL 521, 31–35 (2012), P. Plessow, private communication]. We achieve an average power of 1.2 µW per comb tooth centered at 1450 nm.

Determining the asymptotic performance in single-shot coherent state phase estimation of adaptive protocols based on photon counting measurements

Presenting Author: Marco Antonio Rodríguez García, University of New Mexico CQuIC
Contributing Author(s): M. T. DiMario, P. Barberis Blostein, and F. E. Becerra

In recent years, it has been shown that the non-Gaussian measurements can surpass the sensitivity limits of Gaussian measurements in many quantum information protocols, such as state discrimination [PRA 78, 022320 (2008), Nat. Photonics 9, 48–53 (2015)], state preparation [arXiv:2103.10388], and parameter estimation [PRA 79, 040305 (2019), PRL 125, 120505 (2020)]. However, for the problem of single-shot phase estimation in coherent states, there is no proof that the non-Gaussian measurements can outperform the Gaussian limit. This work shows that a set of adaptive phase estimation strategies based on a non-Gaussian measurement consisting of input field displacements, photon counting, and feedback surpasses the best Gaussian estimation strategy known to date. Our proof shows that these non-Gaussian phase estimation strategies have the same functional form as the canonical phase measurement in the asymptotic limit, differing only by a scaling factor in the second order term. The canonical phase measurement is the ultimate measurement sensitivity allowed by physics, but at present, its physical realizations remain unknown for high dimensional states, such as coherent states. While the best-known Gaussian estimation strategy is far below this ultimate limit, these non-Gaussian estimation strategies provide the highest sensitivity among physically-realizable measurements for single-shot phase estimation of coherent states known to date.

Controlled Carbon Contamination of a Surface Ion Trap

Presenting Author: Benjamin Saarel, University of California Berkeley

Electric field noise is an important error source for high-fidelity operation of ion trap quantum processors. This noise is orders of magnitude larger than expected from known noise sources. Cleaning the trap surface reduces the measured surface contamination and reduces the measured noise, suggesting contamination is responsible for a significant portion of the noise. One of main surface contaminants observed on nearly all trap surfaces is carbon and at least two studies have correlated the amount of surface carbon contamination with the amount of measured noise during a cycle of cleaning. However, different cleaning methods that all successfully remove contamination lead to very different reductions in noise, suggesting the cleaning methods modify the surface in ways besides removing material. In order to study the effect carbon contamination has on surface noise while avoiding additional effects cleaning may have on the surface, our current experiment uses electron-beam-induced deposition using an ethylene precursor gas to deposit several monolayers of carbon onto the surface of an ion trap. Initial measurements of the noise before and after deposition suggests an order-of-magnitude increase in noise due to the carbon contamination. A second deposition experiment with a new trap is underway to confirm these results.

Efficient experimental verification of continuously-parameterized gate sets and analog quantum simulators

Presenting Author: Ryan Shaffer, University of California Berkeley
Contributing Author(s): Hang Ren, Emiliia Dyrenkova, Eli Megidish, Joseph Broz, Wei-Ting Chen, Christopher G. Yale, Daniel S. Lobser, Ashlyn D. Burch, Matthew N. H. Chow, Melissa C. Revelle, Susan M. Clark, Hartmut Häffner

Near-term quantum information processors will not be capable of quantum error correction, but instead will implement algorithms using the physical native interactions of the device. These interactions can be used to implement quantum gates that are often continuously-parameterized (e.g., by rotation angles), as well as to implement analog quantum simulations that seek to explore the dynamics of a particular Hamiltonian of interest. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we introduce the randomized analog verification (RAV) technique for efficient experimental verification of continuously-parameterized quantum gate sets and analog quantum simulators. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking, which thus provides an efficiency advantage when estimating the error rate to some desired precision. We demonstrate the efficiency advantage of this technique both numerically and experimentally. We describe the experimental realization of this technique using a continuously-parameterized quantum gate set on a trapped-ion processor from Sandia QSCOUT and on a superconducting processor from IBM Q.

