# 2017 Poster Abstracts

## 1. Towards quantum information transport through a classical conductor

Da An, University of California, Berkeley

Establishing quantum links between separately trapped ions is a significant step towards scalable trapped ion quantum computation. Here, we present our design, simulation, and ongoing implementation of a novel surface ion trap for studying quantum correlations between separate trapping sights through an ordinary conducting wire. This is a challenging task since the thermal noise in the wire is much greater than the motional ion energy, but as long as the decoherence sources are minimized, we can achieve quantum coupling through the wire. We also include intermediate steps towards this goal, such as characterizing the stability of our novel trap, which has variable trapping height, and establishing a classical link through the wire. This technology may lead to quantum computation with mixed ion species, sympathetic cooling of ion species that cannot be co-trapped, and hybrid quantum devices that couple ion based qubits with superconducting qubits.

## 2. Quantum simulation and sensitive force detection using hundreds of ions in a Penning trap

Justin Bohnet, National Institute of Standards and Technology

Systems of trapped ions have made substantial progress as simulators of quantum magnetic models. But increasing a simulator’s complexity by controlling more than 30 ions is an outstanding challenge. Here we perform quantum simulations of long range Ising spin models far from equilibrium using hundreds of beryillium ions in a Penning trap. We benchmark the fidelity of the quantum simulator by producing entangled states in planar arrays of ions, directly observing spin- squeezed states with up to 6.0 dB of spectroscopic enhancement. We show how the ability to time-reverse the spin dynamics allows for tracking the spread of quantum information through the system by measuring out-of-time-order correlation functions. To study the stability of the center-of-mass mode of the ions, one of the limitations to our simulations, we use the spin-motion coupling of the ions to sense small electric fields, which we present in terms of detection of sub-yoctoNewton forces. In the future, we will apply these techniques to simulations of non-trivial spin models, such as the XY model and the transverse field Ising model with variable range interactions.

## 3. Practical quantum simulators for quantum field theory

Gavin Brennen, Macquarie University

An exciting prospect for quantum simulators is to probe physics that is difficult to compute using analytical methods or classical numerical simulations. An especially compelling direction is to simulate quantum field theory. I will discuss two new approaches in this regard. The first is an analogue quantum simulation of 2+1 dimensional U(1) lattice gauge theory using superconducting fluxonium arrays which allows for non destructive measurements of non local order parameters including space like Wilson loops and 'tHooft strings. The second is a digital quantum simulation of the holographic principle for a critical 1+1 dimensional conformal field theory. The method uses an encoding based on Daubechies wavelets and can be realized as a multimode entangled Gaussian state of continuous variable systems using e.g. trapped ions or frequency modes in photonic networks. Extensions to interacting field theory are described.

## 4. Randomized benchmarking with restricted gate sets

Winton Brown, Northrop Grumman Corporation

Standard randomized benchmarking protocols require sampling from a unitary 2-design, which is not always practical. In this talk I examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2-designs. I show in a variety of cases that one can benchmark the error probability to within a small factor that rapidly approaches unity as the number of qubits in the benchmarking experiment grows.

## 5. Resonant transition based quantum computation

Chen-Fu Chiang, State University of New York Polytechnic Institute

In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians' spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.

## 6. Toward a quasi-probability representation of matchgate circuits

Ninnat Dangniam, Center for Quantum Information and Control (CQuIC), University of New Mexico

Quantum circuits composed of a particular class of gates called matchgates range from circuits that are classically simulatable to those that can perform universal quantum computation. Matchgate computation can also be understood from a more physical point of view as a computation with fermionic modes. We attempt to construct a quasi-probability (phase space) representation of quantum theory in which classically simulatable matchgate circuits are represented positively i.e. non-contextually.

## 7. Approximate reversal of quantum Gaussian dynamics

Siddhartha Das, Louisiana State University

Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to the work of Petz, who showed that the quantum relative entropy between two states stays the same after the action of a quantum channel if and only if there is a {\it reversal channel} that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the "Petz recovery map". Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state and a bosonic Gaussian channel is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of a given Gaussian state and the Gaussian specification of a given Gaussian channel.

