# 2019 Poster Abstracts

### Curvature measures of correlations and entanglement of qudit quantum networks

Shahabeddin Mostafanazhad Aslmarand, Florida Atlantic University

The cornerstone of quantum computing derives from quantum entanglement. We are interested in measures of correlation and entanglement over complex qudit quantum networks. Having scalable measures of these correlations and entanglement for a quantum network with arbitrarily large number of qubits would be of great utility. Following It-from-Bit framework of Wheeler, we introduce a common Shannon-based information geometry measure of distance that applies to binary strings of measurement outcomes, and we introduce a generalization to higher-dimensional volumes. These volumes can be used to define curvature measures over the qudit network. We describe and illustrate our information-geometry-based curvature approach for a few representative qudit networks. Our approach involves repeated experiments made by d observers over a set of identically-prepared qudit states – a “quantum state interrogation in the space of measurements.” Each observer records a 1 if their detector triggers, otherwise they record a 0. This generates a string of 1’s and 0’s at each detector, and each observer can define a binary random variable from this sequence. This approach provides a novel way to characterize quantum networks and it may have favorable scaling with increased number of photons.

### Dissipative self-interference and robustness of continuous error-correction to miscalibration

Victor V. Albert, California Institute of Technology

We derive an effective equation of motion within the steady-state subspace of a large family of Markovian open systems (i.e., Lindbladians) subject to perturbations of their Hamiltonians and system-bath couplings. We derive a set of conditions under which competing dissipative processes destructively interfere, producing no dissipation within the steady-state subspace. Due to the mildness of the conditions, such destructive interference turns out to be much more generic than expected. For quantum error-correction, these effects imply that continuously error-correcting Lindbladians are robust to calibration errors, including miscalibrations consisting of operators undetectable by the code. A similar interference is present in more general systems if one implements a particular Hamiltonian drive, resulting in a coherent cancellation of dissipation. On the opposite extreme, instead of suppressing dissipation, we provide a simple implementation of universal Lindbladian simulation.

### Exact holographic tensor networks for the Motzkin spin chain

Rafael Alexander, University of New Mexico CQuIC

The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated via a tensor-network description. The tensor network's utility in studying short range correlated states in 1D have been thoroughly investigated, with numerous examples where the treatment is essentially exact. Yet, despite the large number of works investigating these networks and their relations to physical models, examples of exact correspondence between the ground state of a quantum critical system and an appropriate scale-invariant tensor network have eluded us so far. Here we show that the features of the quantum-critical Motzkin model can be faithfully captured by an analytic tensor network that exactly represents the ground state of the physical Hamiltonian. In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice. We discuss connections to renormalization and holography.

### Monotonicity under local operations: Linear entropic formulas

Mohammad Alhejji, National Institute of Standards and Technology, Boulder

All correlation measures, classical and quantum, must be monotonic under local operations. In this paper, we characterize monotonic formulas that are linear combinations of the von Neumann entropies associated with the quantum state of a physical system which has n parts. We show that these formulas form a polyhedral convex cone, which we call the monotonicity cone, and enumerate its facets. We illustrate its structure and prove that it is equivalent to the cone of monotonic formulas implied by strong subadditivity. We explicitly compute its extremal rays for n up to 5. We also consider the symmetric monotonicity cone, in which the formulas are required to be invariant under subsystem permutations. We describe this cone fully for all n.

### Damping Bases for the dissipation of Dicke States

William Alvarez-Giron, Universidad Nacional Autónoma de México

One of the obstacles in the control of atom-photon interfaces is the individual spontaneous emission of the atomic system, where the photons are scattered in any direction. But, in systems with coupling between atoms is possible to have a collective dissipation process, where the emission occurs along a specific direction. For the individual and collective dissipation of N two-level atoms, we obtained analytical solutions calculating a base of eigenvectors for the Lindblad operator of the evolution. To do so, we considering symmetry under particle exchange and a maximum in the total of atomic excitations. In particular, we calculated the fraction of energy dissipated through the collective process for some Dicke states, where we find that such a fraction is greater for states with less number of excitations.

### Arbitrary unitary transformation of quantum light pulses

James Ashby, University of Oregon

Controlling the temporal mode shape of a quantum light pulses has wide ranging application to optical quantum technologies, including quantum key distribution with pulsed mode encoding, continuous-variable cluster state manipulation, linear-optics quantum computation, and enhanced quantum sensing. We propose a realistic linear optical system that can perform arbitrary unitary transformations on a set of temporal modes. First we show that any unitary transformation on pulsed modes can be decomposed into a sequence of phase modulations in either the temporal or spectral domain with Fourier transforms between these domains. It is shown that this sequence of transformations can be performed on optical pulses using electro-optic phase modulators and dispersive optical elements. We consider realistic constraints on the bandwidth of the modulator and its driving electronics to simulate the performance of this system for several unitary transformations. Example transformations that we have examined include demultiplexing temporal modes into a sequence of Gaussian pulses, single-qubit pulse-mode gates, and a two-qubit pulse-mode CNOT gate. Numerical results demonstrate that targeted transformations can be achieved with near unit fidelity and efficiency.

### Towards full characterization of photonic gates with weak local oscillators

Arik Avagyan, National Institute of Standards and Technology, Boulder

In the standard homodyne configuration, an unknown optical state is combined with a local oscillator (LO) on a beam splitter. Good quadrature measurements require a high-amplitude LO and two high-efficiency photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is then possible to infer the optical state in the mode or modes matching the LO. For quantum information processing, the states of interest are in well-separated modes, corresponding to a pulsed configuration with one relevant LO mode per measurement. We determine what can be learned about the unknown optical state by counting photons in one or both outgoing paths after the beam splitter, keeping the local oscillator mode fixed but choosing its phase and amplitude. We prove that given the probabilities of photon counts of just one of the counters as a function of LO amplitude, it is possible to determine the content of the unknown optical state in the mode matching the LO conditional on each number of photons in orthogonal modes on the same path. If the unknown optical state has at most n photons, we determine finite sets of LO amplitudes sufficient for inferring the state.

### Symmetric subspace randomized benchmarking

Charles Baldwin, Honeywell Quantum Solutions

Randomized benchmarking is the standard tool for accurately characterizing error rates of quantum hardware. However, multi-qubit benchmarking is complicated by both the exponential growth of the gate set with qubit number and practical experimental challenges of synthesizing such gates. We present a new two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits. By performing benchmarking only in the symmetric subspace, we drastically reduce the number of gates required, and simplify the experimental implementation. We demonstrate the protocol in a trapped-ion experiment using arbitrary global single-qubit rotations and the Molmer-Sorenson interaction. Most expected errors in a Molmer-Sorenson gate keep population in the symmetric subspace but even errors that mix symmetric and anti-symmetric subspaces can be diagnosed. These errors appear as leakage and their rate can by characterized by combining our protocol with recently proposed leakage benchmarking.

### Minimal quantum state representations from denoising auto-encoders

Shiva Barzili, Chapman University

As multi-qubit systems increase in size, the state space scales exponentially. This makes accurate state tomography increasingly challenging and places a high demand on computational resources. This problem is compounded by the addition of experimental noise in tomographic measurements. We investigate the use of supervised machine learning, in the form of modified denoising auto-encoders, to simultaneously remove experimental noise while finding minimal latent representations of the quantum state. These representations can be later decoded into more traditional state representations.