Read this article online: https://arxiv.org/abs/2205.13074, https://doi.org/10.1038/s41534-021-00380-8

A non-orthogonal quantum eigensolver for strongly correlated quantum chemistry

Presenting Author: James Shee, University of California Berkeley
Contributing Author(s): Unpil Baek, Diptarka Hait, Oskar Leimkuhler, William J. Huggins, Torin F. Stetina, Martin Head-Gordon, K. Birgitta Whaley

A balanced description of static and dynamic correlations in electronic systems with nearly degenerate, low-lying states presents a challenge for classical quantum-chemical algorithms. We present a new hybrid quantum-classical algorithm -- the non-orthogonal quantum eigensolver (NOQE) -- to obtain compact, multi-reference wavefunctions formed from non-orthogonal, dynamically-correlated single-reference states. While on classical devices the evaluation of the required off-diagonal matrix elements would incur an exponentially-scaling step, our quantum algorithm accomplishes this with polynomial cost. We explore various single-reference ansatzes inspired by classical quantum chemistry methods, and demonstrate that the NOQE procedure can capture meaningful amounts of electronic correlation energy in both ground and excited states. NOQE is thus an attractive method for the calculation of multi-reference electronic states of a wide range of molecular systems. Preliminary results from the incorporation of noise models and experiments on quantum hardware will be shared.

Read this article online: https://arxiv.org/abs/2205.09039

Quantum advantage with spin squeezed atomic ensembles

Presenting Author: Yueheng Shi, Stanford University
Contributing Author(s): Junheng Shi, Tim Byrnes

We propose a method to achieve quantum supremacy using ensembles of qubits, using only spin squeezing, basis rotations, and Fock state measurements. Each ensemble is assumed to be controllable only with its total spin. Using a repeated sequence of random basis rotations followed by squeezing, we show that the probability distribution of the final measurements quickly approaches a Porter-Thomas distribution. We show that the sampling probability can be related to a #P-hard problem with a complexity scaling as (N+1)^M, where N is the number of qubits in an ensemble and M is the number of ensembles. The scheme can be implemented with hot or cold atomic ensembles. Due to the large number of atoms in typical atomic ensembles, this allows access to the quantum supremacy regime with a modest number of ensembles or gate depth.

Read this article online: https://arxiv.org/abs/2204.11772

Noise-induced barren plateaus in variational quantum algorithms due to non-unital and non-Markovian noise models

Presenting Author: Phattharaporn Singkanipa, University of Southern California
Contributing Author(s): Daniel A. Lidar

Variational Quantum Algorithms (VQAs) are a leading practical application of Noisy Intermediate-Scale Quantum (NISQ) devices. Despite their promise, VQAs suffer from the problem of vanishing gradients, also known as the barren plateau (BP) phenomenon. BP can arise from fundamentally different mechanism, e.g., parameter initialization, structure of the problem Hamiltonian, and noise. Noise-induced barren plateaus (NIBPs) have been shown to exist subject to unital CPTP maps. We generalize this result to non-unital CPTP and non-Markovian noise channels. Our results are illustrated with numerical simulations of various noise models.

Optimized Grover Adaptive Search oracles for Constrained Polynomial Binary Optimization

Presenting Author: Phattharaporn Singkanipa, University of Southern California
Contributing Author(s): Ewan Munro

Grover Adaptive Search (GAS) is a quantum algorithm that can provide a quadratic speed-up for unstructured search. A challenge in GAS is to define an oracle, a procedure that could be non-systematic. An efficient method for constructing oracles to solve Constrained Polynomial Binary Optimization (CPBO) problems has been proposed in arXiv:1912.04088v3. This method is based on converting the problem into the Quadratic Unconstrained Binary Optimization (QUBO) form of Hamiltonian while using an additional CNOT in the oracle for each extra constraint that does not fit in the QUBO form. In this work, we propose a further-optimized way to construct oracles using Quadratic Constrained Binary Optimization (QCBO), which modifies the oracle to account for every constraint and exhibits a linear form of the Hamiltonian for numerous CPBO problems. We demonstrate the validity of this approach by presenting two examples of constructing QCBO form of oracles to solve number partitioning and bin packing problems, both of which show a polynomial reduction in the number of qubits and circuit depth compared to using the QUBO form of oracles.