## 8. Experimental study of an optimized Kennedy receiver for multiple coherent states

Matthew DiMario, Center for Quantum Information and Control (CQuIC), University of New Mexico

Non-Gaussian receivers for coherent states that have discrimination errors below the Quantum Noise Limit (QNL) are a valuable tool in communication. Discrimination of coherent states is fundamentally impossible to do with zero probability of error because of their intrinsic overlap. Therefore, the goal is to design and demonstrate discrimination strategies that minimize the error probability and outperform the perfect Heterodyne (QNL) measurements. We implement a strategy proposed by Sasaki et al. (PRA 86, 042328 (2012)) that is based on testing multiple hypotheses at once within a single-shot measurement to discriminate between quaternary phase-shift-keyed (QPSK) coherent states. The receiver is based on three displacement operations and single photon counting and in principle achieves errors below the QNL without the need for any feedback operations. The three displacement amplitudes are independently optimized to yield the absolute minimum overall probability of error given experimental imperfections. Our results align well with the theoretical predictions and allow us to identify how the critical parameters, such as visibility of the displacement operations and detection efficiency, influence the error probability. We are also able to identify what is required of these parameters for the strategy to out-perform a Heterodyne (QNL) measurement.

## 9. Practical, reliable error bars in quantum tomography

Philippe Faist, Institute for Quantum Information and Matter, Caltech, Pasadena CA 91125, USA

Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments lack a well-justified error analysis, especially in the regime of finite data. For example, maximum likelihood estimation does not provide any estimation of the error of the tomography procedure, and is typically complemented by an ad hoc method such as resampling/bootstrapping. We propose a new method which provides well-justified error bars. The error bars are practical, in that the error bars are typically of the same order of magnitude as those obtained by a resampling analysis. The error bars are determined for a figure of merit (such as the fidelity to a target state) which can be chosen freely. Our method takes as input the measurement data from the experiment, and runs an analysis based on the concept of confidence regions. We then introduce a new representation of the output of the tomography procedure, the quantum error bars. This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the "spread" of the error, and (iii) useful, containing the necessary information for constructing confidence regions. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.

## 10. The statistical framework for "Chained Bell Inequality Experiment with High-Efficiency Measurements"

Scott Glancy, National Institute of Standards and Technology

We recently performed correlation measurements on two 9Be+ ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution and a distribution that violates the inequality. This poster describes the statistical framework used to quantify the maximum local-realistic fraction in the observed distribution without assuming fair-sampling of the measurements or that the distribution was independent and identical across trials. This framework excludes models of our experiment whose local-realistic fraction is above 0.327 at the 95 % confidence level. Supported by IARPA, ONR, and the NIST Quantum Information program

## 11. Semiclassical and quantum control of chaos

Sacha Greenfield, Carleton College

Chaotic systems contain infinitely many unstable periodic trajectories that only appear for very particular initial conditions. Given a system starting at arbitrary initial conditions, we can “control” the system onto one of these trajectories by small, properly timed perturbations in system parameters. While previously only classical chaotic systems have been controlled, we aim to control chaos in a regime where the system is also quantum mechanical. We have controlled chaos in computer simulations of the classical and semiclassical damped driven double-well Duffing oscillators, and are currently implementing control using noisy semiclassical versions and stochastic Schrodinger equation trajectories of the same system.

## 12. Rank deficiency and the Euclidean geometry of quantum states

Jonathan A Gross, Center for Quantum Information and Control (CQuIC), University of New Mexico

Quantum state tomography requires characterizing a collection of parameters whose size grows rapidly with the size of the quantum system under consideration. In practice one hopes that prior information about the system can reduce the number of parameters in need of characterization—for example, one might expect to find high-quality quantum systems in states of low rank. Interest in tomographic schemes that return rank-deficient estimates leads us to explore some geometric properties of the space of quantum states that are analogous to solid angles in three-dimensional Euclidean geometry.

## 13. Optical CNOT gate from two level system

Dawit Hailu, Ben Gurion University of the Negev

The solution of a two level system driven by a Laser in the adiabatic limit is determined using third order Magnus expansion. We made the assumption that the laser is on resonance or close to resonance with the Bohr transition. As a consequence of which we are able to obtain a Hamiltonian which commute with itself at different times. We solve the problem using the Sylvester Formula where we make use of the eigenvalues. We propose that the dynamics mimics the behaviour of CNOT gate. To achieve this we make use of the observables (Population and coherences) as input/output of the gate.

## 14. Realizable quantum spatial search

Itay Hen, University of Southern California

Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its implementability however has been questioned by many due to its oracular nature. In this talk, I propose a mechanism to carry out a quantum adiabatic variant of Grover's search algorithm using a single boson placed in an optical lattice.