### AOA digitizes an asymptotic curve: A path sum approach

Lucas Brady, National Institute of Standards and Technology, Maryland

We numerically and analytically explore the behavior of the Quantum Approximate Optimization Algorithm (QAOA) as the number of steps p is increased. QAOA alternates between two operators, keeping one on for a variable time and then switching to the other for a different length of time, repeating this procedure for p steps with varying optimized timings. We develop a path sum approach to analyzing QAOA that provides analytic insight into the state dynamics under QAOA, and allows us to derive several results analytically. One such is that we find that the optimal timings form a curve that approaches an asymptotic form as p increases, allowing researchers to predict the optimal times for p+1 steps given the optimal angles for p steps. We additionally use our methods to analyze low p cases, reproducing important existing results. We present numerics that confirm the analytically suggested results, even for relatively low p, focusing on the transverse field Ising model but with similar results in other models.

### Adiabatic preparation of quantum ground states in coupled cavity arrays

Kang Cai, University of California, Merced

Coupled cavity array (CCA) can be used to explore quantum phase transition in strongly-correlated polaritons. At integer fillings, such systems demonstrate the Mott-insulator-to-superfluid phase transition. However, it is nontrivial to prepare such systems in their quantum ground states near a quantum critical point, where the energy gap often diminishes. Here, we study an adiabatic process to prepare the ground states in a finite-size CCA model. In our scheme, the CCA is initially biased in the deep Mott-insulating or the deep superfluid regime far from the quantum critical point, where the ground state can be prepared with high fidelity. During the evolution, the system parameters are tuned adiabatically towards the target parameters near the quantum critical point. We characterize the fidelity of the final state under various ramping schemes. Our result shows that the fidelity can be greatly improved by choosing the adiabatic sweeping protocol.

### Demonstrations of one-way EPR steerable polarization-entangled photon states

Lorenzo Calvano, Harvey Mudd College

EPR steering is a signature of a class of two-qubit states for which one party, who holds one qubit of the pair, can prove to the possessor of the other qubit that their states are entangled. The protocol requires many copies of the two-qubit state, and involves the first party demonstrating that their measurement choices and results alter the one-qubit state held by the second party, thus “steering” the second party’s state. EPR steerable states form a strict superset of Bell nonlocal states, since they include states with too little entanglement to be Bell nonlocal. Surprisingly, given the mutual nature of bipartite entanglement, certain two-qubit states are actually one-way steerable, with Alice being able to “steer,” Bob, but not vice versa. We demonstrate experimental violation of an all-versus-nothing (AVN) steering inequality for partially polarization-entangled photon pairs. Using this AVN steering inequality, we further demonstrate an asymmetry between the parties in which Alice steers Bob, but Bob cannot steer Alice. We discuss further studies of the parameter regime over which this one-way steering phenomenon can be observed. EPR steering, both mutual and one-way, could be useful as a signature of partial entanglement in a variety of quantum communication or distributed quantum computing schemes. One-way steering has the potential for further application in communication protocols where the level of trust is asymmetric between the parties.

### Characterizing quantum circuits by short-cutting quantum channels and a ''polar'' decomposition for quantum channels

Arnaud Carignan-Dugas, University of Waterloo

When characterizing a quantum computer, the jump from a characterization of elementary operations to a quantified assertion on the overall device performance is quite involved; errors can coherently interfere and propagate through the entire device via multi-qubit operations. The richness of quantum dynamics allows for a plethora of noise models which, given only a partial knowledge of the device's components, can result in widely different conclusions regarding the quality of larger circuits. In fact, the sole formulation of a conclusion is demanding in that it typically requires invoking a broad range of quantum dynamical scenarios. In this work, we pave the way between partially characterized elementary operations and circuits thereof. Our paving stone consists of a simplified picture of quantum processes that we refer to as the leading Kraus (LK) approximation. This incomplete dynamical representation closely prescribes the evolution of celebrated characterization figures of merit, namely the average gate fidelity, which captures the overlap between an implemented operations and their targets, and the unitarity, which captures the level of coherence in the noise. The simplicity of the LK approximation clarifies the path that follows those quantities as elementary components aggregate into larger circuits. Moreover, the same transparency in the LK parametrization allows the derivation of a quantum unitary-incoherent (polar) factorization for quantum channels.

### Reliable analog quantum simulation and quantum complexity

Karthik Chinni, University of New Mexico

An analog quantum simulator does not employ digital gates and typically does not employ quantum error correction. Yet, one hopes such devices can achieve a “quantum advantage,” i.e., enable the simulation of some property that cannot be simulated efficiently on a classical computer. Typically, one considers “universal” properties in condensed matter, as these are the quantities that are robust in the presence of perturbations [1]. What is the relationship between robustness and complexity? Are the robust properties efficiently simulatable on a classical computer, and the complex properties hyper-sensitive to perturbation? To address these questions, we seek to quantify the reliability of an analog quantum simulator while simulating complex systems and thereby identify these universal quantities. We study a “programmable” analog quantum simulator in the 16-dimensional Hilbert space based on optimal control of atomic spins in cesium [2], and study the basic paradigms such as the excited state quantum phase transitions [3] in the Lipkin-Meshkov-Glick (LMG) model [3].

### Entropic energy-time uncertainty relation

Patrick Coles, Los Alamos National Laboratory

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Due to the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.

### Variational quantum state diagonalization

Patrick Coles, Los Alamos National Laboratory

Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum state $\rho$ and gate sequence $U$, our cost function quantifies how far $ U\rho U^{\dagger}$ is from being diagonal. We introduce novel short-depth quantum circuits to quantify our cost. Minimizing this cost returns a gate sequence that approximately diagonalizes $\rho$. One can then read out approximations of the largest eigenvalues, and the associated eigenvectors, of $\rho$. As a proof-of-principle, we implement our algorithm on Rigetti's quantum computer to diagonalize one-qubit states and on a simulator to find the entanglement spectrum of the Heisenberg model ground state.

### Classification of 2D cluster phases by subsystem symmetry and measurement-based computational capability

Austin Daniel, University of New Mexico CQuIC

A long standing open problem for measurement-based quantum computation (MBQC) is classifying which many-body states can be used as a universal resource state. Recently it has been found that certain 2D symmetry protected topological phases which possess subsystem symmetries corresponding to an underlying quantum cellular automaton (QCA) structure, can act as an universal resource phase in which every state can be used to do universal MBQC (Raussendorf et. al., arXiv:1803.00095). We analyze subsystem symmetries and classify cluster phases on 2D lattices according to their underlying QCA structure and usefulness for MBQC.

### Robust topological information storage in warm alkali vapor using slow twisted light

Kenneth DeRose, Miami University

We create slow light pulses propagating at 350 m/s through warm Rubidium gas, and elucidate experimentally the role played by the narrow spectral window of a few kHz due to electromagnetically induced transparency (EIT). The importance of pump intensity optimization is emphasized. Further, by measuring the EIT linewidth as a function of relative pump-probe angle we obtain direct experimental proof of Dicke narrowing. An application of slow light to the field of quantum information is that now the experimenter supposedly has more time to encode/decode information. However, this also means the stored information has more time available to dissipate away. We describe our experimental progress toward propagating a slow twisted light pulse through warm Rb vapor, and showing that the topology of the pulse allows for robust storage of information.