Quantum Parallel Tempering

Presenting Author: Sam Slezak, University of New Mexico CQuIC
Contributing Author(s): Tameem Albash

Accurate and efficient sampling from thermal states of quantum systems is an essential ingredient for many computational tasks. On a quantum computer, the task of sampling from thermal states can be accomplished using the quantum Metropolis sampling algorithm, a quantum generalization of Markov chain Monte Carlo (MCMC) algorithms. In this work, we build on the quantum Metropolis sampling algorithm by introducing a quantum version of the parallel tempering algorithm, whereby many copies of the system called replicas are allowed to swap states and which classically is known to improve convergence times of MCMC algorithms. Our algorithm allows for the different replicas to not only have different temperatures but also to have different Hamiltonians, which allows for an interpolation between purely thermal tempering, where only the inverse-temperature is varied, and quantum tempering methods where specific terms in a Hamiltonian are varied.

Scalable unfolding of measurement errors

Presenting Author: Siddarth Srinivasan, University of Washington
Contributing Author(s): Bibek Pokharel Gregory Quiroz Byron Boots

Measurement error mitigation (MEM) techniques are postprocessing strategies to counteract systematic readout errors on programmable quantum computers. Most MEM strategies model these errors as a linear stochastic map also called the response matrix, and aim to invert the effect of this map. Unfortunately, the response matrix scales exponentially with the number of qubits, and its inverse is not stochastic so the mitigated distribution can contain negative probabilities. There are strategies to address scalability concerns, e.g. by assuming that measurement errors are mostly uncorrelated and that reduced mitigation accuracy is tolerable. However, these scalable strategies still return quasiprobabilities. On the other hand, existing methods that guarantee a non-negative mitigated distribution are not scalable. In this work, we demonstrate a scalable MEM strategy that avoids quasiprobability distributions. In particular, we implement a scalable implementation of iterative Bayesian unfolding, a standard mitigation technique in high-energy physics experiments. We demonstrate our method with experimental preparation of GHZ states up to 127 qubits and the implementation of the Bernstein-Vazirani algorithm on up to 26 qubits.

Generative Quantum Machine Learning for Quantum Chemistry

Presenting Author: Torin Stetina, University of California Berkeley
Contributing Author(s): Jack Ceroni, Juan Miguel Arrazola, Carlos Ortiz, Mária Kieferová, Nathan Wiebe

The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. In short, the PES is a high dimensional landscape that in principle, contains all the information needed to predict reaction rates. Each point on the PES is associated with a parameterized Hamiltonian, defined by its nuclear coordinates. However, obtaining this information is complicated by the fact that at each coordinate on the PES, ground state energies must be computed, which is in general a QMA-Complete problem. With some assumptions, this can be alleviated by the fact that there exist efficiently preparable high-fidelity approximations of the true ground state for many molecular systems, but sampling a large number of ground states over a high dimensional PES can require a vast number of state preparations. In this work, we investigate the utility of a generative quantum machine learning model trained using quantum data associated with the classical nuclear coordinate information, where a subset of ground state wavefunctions are sampled along the PES. In this regime, a successful generative model takes a set of classical nuclear coordinates as an input, and outputs the quantum electronic ground state at the requested nuclear configuration with high efficiency. Theoretical bounds and numerical investigations of a select set of molecular systems are investigated within this work.

Continuous-variable SWAP test

Presenting Author: Yigit Subasi, Los Alamos National Laboratory
Contributing Author(s): Tyler Volkoff

We propose a continuous-variable (CV) SWAP test that requires no ancilla register, thereby generalizing the ancilla-free SWAP test for qubits. In this ancilla-free CV SWAP test, the computational basis measurement is replaced by photon number-resolving measurement, and we calculate an upper bound on the error of the overlap estimate obtained from a finite Fock cutoff in the detector. As an example, we show that estimation of the overlap of pure, centered, single-mode Gaussian states of energy $E$ and squeezed in opposite quadratures can be obtained to error $\epsilon$ using photon statistics below a Fock basis cutoff $O(E\ln \epsilon^{-1})$. This cutoff is greatly reduced to $E + O(\sqrt{E}\ln \epsilon^{-1})$ when the states have rapidly decaying Fock tails, such as coherent states. We show how the ancilla-free CV SWAP test can be extended to many modes and applied to quantum algorithms such as variational compiling and entanglement spectroscopy in the CV setting. For the latter we also provide a new algorithm which does not have an analog in qubit systems. The qudit and the CV SWAP tests can be combined to give a SWAP test valid for hybrid DV-CV states, such as cavity QED system. We have implemented the ancilla-free CV SWAP test on Xanadu's 8-mode photonic processor in order to estimate the vacuum probability of a two-mode squeezed state.