## 15. Benchmarking a qutrit

Ian Hincks, Institute for Quantum Computing, Waterloo, Canada

Randomized Benchmarking and related twirling-based protocols have become mainstays in assessing the quality of quantum logic gates. These protocols physically implement symmetrization by unitary groups in such a way as to exponentially reduce the number of parameters describing a gate or gateset down to just a few, including average fidelity or unitarity. In this talk, we provide a holistic account of performing randomized benchmarking on an Nitrogen Vacancy defect in diamond. This quantum system has three controllable energy levels, and several physical characteristics which make it ideal for experimentally studying quantum control and inference. We discuss methodologies of cosine-modulated gate design with numerical optimal control, characterizing Hamiltonian parameters with Bayesian inference, and driving microwave transitions in the non-linear regime of an amplifier. We find a 72-element Clifford subgroup, which is the smallest 2-design sufficient for the randomized benchmarking and unitarity protocols. We show the results of these experiments, emphasizing that rigorous statistical analysis improves the credibility of parameter estimates.

## 16. Thresholds for universal concatenated quantum codes

Tomas Jochym-O'Connor, California Institute of Technology

Quantum computing algorithms will require fault-tolerance in order to suppress errors to sufficiently small levels for growing algorithmic complexity. Possible fault-tolerant implementations are far-ranging, all requiring qubit and computational resource overheads. Moreover, the level of precision required to implement a computation fault-tolerantly can differ greatly depending on the type of implementation used. In practice, the choice of fault-tolerant architecture will likely depend on the physical qubit architecture and the particular algorithm that is desired to be implemented, and as such it is of particular importance to understand the parameters at which fault-tolerant computation becomes possible for different proposals. The surface code is the leading contender for a fault-tolerant architecture due to the low weight of its stabilizer generators as well as its high fault-tolerance threshold rate, the physical error rate below which errors can be suppressed in an exponential manner. However, in order to complete a universal gate set for quantum computation, the surface code requires the preparation of a special ancillary state, a magic state. As such, to prepare a magic state with high fidelity, a process called magic state distillation is used, leading to high offline qubit overhead. In order to circumvent the need for magic state distillation, recent research efforts in quantum error correction have focused on finding alternative methods to implementing universal fault-tolerant gate sets. The first step towards determining whether these alternative methods will provide potential improvements over the surface code is to consider their fault-tolerance threshold. In this work, we present an upper bound on the asymptotic threshold for a concatenated scheme for universal fault-tolerant computation without magic state distillation. We show that the upper bound on the asymptotic threshold of \(1.28~\times~10^{-3}\) is competitive with other concatenated schemes, such as the Golay code.

## 17. Dissipative quasi-local stabilization of generic pure quantum states

Salini Karuvade, Dartmouth College

Dissipative control techniques with physically realizable resource constraints are attracting increasing attention across quantum information processing. A pure quantum state is called "dissipatively quasi-locally stabilizable" (DQLS) if it can be prepared by using purely dissipative continuous-time or discrete-time dynamics with respect to a fixed locality constraint. We characterize the DQLS nature of generic quantum states in finite dimensions for some simple yet important locality constraints, and provide conditions that must be satisifed if the states are DQLS, in more general cases. Our results shed light on approximate stabilization techniques for target pure states that are otherwise non-DQLS. Further, we describe how a state being DQLS ensures that the state is uniquely determined by its corresponding reduced states, illustrating a connection between the tasks of state preparation and local tomography. In the process, we give a constructive procedure for uniquely reconstructing a generic global state from its reduced neighborhood states, leveraging its stabilizability properties.

## 18. Conditional mutual information and quantum steering

Eneet Kaur, Louisiana State University

Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. We propose the intrinsic steerability as an information-theoretic quantifier of steering that uses conditional mutual information to measure the deviation of a given assemblage from an assemblage having a local hidden-state model. We prove that this quantifier is a steering monotone (i.e., it is faithful, convex, and non-increasing under one-way local operations and classical communication). This suggests that the intrinsic steerability should find applications in protocols where steering is relevant. We then consider a restricted version of intrinsic steerability, which is a steering monotone under a restricted set of free operations. The restricted intrinsic steerability is additive with respect to tensor-product assemblages, and it is also monogamous.