### Phase tracking and correction for non-Gaussian state discrimination measurements of coherent states

Matthew DiMario, University of New Mexico CQuIC

Non-Gaussian measurements for discriminating coherent states of light with different phases enable information transfer beyond what conventional technologies can achieve with an ideal Gaussian measurement, referred to as the quantum noise limit (QNL). However, random phase drifts in any real-world communication channel make the task of extracting the information encoded in the states very challenging. The current approach for overcoming this problem in conventional optical communications, based on heterodyne detection, is to perform parameter estimation in the digital domain. While this technique works in conventional communications, they are incompatible with non-Gaussian receivers. This puts in question the potential advantages of quantum receivers surpassing the conventional limits of detection in real channels with random phase drifts. We develop and demonstrate an algorithm which performs real time parameter estimation using only the data collected by the non-Gaussian discrimination measurement itself. The phase correction is applied to the local oscillator to actively and adaptively correct for any phase changes that diminish the benefit over a heterodyne measurement. Our demonstration allows non-Gaussian receivers to overcome phase drifts in real channels while enabling discrimination below QNL. This demonstration makes non-Gaussian receivers more robust and a much more practical quantum technology for future applications in communication and information processing.

### Toward many-body cavity QED with addressable ultracold atoms

Emma Dowd, University of California Berkeley

Ultracold atoms trapped within a high-finesse optical cavity provide a flexible platform for observing and controlling the dynamics of quantum many-body systems. I will report on our progress toward a new experimental apparatus that will consist of addressable arrays of atoms interacting with a near-resonant mode of a near-concentric optical cavity. Light leaking out of the cavity allows non-destructive observation of atomic dynamics imprinted dispersively onto the phase of the cavity field, making this a natural system for studying weak measurement of many-body dynamics. The cavity mode also mediates infinite-range interactions between the atoms in the cavity; adding spatially patterned transverse pump beams allows one to turn these into finite-range interactions of many different flavors, to be used for novel Hamiltonian engineering and quantum simulation. Actuating local control using spatially resolved pump beams based on the measurement record imprinted on the cavity field, we will also explore dissipative state preparation and nonequilibrium many-body dynamics under local measurement and feedback.

### Quantum gate teleportation between separated zones of a trapped-ion processor

Scott Glancy, National Institute of Standards and Technology, Boulder

Large-scale quantum computers will inevitably require quantum gate operations between widely separated qubits, even within a single quantum information processing device. Nearly two decades ago, Gottesman and Chuang proposed a method for implementing such operations, known as quantum gate teleportation. It requires only local operations on the remote qubits, classical communication, and shared entanglement that is prepared before the logical operation. We demonstrate this approach in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two computational qubits in spatially separated zones of a segmented ion trap. Our teleported CNOT's entanglement fidelity is in the interval [0.845, 0.872] at the 95 % confidence level. The implementation combines ion shuttling with individually-addressed single-qubit rotations and detections, same- and mixed-species two qubit gates, and real time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.

### Out-of-time-ordered-correlator quasi-probabilities for the quantum kicked top

Jose Raul Gonzalez Alonso, Chapman University

The cumulative nonclassicality of the quasi-probability distribution (QPD) behind the out-of-time-ordered correlator (OTOC) exhibits different time scales that have been conjectured to be useful for distinguishing integrable and nonintegrable Hamiltonians (arXiv: 1806.09637). We further investigate the QPD for a quantum kicked top, and use the time scales of its nonclassicality to understand the relationship between entanglement and chaos for different parameter regimes.

### A local non-contextual model of non-interacting measurement

Sacha Greenfield, Carleton College

Measurement of photon number in one mode of a two-mode optical cavity allows for high-fidelity detection of an object in the other mode. In the single-photon limit, measurement of the photon in one mode collapses the superposition state of the photon, indicating that the photon was never present in the object-containing mode. This seemingly non-local detection, originally formulated as the Elitzur-Vaidman bomb test, has thus been dubbed "non-interacting measurement." However, building off of previously formulated models, we develop an explicitly local realist model of a qubit that is non-contextual for pure states. The possibility of such a model indicates that neither non-locality nor contextuality is a necessary condition for "quantum-ness." Instead, non-interacting measurement's "spooky action at a distance" may be attributed to the existence of an information-carrying vacuum that provides a reference frame for the particle evolution.

### Spin squeezing and magnetometry with magnetic field-sensitive states

Daniel Hemmer, University of Arizona

Collective spin squeezing can be produced through quantum backaction from a quantum non-demolition measurement. In our experiment we start with the collective angular momentum of a million spin-4 Cs atoms prepared in a spin coherent state (SCS), and generate upwards of 4 dB of metrologically relevant spin squeezing though measurement backaction. By introducing real-time feedback in the form of a radio-frequency (RF) magnetic field we can generate deterministic spin squeezing and use the atomic ensemble as a RF magnetometer. Moving forward, we plan to use internal state control to further increase the amount of spin squeezing. Preliminary results show that up to 8 dB of metrologically relevant squeezing can be produced by preparing the internal atomic spins in a “cat” state before performing the QND measurement. To be metrologically useful, squeezing in the “cat” state basis must be coherently mapped to the SCS basis. So far fluctuating background magnetic fields at frequencies up to tens of kHz have prevented us from doing this reliably. To mitigate the problem we designed and installed a triple-layered magnetic shield which suppresses these fields by more than a factor of 10,000, and have now rebuilt the experiment inside it. We will discuss progress using composite pulses to diagnose and correct for control errors due to residual fields and other experimental imperfections.

### Coherence in logical quantum channels

Joseph Iverson, California Institute of Technology

We study the effectiveness of quantum error correction against coherent noise. Coherent noise can cause the infidelity to accumulate quadratically when a fixed channel is applied many times in succession, rather than linearly as in the case of incoherent noise. We consider stabilizer quantum codes, and describe how to characterize coherence of the residual logical noise after applying coherent physical noise followed by error recovery. For the case of the toric code subjected to independent coherent noise, and for minimal weight decoding, we prove that the logical channel becomes incoherent as the size of the code increases, assuming that the physical noise strength is below a specified constant. A similar conclusion holds for weakly correlated coherent noise. We also comment on extensions of these results to other codes and other decoders. Our work provides evidence indicating that fault-tolerant quantum computing schemes will work effectively against coherent noise.

### Photon number discrimination with linear optics

Kevin Valson Jacob, Louisiana State University

Photon number resolution is important for a wide range of applications. Conventional techniques for photon number resolution are prohibitively expensive. However, schemes which are easier to implement can be found when the single shot criterion for detection is relaxed. In this poster, we show a simple linear optical scheme which can discriminate between various Fock state inputs. We compare two measurement strategies: coincidence measurements and homodyne detection. We find the minimum number of trials needed to discriminate between various Fock states.

### The Ryu-Takayanagi formula from quantum error correction: An algebraic treatment of the boundary CFT

Helia Kamal, University of California Berkeley

In recent years, an interpretation of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence in the language of quantum error correction has been developed. This language shines light on several puzzling features of the correspondence and has therefore played a crucial role in advancing our understanding of AdS/CFT. In particular, in a recent work by Daniel Harlow, it is shown that sub-algebra quantum erasure-correcting codes with complementary recovery naturally give rise to a version of quantum-corrected Ryu-Takayanagi formula that captures the physics of AdS/CFT. Harlow’s key insight was that the realistic and accurate treatment of the code space is using Von Neumann algebras. In his interpretation of AdS/CFT, a Von Neumann algebra is defined on the bulk, while a simple tensor product structure is assumed for the boundary Hilbert space. In this work, we develop the mathematical framework for extending Harlow's results to the more physical case where a Von Neumann algebra is also given on the boundary CFT. By obtaining an algebraic version of Ryu-Takayanagi that very closely resembles the original formula, we show that our code more accurately captures the properties of AdS/CFT.