Read this article online: https://arxiv.org/abs/2202.09923

On nonlinear transformations in quantum computation

Presenting Author: Yigit Subasi, Los Alamos National Laboratory
Contributing Author(s): Zoë Holmes, Nolan J. Coble, Andrew T. Sornborger.

While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop algorithms for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.

Read this article online: https://arxiv.org/abs/2112.12307

Tensor network simulations of variational Bayesian metrology with correlated noise

Presenting Author: Tyler Thurtell, University of New Mexico CQuIC
Contributing Author(s): Akimasa Miyake

We consider variational metrology in the global, or Bayesian, framework. We first introduce a new family of ansatzes which we call arbitrary-axis twist ansatzes. This family of ansatzes amounts to taking both the encoding and decoding circuits to be an alternating sequence of rotations and one-axis twists about arbitrary directions. We find that this family of ansatzes can preform at least as well, and in some cases better, than previous approaches despite having fewer entangling one-axis twists. We also study these ansatzes in the presence of spatially correlated noise. This breaks the permutation symmetry of the noiseless dynamics meaning that symmetric subspace techniques cannot be used. To facilitate this numerical study, we introduce a matrix product operator based simulation scheme. As long as the matrix product operator associated with the noise has a bond dimension that is at most polynomial in the size of the system, the result is an exact simulation algorithm that has cost polynomial in the system size but exponential in the number segments of the evolution that break the permutation symmetry. In addition, we use these techniques to study the effect of various types of spatially correlated noise in twist-untwist protocols.

Quantum Key Distribution Simulation using Entangled Bell States

Presenting Author: Nayana Tiwari, California Polytechnic State University
Contributing Author(s): Dr. Katharina Gillen

To communicate information securely, the sender and recipient of the information need to have a shared, secret key. Quantum key distribution (QKD) is a proposed method for this and takes advantage of the laws of quantum mechanics. The users, Alice and Bob, exchange quantum information in the form of entangled qubits over a quantum channel as well as exchanging measurement information over a classical channel. A successful QKD algorithm will ensure that when an eavesdropper has access to both the quantum and classical information channels, they cannot deduce the key, and they will be detected by the key generators. This presentation will introduce quantum key distribution and explain the implemented simulation of a proposed QKD algorithm using entangled Bell states. The proposed T22 protocol was compared against the more common BB84 QKD protocol. The results show that it takes 3x longer to generate a key of length m bits using the T22 protocol, however the T22 protocol is 36x more secure than BB84.

Modeling of environmental noise in transmon qubits using dynamical decoupling

Presenting Author: Vinay Tripathi, University of Southern California
Contributing Author(s): Huo Chen, Mostafa Khezri, Ka-Wa Yip, Eli Levenson-Falk, Daniel A. Lidar

Tackling decoherence is one of the core challenges in the field of quantum computing. For superconducting qubits, coupling to the environment results into several noise channels. A rigorous characterization of the open system dynamics at the circuit Hamiltonian level is essential for a better understanding of these noise processes. Here we model the open quantum system effects for a qubit modeled as transmon circuit Hamiltonian. We use the Redfield master equation with a hybrid bath consisting of both high and low frequency components to model the effects of environment. We develop a fitting procedure using dynamical decoupling to learn the behavior of noise and use it to reproduce the experiments on real hardware available through IBM Quantum experience. We test our model with quantum state fidelity experiments for random initial states. We further reproduce the effects of actual time-dependent dynamical decoupling pulses.

Quantum Adversarial Learning in Emulation of Monte-Carlo Methods for Max-cut Approximation: QAOA is not optimal

Presenting Author: Cem Unsal, University of Maryland
Contributing Author(s): Lucas Brady

One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms, but these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters increases. Therefore, it is important to understand the expressibility and power of various ansätze to produce target states and distributions. To this end, we apply notions of emulation to Variational Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA). We show that QAOA is outperformed by variational annealing schedules with equivalent numbers of parameters. Our Variational Quantum Annealing schedule is based on a novel polynomial parameterization that can be optimized in a similar gradient-free way as QAOA, using the same physical ingredients. We also develop and incorporate statistical notions of Monte-carlo methods (not to be confused with Monte Carlo integration) to further elucidate the theoretical framework around these quantum algorithms.

Matchgate shadows for fermionic quantum simulation

Presenting Author: Kianna Wan, Google
Contributing Author(s): William J. Huggins, Joonho Lee, Ryan Babbush

"Classical shadows" are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state [Nature Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using random matchgate circuits, which correspond to fermionic Gaussian unitaries. We prove that the first three moments of the Haar distribution over the continuous group of matchgate circuits are equal to those of the discrete uniform distribution over only the matchgate circuits that are also Clifford unitaries; thus, the latter forms a "matchgate 3-design." This implies that the classical shadows resulting from the two ensembles are functionally equivalent. We show how one can use these matchgate shadows to efficiently estimate inner products between an arbitrary quantum state and fermionic Gaussian states, as well as the expectation values of local fermionic operators and various other quantities, thus surpassing the capabilities of prior work. As a concrete application, this enables us to apply wavefunction constraints that control the fermion sign problem in the quantum-classical auxiliary-field quantum Monte Carlo algorithm (QC-AFQMC) [Nature 603, 416-420], without the exponential post-processing cost incurred by the original approach.

Read this article online: https://arxiv.org/abs/2207.13723

Observation of stochastic resonance in directed propagation of cold atoms

Presenting Author: Daniel Wingert, Miami University
Contributing Author(s): Alexander Staron, Kefeng Jiang, Ian Dilyard, Casey Scoggins, Ajitha Dharmasiri, Anthony Rapp, Jordan Churi, David Cubero, Samir Bali

We present unambiguous evidence for stochastic resonance in a weakly modulated dissipative optical lattice. Here, stochastic resonance refers to a resonant enhancement in the directed propagation of the confined atoms as we vary the rate of random photon scattering. The lattice is modulated with a weak probe beam. The probe induces a directed propagation of atoms in a direction perpendicular to the probe propagation. By observing the probe transmission spectrum we present evidence that the photon scattering rate at which stochastic resonance occurs is independent of the modulation strength (i.e., the probe intensity) for probe intensities less than 1% of the lattice. We also show that the stochastic resonance frequency can be controlled by varying the lattice well depth. Remarkably, the data agrees well with theory based on a simple F_g = 1/2 to F_e = 3/2 atom without the use of any fitting parameters. A recent novel theory has permitted us to precisely determine the contribution to the directed motion of the atomic density waves excited by the perturbing probe, and how these density fluctuations conspire with the optical pumping rates to create resonant directional atomic propagation within a randomly diffusing cold atom cloud.

Bipartite Control of Noisy Qubits Using the Quantum Approximate Optimization Algorithm

Presenting Author: Zhibo Yang, University of California Berkeley
Contributing Author(s): Robert Kosut, K. Birgitta Whaley

We employ bipartite control with a Quantum Approximate Optimization Algorithm (QAOA) control ansatz to mitigate noise on qubits. We illustrate the approach with application to the protection of quantum gates performed on a central spin qubit coupling to bath spins through isotropic Heisenberg interactions, on superconducting transmon qubits coupling to environmental two-level-systems (TLS) through dipole-dipole interactions, and on qubits coupled to both TLS and a Lindblad bath. The control field is classical and only acts on the system qubits. We use policy gradient (PG) and sequential convex programming (SCP) as classical optimization methods to optimize the QAOA control protocols with a fidelity objective defined with respect to specific target quantum gates. We demonstrate effective suppression of coherent noise, with numerical studies achieving target gate fidelities over 0.9999 in the majority of test cases for this. We analyze how specific implementations determine the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite QAOA control of quantum gates.

Optimizing over orthogonal groups with quantum states

Presenting Author: Andrew Zhao, Google
Contributing Author(s): Nicholas Rubin

Quadratic optimization over the (special) orthogonal group encompasses a broad class of optimization problems such as group synchronization, point-set registration, and simultaneous localization and mapping. Such problems are instances of the little noncommutative Grothendieck problem (LNCG), a natural generalization of the MAXCUT problem. In this work, we establish an encoding of LNCG onto a quantum Hamiltonian and investigate its approximation quality compared to standard classical approaches. This encoding is accomplished by identifying orthogonal matrices with quantum states via a Clifford-algebraic construction. We further connect this representation to the theory of free fermions, which leads to a natural interpretation of the LNCG Hamiltonian terms as two-body interactions. Notably, this quantum formalism features an explicit restriction to the special orthogonal group, whereas classically optimizing over this subgroup can involve expensive determinant constraints.