### Generalizing the OTOC to yield Lyapunov exponents in the classical limit

Charlie Kapsiak, Carleton College

The out-of-time-ordered correlator is OTOC is used as a tool to diagnose quantum chaos. When applied to the position and time operators, it yields the Lyapunov exponent in the classical limit but only for the one-dimensional case or for a uniformly hyperbolic map such as the Cat Map. We construct the correct generalization to higher dimensional canonical phase spaces by demonstrating that a matrix of OTOCs yields the Jacobian of the dynamics in the classical limit and hence is able to recover the correct classical maximal Lyapunov exponent. We also construct the correct generalization for OTOCs for dynamics governed by Lie Algebras. We discuss the behavior of these generalized measures.

### Quantum-assisted quantum compiling

Sumeet Khatri, Louisiana State University

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm’s cost on a quantum computer. To this end, we propose quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary U and a trainable unitary V as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost function involves not only the global overlap Tr(V†U) but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we present both gradient-free and gradient-based approaches to minimizing this function. As a demonstration of QAQC, we compile various one-qubit gates on IBM’s and Rigetti’s quantum computers into their respective native gate alphabets. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.

### Quantum proofs for approximate counting

**William Kretschmer, University of Texas, Austin**

We prove a QMA query complexity lower bound for approximate counting: estimating the size of a set given a membership oracle and a quantum witness. This gives rise to an oracle relative to which SBP is not contained in QMA, resolving an open problem of Aaronson [arXiv:1808.02420]. More generally, we prove a lower bound tradeoff between query complexity and witness length for this problem.

### Improving optimal control in a cold-atom qudit analog quantum simulator

Kevin Kuper, University of Arizona

As noisy intermediate-scale quantum devices become commonly realized, it is unclear how useful they will be when attempting classically hard problems such as analog quantum simulation (AQS) in the presence of imperfections. We aim to understand the limitations of such devices by studying the behavior of our own small-scale, high fidelity quantum processor. Operating in the 16-dimensional hyperfine ground manifold of a single Cs atom, this system is controllable with a combination of rf and µw magnetic fields, each subject to arbitrary piece-wise linear phase modulation. Gradient-ascent optimal control allows us to find a set of phase modulation control waveforms that implement any arbitrarily-chosen unitary map with high accuracy. This property of our general-purpose simulator allows us to not only simulate any given system in Hilbert space dimensions up to 16, but also to do so in an arbitrary basis. If we allow this basis to be unconstrained when using our optimal control protocol, we reduce the number of control parameters and obtain both shorter control times and higher experimental fidelities. However, there remain classes of unitaries for which it is difficult to find high-performing control waveforms and to simulate for long times while maintaining good fidelity. One important factor could be the presence or absence of degeneracies in the spectrum of the model Hamiltonian. Further study of these limitations may illuminate how errors can impact AQS of complex dynamics.

### Quantum codes from neural networks

Felix Leditzky, University of Colorado JILA

We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we supply further evidence for the usefulness of neural network states to describe multipartite entanglement. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction. In particular, we show that a) neural network states yield quantum codes with a high coherent information for two important quantum channels, the depolarizing channel and the dephrasure channel; b) neural network states can be used to represent absolutely maximally entangled states, a special type of quantum error-correcting codes. In both cases, the neural network state ansatz provides an efficient and versatile means as variational parametrization of these states.

### Monotonic measures of quantum correlations

Josh Levin, University of Colorado JILA

We perform a systematic search for new measures of bipartite quantum correlation. We require monotonicity so that our quantities may be identified as information. Several types of monotonicity are defined, and enforced by requiring quantities to satisfy particular pairs of inequalities which we derive. We find three measures of correlation, one of which is the entanglement of purification, the other two have not been thoroughly studied. We hope to eventually find geometric interpretations for these quantities in the context of holography, since such an interpretation already exists for the entanglement of purification.

### Self-testing Majorana parity measurements

Karl Mayer, University of Colorado

We present a self-testing protocol for certifying a set of Majorana parity operators under minimal physical assumptions. The scenario involves measurements which ideally are of parities acting on two logical qubits encoded in six Majorana modes. Our only assumptions are that an unknown state is repeatedly prepared, that the measurements are two-outcome POVMs, and that measurements corresponding to disjoint modes are compatible. We prove a rigidity theorem stating that an observation of the ideal statistics implies that the prepared state is contained in a subspace on which the action of the measurement operators is equivalent to that of ideal parities. The proof is based on a mapping between Majorana parities and two qubit Pauli operators arranged in a Peres-Mermin magic square. A version of the protocol robust to errors is the subject of ongoing work. A successful application of such a protocol would constitute strong evidence for the existence of Majorana zero modes, which are potential building blocks for a topological quantum computer.

### Nonclassical effects in multilevel electromagnetically induced transparency

Mitch Mazzei, Miami University

We examine a multilevel system that can exhibit EIT or EIA under appropriate conditions. These effects can be understood in terms of classical coupled oscillators. We examine whether nonclassical behavior is exhibited in the EIT/EIA regime, and elsewhere. Specifically, the second order intensity correlation function $\g^{(2)}(/tau)$ and the intensity-field correlation function $\h_{/theta}(/tau)$ are calculated for various EIT/EIA parameters and then analyzed in the context of classical inequalities. Nonclassical behavior cannot be described by a classical stochastic process, no mean field plus noise. Those cannot be described by two classical oscillators. We propose a multilevel photonic memory in this system as well.

### Robust quantum logic gates via quantum optimal control in Rydberg dressed atoms

Anupam Mitra, University of New Mexico CQuIC

The Rydberg blockade mechanism has been used to entangle two qubits encoded in the hyperfine ground manifold of neutral atoms. Thermal motion of atoms limits the gate fidelity in the standard fast-pulse protocol, which involves direct, resonant excitation to Rydberg states, as the internal atomic states and external motional states become entangled, leading to different random phases accumulated by the computational basis states. Adiabatically dressing ground and Rydberg states provides some robustness against these random phases, leaving only a residual Doppler detuning error. We analyze methods to overcome the effect of thermal motion of the atoms through quantum control techniques, combining adiabatically dressing and undressing of the hyperfine ground states with an ultraviolet laser to accumulate entangling phases and driving the atomic states with microwaves (or Raman lasers) near-resonant to the qubit transition. This protocol is amenable to further correction through quantum optimal control.

### Always-on quantum error tracking with continuous parity measurements

Razieh Mohseninia, Chapman University

We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates passive error tracking in real time. However, the noisy analog signals from continuous parity measurements mandate more complicated signal processing to interpret syndromes accurately. To this end we introduce different filters. As an optimal filter, we discuss an unnormalized (linear) Bayesian filter, with improved computational efficiency compared to the related Wonham filter. We then compare this optimal filter to several filters that are better suited for real time implementation with low-latency circuitry, based on straightforward boxcar-averaging and thresholding.

### Correlators of a detector cavity coupled to quantum simulators

Alessandro Monteros, University of California Merced

Cavity modes can serve as detector of quantum simulators. Here we examine how a cavity's correlator changes when coupled to one of two quantum simulators: a qubit and the transverse field Ising model using a diagrammatic technique. Using this approach, we determine whether reliable detection of the simulator's many-body correlator can be achieved. We also calculate the backaction of the detector on the quantum simulators. In the case of the qubit, this allows us to obtain a simple expression for the cavity correlator without the need for the rotating wave approximation.

### Long range multibody coupling of flux qubits that preserves the gap in quantum annealing

Evgeny Mozgunov, University of Southern California

Quantum annealing was proven to be an effective optimization algorithm in all-to-all connected systems. Unfortunately, realistic devices so far have been limited to 2-body spatially local 2d lattice of interactions. A promising approach to overcome these limitations is to realize couplers as paramagnetic trees: locally-interacting trees of ancillae obeying a transverse-field Ising model with the gap large compared to qubit energy. We present the conditions under which the minimal gap of the non-local multibody system Hamiltonian along the quantum annealing schedule is unchanged if the couplings are implemented as paramagnetic trees. The caveats in this approach are that the circuit model of the tree nodes in practice will be operated outside the limit where the effective qubit description is accurate, and the noise is amplified by the tree.

### Exploring the emergence of classical nonlinear dynamics with an atomic feedback-based architecture

Manuel Munoz-Arias, University of New Mexico CQuIC

We propose a feedback-based protocol for the time evolution of the collective spin in an ultracold atomic ensemble. The protocol consists of a measurement process which yields information about the z-component of the collective spin, followed by an unitary part which is conditioned on the value of the measurement outcome. We study, an intermediate regime, where the measurement is strong enough to keep the spin wavepacket localized, but not so strong that measurement backaction dominates the dynamics. In that regime, we see the emergence of nonlinear dynamics in individual quantum trajectories. As a particular example, we show how this protocol allow us to recover the well known nonlinear kicked top, a paradigm of quantum chaos. We develop an analytical description of the resulting dynamics under the Gaussian approximation, and explicitly show how the regular, mixed and chaotic features of the kicked top phase space emerge from the noisy dynamics as the size of the ensemble increases. We finally characterize the chaotic dynamics by means of time series analysis and study the corresponding Lyapunov exponents.

### Computational complexity of quantum channels

Bradley Pearlman, University of Colorado JILA

We study the computational complexity of various optimized quantities of quantum channels. Throughout this work, there is a recurring theme that the size of the description of the channel (polynomial in either the input dimension or the number of input qubits) directly influences the complexity of every quantity. The study of quantum channel complexity was most notably initiated by Beigi and Shor [BS08]. Our work extends the machinery they developed in a natural way to prove NP-completeness for computing the coherent information $\mathcal{I}^\textnormal{coh}$ of a multiple-access quantum channel in the long-circuit regime. QMA-hardness results for several quantities (including $\mathcal{I}^\textnormal{coh}$) in the normal-circuit regime are also proven. These hardness results serve as lower bounds for the computational complexity of the associated problem. We define the Maximum Entanglement Transmission problem, which is then shown to be QMA-complete in the normal-circuit regime, and contained in BQP for the long-circuit regime. A pedagogical introduction to quantum circuits, channels and complexity is given in order to make this work as self-contained as possible.

### Limits to single photon detection: Transmission and amplification

Tzula Propp, University of Oregon

We construct a model of photo detection that is both idealized and realistic enough to calculate the limits and tradeoffs inherent to single photon detector (SPD) figures of merit. A linear quantum network comprised of discrete states and continua provides a general description of a passive SPD in the single-photon limit. We analyze criteria for perfect transmission through a such a network and analyze potential tradeoffs between transmission efficiency, spectral bandwidth, and group delay. Once a photon has been transmitted through the network, we consider the effects of signal amplification; by writing correct commutator-preserving transformations for non-linear photon-number amplification (e.g. avalanche photodiode, electron-hole pair creation), we can derive noise limits that show a marked improvement over the well-known Caves limit for linear amplification of bosonic modes. Lastly, we briefly discuss the construction of POVMs completely describing SPDs, from which we can calculate standard SPD figures of merit.

### Simulating quantum circuits by shuffling Paulis

Patrick Rall, University of Texas, Austin

The stabilizer formalism can make probability estimation of some large quantum circuits tractable. Quasiprobability methods extend stabilizer techniques to arbitrary noisy quantum circuits, sometimes maintaining polynomial runtime (Phys. Rev. A 95, 062337). We study a simplified strategy that uses quasiprobability distributions over Pauli matrices. The method achieves linear-time probability estimation of Clifford circuits and achieves tractable simulation some non-stabilizer states and channels. We classify the capabilities of the technique and apply it to 64-qubit QAOA circuits.

### Disorder-free localization in the Kitaev honeycomb model

Sayonee Ray, University of New Mexico CQuIC

Philip Anderson's seminal insight is that a quantum particle propagating in a disordered medium is confined, or localized, to a bounded region near its initial position. Recently, this intuition has been challenged by the concept of disorder-free localization, whereby this confinement is dynamically self-induced, even in translationally invariant systems. In this ongoing work, we study how local disturbances propagate in the two-dimensional Kitaev honeycomb model by calculating the infinite temperature out-of-time-ordered correlator (OTOC) for Pauli observables. The Kitaev honeycomb model consists of non-commuting two-body Hamiltonian terms whose ferromagnetic interaction directions are in correspondence with the ''compass" directions of a honeycomb lattice. Surprisingly, this model is exactly solvable, and lies in the same phase as the toric code. We find that our quantity of interest reduces to an average of free-fermion evolution over disordered hopping amplitudes. We therefore observe that Pauli ZZ disturbances reach a localized equilibrium which persists for very long times, and we conjecture that this indeed constitutes a signature of genuine localization. A future direction of this work is to extend our analysis to the finite temperature OTOC and study the effect of temperature on our result.

### Demonstration of sideband cooling on the 171Yb+ quadrupole transition

Melissa Revelle, Sandia National Laboratories

Trapped ions can be used for a physical realization of a quantum information system in which qubits are encoded in hyperfine energy states. In this system, a high-fidelity two-qubit gate operation requires the ions to be cooled close to the motional ground state of the trap. This is typically accomplished by using Raman laser beams to perform resolved sideband cooling on the motional sideband of the qubit transition itself. In an alternative approach, we take advantage of the narrow linewidth of the quadrupole 2S1/2 to 2D3/2 transition to resolve the motional sidebands by employing a narrow linewidth continuous wave (CW) laser. In addition to 171Yb+, this method can also be applied to ytterbium isotopes without hyperfine structure. Here, we demonstrate this alternative sideband cooling method by applying it to 171Yb+, cooling the ion to the motional ground state, and measuring the residual motional excitation of the ion also using the 2S1/2 to 2D3/2 transition. *Funded, in part, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA). *Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & 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-NA0003525.

### Quantum walk search on the complete bipartite graph

Mason Rhodes, Creighton University

The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of N vertices for one of k marked vertices with different initial states. We prove intriguing dependence on the number of marked and unmarked vertices in each partite set. For example, when the graph is irregular and the initial state is the typical uniform superposition over the vertices, then the success probability can vary greatly from one timestep to the next, even alternating between 0 and 1, so the precise time at which measurement occurs is crucial. When the initial state is a uniform superposition over the edges, however, the success probability evolves smoothly. As another example, if the complete bipartite graph is regular, then the two initial states are equivalent. Then if two marked vertices are in the same partite set, the success probability reaches 1/2, but if they are in different partite sets, it instead reaches 1. This differs from the complete graph, which is the quantum walk formulation of Grover’s algorithm, where the success probability with two marked vertices is 8/9. This reveals a contrast to the continuous-time quantum walk, whose evolution is governed by Schrödinger’s equation, since its success probability reaches 1 for either arrangement of marked vertices and also for the complete graph.

### Quantum noise properties of PT symmetric systems

Perry Rice, University of Oregon

We examine the quantum noise properties of a simple PT system comprising of two coupled oscillators, one with gain and one with loss. We show that claims of a zero width resonances in these systems are incorrect. Essentially the noise introduced by the gain is excluded. We find that the usual implementation of PT symmetry is equivalent to quantum trajectory theory, but with no jump processes. As such it is essentially a wave description with no concept of the photon included. We discuss the relation of PT to more traditional ways of treating open quantum systems, showing that {\cal PT} quantum mechanics is {\it not} an extension of quantum mechanics into the complex plane.

### Van Trees information for phase estimation

Marco Antonio Rodriguez Garcia, Universidad Nacional Autonoma de Mexico

In the problem of parameter estimation, the Fisher information is a way of measuring the amount of information that a sample carries about an unknown parameter. In the problem of quantum parameter estimation, the Van Trees information is the maximum of the Bayesian analog of Fisher information over the set of POVMs. Moreover, the inverse of the Van Trees information gives us a lower bound for the Bayesian error of estimations. However, the set of POVMs has a complicated mathematical structure; for this reason, the Van Trees information is arduous to calculate. The aim of this work is to present a result that allows us to calculate the Van Trees information for the case of covariant transitive phase estimation.

### Determining the maximum distinguishability for generalized Bell states with linear evolution local measurement devices

Thomas Schneider, Harvey Mudd College

We investigate the maximum distinguishability of high dimensional Bell states using LELM devices. It has been shown that projective LELM devices cannot distinguish all four qubit Bell states; they can only reliably distinguish three. In the case of bosonic qutrit Bell states, it has been shown that only three of the nine Bell states are distinguishable. By analyzing a group action that preserves the distinguishability of the possible input sets, we are able to greatly reduce the number of possible inputs that need to be checked. Moreover, we provide insight into why the distinguishability question is more difficult to answer for Bell states of fermions as opposed to bosons or non-identical particles. We discuss distinguishability of d=4 qudit Bell states and compare to the previously solved case of hyperentangled Bell states in two (or n) qubit variables.

### Machine-learned QCVV for distinguishing single-qubit noise

Travis Scholten, IBM

We investigate the use of machine learning (ML) algorithms for developing new QCVV protocols. ML algorithms learn approximations to functions that relate experimental data to some property of interest. As an example, we show ML algorithms can successfully learn separating surfaces for distinguishing coherent and stochastic noise affecting a single qubit. The performance of various ML algorithms depends strongly on the geometry of experimental data (in this case, data from gate set tomography experiments). We show performance can be boosted by hyperparameter tuning and feature engineering. Sandia National Labs is managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The views expressed in this abstract do not necessarily represent the views of the DOE or the U.S. Government. Contributions to this work by NIST, an agency of the US government, are not subject to US copyright. Any mention of commercial products does not indicate endorsement by NIST.

### Investigating experimental verification of quantum simulations

Ryan Shaffer, University of California Berkeley

Quantum simulation is expected to be an important application of quantum computers in the near future. When the simulation is occurring within a Hilbert space that is small enough to simulate classically, one can easily verify the results of a quantum experiment by comparing to the results of the classical simulation. However, when the computational complexity increases, one needs a way to verify the result of the quantum simulation without knowing independently what the result should be. For example, we have run vibrationally assisted energy transfer (VAET) simulations on two trapped-ion qubits, which is simple to verify classically; but if we wanted to verify such a simulation on a larger system, the problem quickly becomes intractable. We are exploring approaches to gain confidence in the results of such quantum simulations, such as providing bounds on possible errors, in a regime which cannot be verified classically.

### Continuous real-time tracking of a quantum phase below the standard quantum limit

Athreya Shankar, University of Colorado JILA

We propose a scheme for continuously measuring an evolving quantum phase with precision beyond the standard quantum limit of $\Delta \phi_\text{SQL} = 1/\sqrt{N}$ radians, where $N$ is the number of pseudospins. Quantum non-demolition measurements of a lossy cavity mode interacting with an atomic ensemble are used to directly probe the phase of the collective atomic spin without converting it into a population difference. Unlike traditional Ramsey measurement sequences, our scheme allows for real-time tracking of time-varying signals. As a bonus, spin-squeezed states develop naturally, providing real-time phase estimation significantly more precise than $\Delta \phi_\text{SQL}$.

### Enhanced quantum-classical dynamics difference via control of weak measurement

Yueheng Shi, Carleton College

Back-action induced by weak measurement can dramatically affect the quantum state dynamics of a nonlinear quantum system. We devise a measurement control protocol using the local oscillator phase $\phi$ for a homodyne measurement of a signal from the system. We use the the percentage of non-classical energy in the system $Q$ as a measure of quantumness, and find that adaptive control of $\phi$ increases $Q$ by several orders of magnitude. Thus, measurement can induce quantum behavior in a system significantly more easily than changing system size, and particularly visible in the energy dynamics which map to system trajectories as well. We are discuss applications our control mechanisms for quantum thermal engines and work extraction via measurement.

### Implementation and applications of generalized coherent-state measurement: Case study: SU(2) and SU(1,1)

Ezad Shojaee, University of New Mexico CQuIC

Generalized coherent-states (GCS) are obtained by applying the unitary representations of elements of a Lie group onto a chosen fiducial state in Hilbert space. These states form an over-complete basis set which resolves the identity and form a positive-operator-valued-measure (POVM). The measurement with POVM elements proportional to GCSs is called the coherent-state measurement. In this work, we show how any such POVM can be obtained through a sequence of weak measurements of a fiducial operator, conjugated by Haar-random elements of the group. We study two important groups: SU(2) and SU(1,1). The SU(2) coherent-state measurement is a way to optimally estimate the state of an unknown pure qubit given a finite number of copies and can be implemented by doing a sequence of collective isotropic weak measurements of the collective spin projection. SU(1,1) coherent-state measurement forms a POVM over the set of squeezed-vacuum states. This measurement can be implemented by weakly measuring the number operator isotropically conjugated with squeezers. We consider its applications in metrology.

### Progress towards development and quantum theoretic analyses of a physical model for RC

Karpur Shukla, Centre for Mathematical Modelling, Flame University

We present new developments in the application of nonequilibrium fluctuation theorems to logically and physically reversible models of computation, in particular examining the synthesis of two complementary views of stochastic and quantum thermodynamics as they relate to reversible computing (RC). First, by examining the nonequilibrium thermodynamic properties of different information measures used by Sagawa and Anderson on the energy cost of information erasure and the Landauer-Bennett limit as they relate to transformations on memory states, we demonstrate the complementarity of their descriptions of energy costs of computational processes. This demonstration is made clear by examining recent work on nonequilibrium memory state transformations, collective operations, and nonequilibrium quantum Maxwell's demons in the framework provided by Sagawa and Anderson. Finally, we discuss progress in developing a concrete model of nonequilibrium reversible computation, in particular through the application of fluctuation theorems to conformal field theories. We discuss progress in developing work distribution functions for a model of SO(2,1) nonrelativistic non-Abelian anyons, and the relevance this has for models of topological quantum computation. By applying Sagawa's and Anderson's arguments to this system and examining the fluctuations of braiding operations, we sketch out how to apply lessons from this model to RC more broadly, allowing us to develop more applicable RC models.

### Efficient quantum annealing and thermalization

Nikolai Sinitsyn, Los Alamos National Laboratory

We provide arguments for existence of a completely alternative mechanism of quantum thermalization. We show that integrable quantum systems contain a symmetry that enforces detailed balance constraints on the excitation probabilities during non-adiabatic quantum annealing. Thus, contrary to the common belief, the emergence of a perfect Gibbs distribution from a single eigenstate of a Hamiltonian is natural in closed integrable quantum systems. This mechanism does not require any randomness or parameter uncertainties. The model that we solve for demonstration also shows the possibility of the arbitrarily fast quantum annealing computations at a vanishingly small error rate.

### Brownian ratchets in cold atom dissipative lattices

Alexander Staron, Miami University

Natural biological machines significantly outperform artificial nanodevices by efficiently harnessing energy from random noise/fluctuations. Dissipative optical lattices are ideal for elucidating mechanisms to optimize efficiency in artificial nanomachines, with the goal of rivaling biomolecular motors. We reduce the complicated problem of biomolecular ratchets to three basic conditions – there must be present in the system random noise, asymmetry, and non-equilibrium. We show how these conditions can be analyzed in dissipative optical lattices in terms of three distinct frequencies – the photon scattering rate (a measure of the noise), the vibrational frequency of atoms oscillating at the bottoms of potential wells of the lattice (a measure of the symmetry of the confining potential), and the driving frequency at which the potential wells are modulated (a measure of the asymmetry, and also non-equilibrium, introduced). We show experimentally that by shining an additional probe laser beam onto a tetrahedral 3D dissipative optical lattice we introduce a propagating modulation that forms a ratchet for a specific velocity-class of atoms. We distinguish between “stochastic resonance” where the vibrational frequency of the confined atoms is brought into resonance with the photon scattering rate, and “resonant activation” where the asymmetrizing driving frequency is brought into resonance with the vibrational frequency. We show that our ratchet is an example of resonant activation.

### Quantum Approximate Optimization Algorithm (QAOA) on constrained optimization problems

Jaimie S. Stephens, University of New Mexico CQuIC

While it is not widely believed that quantum computers will solve NP-Hard problems, they may be able to approximate the solution of such problems faster or with a better approximation than a classical computer can. In 2014, Farhi et.al. proposed the Quantum Approximate Optimization Algorithm, QAOA, to approximate hard optimization problems on a quantum computer. QAOA is naturally constructed to approximate unconstrained optimization problems but was not originally designed to account for constraints. In 2017, Hadfield et. al. proposed an adjustment to QAOA (QAOA++), so that it may be applied to constrained optimization problems. We compare this to Hen and Spedalieri's (2016) proposed method for Constrained Quantum Annealing (CQA). We show that these two methods for choosing a driving (mixing in Hadfield et. al.) Hamiltonian yield equivalent Hamiltonians for a given problem. This allows one to directly compare how QAOA++ and CQA perform on a given problem. In addition to these existing methods, we propose a new way of using QAOA to solve constrained optimization problems by adding a penalty Hamiltonian to the problem Hamiltonian, QAOA with penalties. Sandia National Labs is managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA0003525.

### Entanglement spectroscopy with a depth-two quantum circuit

Yigit Subasi, Los Alamos National Laboratory

Noisy intermediate-scale quantum (NISQ) computers have gate errors and decoherence, limiting the depth of circuits that can be implemented on them. A strategy for NISQ algorithms is to reduce the circuit depth at the expense of increasing the qubit count. In this work we describe how this trade-off can be exploited for an application called entanglement spectroscopy. Here the goal is to compute the entanglement of a pure state on systems \(A\) and \(B\) by evaluating the Rényi entropy of the reduced state on subsystem \(A\). This can be done by computing the trace of integer powers of the reduced density matrix of \(A\). Johri, Steiger, and Troyer [PRB 96, 195136 (2017)] introduced a quantum algorithm that requires \(n\) copies of the state and whose depth scales linearly in \(k\) times \(n\), where \(n\) is the integer power to which the density matrix is raised and \(k\) is the number of qubits in the subsystem \(A\). Here, we present a quantum algorithm requiring twice the qubit resources (2n copies) but with a depth that is independent of both \(k\) and \(n\). Surprisingly this depth is only two gates. Numerical simulations show that this short depth leads to an increased robustness to noise.

### Advancing elements of the trapped-ion quantum-CCD computing architecture

Susanna Todaro, National Institute of Standards and Technology, Boulder

Despite significant progress in trapped-ion quantum computation, scaling to increasingly large number of qubits remains a challenge. In one proposal, the 'quantum-CCD' architecture[1], ion qubits are transported between trapping zones dedicated to memory, readout, or gate operations. Here, we seek to address two aspects of the quantum-CCD: fast transport and trap-integrated readout. 1) In most prior quantum-CCD experiments, ion transport between zones has been performed adiabatically, which generally takes an order of magnitude more time than typical laser-driven gate operations. We report progress towards transport in a surface-electrode trap on a timescale comparable to gate operations. 2) Qubit readout is typically performed by imaging ion fluorescence on a high-quantum-efficiency sensor using high-NA objectives; however, these this approach does not scale easily to parallel ion readout across spatially separated trapping zones. One solution integrates multiple photon detectors into the trap electrodes as separate readout devices. With short detector-ion distances, these would see a large fraction of the photons emitted from an ion in a readout zone but be less sensitive to distant ions. We report results from a single trap-integrated superconducting nanowire single-photon detector (SNSPD), with about 70% internal quantum efficiency, used for ion readout. This research is supported by IARPA and the NIST Quantum Information Program. [1] Wineland, et al., J Res NIST 1998

### Coherent control of angular momentum states with a freely rotating Coulomb crystal

Erik Urban, University of California Berkeley

Rings of trapped ions provide unique access to experiments requiring periodic boundary conditions, spatial symmetry, and rotational modes. Here we demonstrate preparation and coherent control of rotational states in a two-ion ring. First, an in-plane quadrupole is used to accelerate the ions to a rotational velocity around 100 kHz. Then, the quadrupole is reduced to 0 which releases the ions into cylindrically symmetric harmonic potential in a high angular momentum state. In such a potential, the ion crystal acts as a 2D semirigid rotor with angular momentum eigenstates labeled by l. Finally, optical addressing of resolved rotational sidebands allows us to coherently drive population between angular momentum states l and l + dl where dl is between -4 and 4 with fidelities over 90%. Motional flop fidelities are increased by reducing the number of rotational eigenstates that are occupied. This is done through cooling the harmonic oscillator mode that eventually maps into the rotational mode before the ion crystal is spun up. Dynamically decoupled Ramsey experiments show coherence times of a few milliseconds, inversely correlated with dl.

### Approximate exchange-only entangling gates for the three-spin-1/2 decoherence-free subsystem

Jim van Meter, National Institute of Standards and Technology, Boulder

The three-spin-1/2 decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well-suited for implementation with electrically-defined quantum dots. Exact exchange-only entangling logical gates exist but are challenging to construct and understand. We use a decoupling strategy to obtain straightforward approximate entangling gates. A benefit of the strategy is that if the physical spins are aligned, then it can implement evolution under entangling Hamiltonians. Hamiltonians expressible as linear combinations of logical Pauli products not involving $\sigma_y$ can be implemented directly. Gates such as the CNOT can be implemented without the assumption on the physical spins. We compare the control complexity of implementing CNOT to previous methods and find that the complexity for fault-tolerant fidelities is competitive.

### Hamiltonian simulation in the interaction picture

Nathan Wiebe, Microsoft Research

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture, where some portions are made time-dependent. This can provide a favorable complexity trade-off as the algorithm scales exponentially better with derivatives of the time-dependent component than the original Hamiltonian. We show that this leads to an exponential improvement in gate complexity for simulating some classes of diagonally dominant Hamiltonian. Additionally we show that this can reduce the gate-complexity scaling for simulating N-site Hubbard models for time with arbitrary long-range interactions as well as reduce the cost of quantum chemistry simulations within a similar-sized plane-wave basis to O(N^2) from O(N^(11/3)). We also show a quadratic improvement in query complexity for simulating sparse time-dependent Hamiltonians, which may be of independent interest.

### Quantum walk search on Kronecker graphs

Thomas Wong, Creighton University

In network science, graphs obtained by taking the Kronecker or tensor power of the adjacency matrix of an initiator graph are used to construct complex networks. In this paper, we analytically prove sufficient conditions under which such Kronecker graphs can be searched by a continuous-time quantum walk in optimal $\Theta(\sqrt{N})$ time. First, if the initiator is regular and its adjacency matrix has a dominant principal eigenvalue, meaning its unique largest eigenvalue asymptotically dominates the other eigenvalues in magnitude, then the Kronecker graphs generated by this initiator can be quantum searched with probability $1$ in $\pi\sqrt{N}/2$ time, asymptotically, and we give the critical jumping rate of the walk that enables this. Second, for any fixed initiator that is regular, non-bipartite, and connected, the Kronecker graphs generated by it are quantum searched in $\Theta(\sqrt{N})$ time. This greatly extends the number of Kronecker graphs on which quantum walks are known to optimally search. If the fixed, regular, connected initiator is bipartite, however, then search on its Kronecker powers is not optimal, but is still better than classical computer's $O(N)$ runtime if the initiator has more than two vertices.

### Experimental saturation of the quantum Cramer-Rao bound for transmission measurements

Tim Woodworth, University of Oklahoma

The minimum possible uncertainty when estimating a parameter, in this case transmission, through measurements with a given state is bounded by the quantum Cram\'er-Rao bound (QCRB). This bound is independent of the measurement technique and as result can be used to quantify how close a measurement is to the optimal one for a given system, as an optimal measurement will saturate the QCRB. In particular, the ability to perform measurements of the transmission through an optical element at the QCRB can lead to enhancements in the calibration of optimal states for interferometers, the characterization of high efficiency photodetectors, or the sensitivity of sensing devices based on transmission, such as plasmonic sensors or ellipsometry. Here, we shown experimentally that the two-mode squeezed state (TMSS) QCRB for transmission can be saturated using unbalanced intensity difference measurements and that the classical coherent state QCRB can be saturated with single beam intensity measurements. We also show theoretically that as the level of intensity difference squeezing increases the QCRB for transmission for a TMSS approaches the one for a Fock state, which has been shown to be an optimal state for transmission measurements.

### A cryogenic environment for microfabricated surface ion traps

Christopher G. Yale, Sandia National Laboratories

Trapped ions are a promising system to realize quantum information processing due to their indistinguishability and high degree of interconnectivity. Microfabricated surface electrode traps offer a route to scalability, but the fidelity of gate operations is limited by anomalous heating rates. Also, ion chain lifetimes in room temperature chambers are hampered by background collisions. Here, we investigate the performance of Sandia’s High-Optical-Access surface electrode trap in a cryogenic environment. We present the design of the cryogenic chamber with an internal toroidal circuit board RF resonator [1] to create the trapping potential. In addition, we demonstrate ablation loading of ions [2] to avoid thermal shifts created by a thermal loading oven. Finally, we measure preliminary heating rates and background gas collision rates by observing jumps in a double well potential. SNL is managed and operated by NTESS, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy’s (DOE) National Nuclear Security Administration under contract DE-NA0003525. This research was funded by the Intelligence Advanced Research Projects Activity (IARPA) and by the DOE Office of Advanced Scientific Computing Research Quantum Testbed Program. The views expressed here do not necessarily represent the views of the DOE, IARPA, or the U.S. Government. 1. M. F. Brandl, et al., Appl. Phys. B. 122, 157 (2016) 2. R. J. Hendricks, et al., Appl. Phys. B. 88, 507 (2007)

### Optomechanical cooling with time dependent parameters

Pablo Enrique Yanes Thomas, Universidad Nacional Autónoma de México

The usual master equation employed in optomechanical cooling does not account for the cavity's frequency not being constant. We formulate an optomechanical master equation with a dissipation model than incorporates the time dependent frequency of the cavity modes.

### Conclusive precision bounds for SU(1,1) interferometers

Chenglong You, Louisiana State University

We revisit the quantum Fisher information (QFI) calculation in SU(1,1) interferometer considering different phase configurations. Firstly, when one of the input modes is a vacuum state, we show by using phase averaging, different phase configurations give same QFI. In this case, the QFI is linearly proportional to the average photon number of the second input state, and quadratically proportional to the average photon number generated by the OPA. This suggests that when fixing the squeezing strength of the OPA, to achieve higher sensitivity, one simply needs to inject a state with higher average photon number. Secondly, we compared the results of the phase-averaging method and the quantum Fisher information matrix method, and then we argued that for a SU(1,1) interferometer, phase averaging or quantum Fisher information matrix method is generally required, and they are essentially equivalent. Finally, we used the quantum Fisher information matrix method to calculate the precision limit for other common input states, such as two coherent state inputs or coherent state with squeezed vacuum inputs.

### Drift of quantum gates

Kevin Young, Sandia National Laboratories

The performance of a quantum computer depends critically on a large number of highly-tuned parameters. Time dependence (drift) in these parameters is generally unheralded, but can have a pernicious and possibly devastating impact on quantum gate fidelities. Identifying the source of this drift is a critical first step on the path to mitigating it, but techniques to do so have been cumbersome at best. In this talk, we discuss a suite of quantum circuit experiments and data analysis tools that is capable of identifying and characterizing Fourier-sparse drift in quantum gates, measurements, and state preparation operations. By incorporating a model of the experiment that is aware of the controllable parameters, these tools can often help to establish the precise source of any unwanted time dependence. We illustrate our work with data from both simulation and experiment. Sandia National Labs is managed and operated by NTESS, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy’s NNSA under contract DE-NA0003525. This research was funded in part by IARPA. The views expressed herein do not necessarily represent the views of the DOE, IARPA, the ODNI, or the U.S. Government.

### Demonstration of channel-optimized quantum error correction on cloud-based quantum computers

Haimeng Zhang, University of Southern California

With the introduction of several cloud-based quantum computers, for example, from IBM and Rigetti, there is a growing interest in experimenting with quantum algorithms and protocols on such platforms. We are specifically interested in testing quantum error correction protocols since noise is an important factor that limits their performance. We demonstrate the channel-optimized quantum error correction protocol [R.L. Kosut, A. Shabani, and D.A. Lidar, PRL 100, 020502 (2008)] on the IBM and Rigetti machines. Our goal is to protect quantum states from noise. The noise on the IBM machine is characterized by standard process tomography. The optimal encoding and recovery map are found numerically by solving a bi-convex optimization problem which maximizes the average channel fidelity. We implement the optimal encoding and recovery maps by decomposing them into directly implementable gate operations. This error correction protocol does not require post-selection and is designed specifically for the physically relevant noise to the platform.

### Efficient sympathetic cooling in mixed barium and ytterbium ion chains

Liudmila Zhukas, University of Washington

138Ba+ (barium) and 171Yb+ (ytterbium) ions are excellent qubit candidates due to unique properties of these species. In one proposal of using mixed species linear chains, ytterbium is used as the main computational qubit species whereas barium undergoes cooling; mechanical coupling of barium and ytterbium thus provides sympathetic cooling of the latter. However, even the relatively small 25% mass difference between barium and ytterbium can reduce the vibrational modes coupling that affects cooling of the ytterbium ions. Here we Doppler cool barium ions in mixed barium-ytterbium chains confined in a linear RF trap and measure the motional average occupation quantum numbers of all radial normal modes. The full set of orderings in a chain of two barium and two ytterbium ions have been probed, and we show that the motional average occupation quantum numbers of all chain configurations strongly depends on the trap aspect ratio. We demonstrate efficient sympathetic cooling of all radial normal modes for the trap aspect ratio of 2.9.