## 19. Symmetric Extendability of Quantum States and the Extreme Limits of Quantum Key Distribution

Sumeet Khatri, Louisiana State University

We investigate QKD protocols with two-way communication that are based on the quantum phase of the well-known BB84 and six-state protocols. The quantum phase consists of the source sending quantum signals to the receiver, who measures them, leaving only classical data on both sides. Our goal is to find the highest value of the quantum bit error rate $Q$ for which two-way classical post-processing protocols on the data can create secret keys. Using the BB84 quantum phase, such protocols currently exist for $Q\leq\frac{1}{5}$. On the other hand, for $Q\geq\frac{1}{4}$ no such protocol can exist as the observed data is compatible with an intercept-resend channel. This leaves the interesting question of whether successful protocols exist in the gap $\frac{1}{5}\leq Q\leq\frac{1}{4}$. For the six-state protocol, the corresponding gap is known to be $\frac{5-\sqrt{5}}{10}\leq Q\leq\frac{1}{3}$. The current lower bounds have previously been shown to come from the symmetric extendability of the underlying quantum state shared between Alice and Bob after a two-way protocol called advantage distillation. Our work looks more generally at two-way post-processing protocols within the gap and asks the question of symmetric extendability of the states after them, for if they are symmetrically extendable then no secret key is possible. We have analytically constructed a symmetric extension throughout the gap for a particular class of protocols using a two-step procedure. Numerical analysis shows that for other arbitrary protocols the states are also symmetrically extendable throughout the gap. Moreover, for a very large percentage of protocols tested, our two-step construction works. We thus have very strong evidence to believe that there does not exist a two-way classical post-processing protocol to create a secret key beyond the current bounds, so that there is a point beyond which classical correlations of quantum origin are no longer useful in creating a secret key.

## 20. Quantum circuits synthesis using lattices over number fields

Vadym Kliuchnikov, Microsoft Research

We present new algorithms for multiple qubit exact synthesis and exact state preparation. The algorithms work for the unitaries related to Clifford+T, Real Clifford+Controlled-H, and other similar gate sets. The algorithms run-time is polynomial in the bit-size of the input when the number of qubits is fixed. We prove the correctness of the algorithms for two qubits. For three and more qubits our algorithms either solve the problem in polynomial time or report that the solution was not found. We conjecture that the second outcome never happens based on empirical results. Experiments show that our algorithms produce circuits with a smaller number of T-gates than the algorithms for state preparation and exact synthesis by Giles and Selinger [10.1103/PhysRevA.87.032332].

## 21. Q-plates for entangling photon spin and orbital angular momentum

Hannah Knaack, Harvey Mudd College

Photon polarization is a popular qubit variable, partially because it is so accessible, while orbital angular momentum is more difficult to manipulate and measure. However, the dimensionality of orbital angular momentum as a qudit is limited only by our technical ability to create and manipulate it. Q-plates shift orbital angular momentum in photons based on their incoming polarization, enabling the creation of entangled qubit-qudit systems on a single particle. A q-plate consists of a liquid crystal half-wave plates with a spatially varying axis. The “q” of the plate is defined by the number of complete revolutions the axis makes around the plate, and determines the magnitude of the angular momentum imparted. We are working to fabricate q-plates for use in quantum communications applications. We plan to create entanglement between the spin and orbital angular momentum degrees of freedom of a single photon, then to create multipartite entanglement on a photon pair produced by spontaneous parametric down-conversion.

## 22. Joint measurement on the reflecting hyperplane in generalized probability theories

Masatomo Kobayashi, Kyoto University

The existence of a pair of observables which is not jointly measurable is one of the most crucial aspects in quantum theory. The problem to find the necessary and sufficient conditions for effects to be coexistent is hard and has been only partially solved. It is, however, known that this peculiar property is not specific to the quantum theory in the general framework called Generalized Probability Theories. They have been studied from various points of view such as Bell's inequality, teleportaion, broadcasting and so on. In these articles, some authors indicated that the regular polygon systems are grouped into two series by the number of the vertexes, i.e. even or odd. We study the even-sided ones and show that the corresponding effect spaces have a nice symmetrical hyperplane which contains all (nontrivial) extremal effects and divides the whole effect space into reflection symmetric two subsets. We call it "reflecting hyperplane". Analyzing the coexistence problem in the polygon systems, we give necessary and sufficient conditions for a pair of effects on the hyperplane to be coexistent. Furthermore, we examine general systems (other than regular polygons) which have the reflecting hyperplane and show that the volume of the set of all effects coexistent with a nontrivial extreme effect is vanishing.

## 23. Distinguishability of qubit and qutrit Bell states with projective and non-projective linear measurement

Nathaniel Leslie, Harvey Mudd College

We present new maximal distinguishability limits for qudit Bell states with projective and non-projective linear evolution and local measurement (LELM) devices. A well-known no-go theorem establishes that projective LELM detection schemes cannot reliably distinguish all four qubit Bell states; they can only reliably distinguish three. We show that only 3 out of 9 qutrit Bell states can be distinguished with projective LELM measurements. We also consider the case of non-projective measurements, and show that even general POVM-based LELM measurements cannot reliably distinguish all four qubit Bell states. We also establish that no more than 2d qudit Bell states may be distinguishable with general LELM measurements and in the qutrit case, at most 5 may be distinguishable.

## 24. Boson sampling of many-body quantum random walkers on a lattice

Gopikrishnan Muraleedharan, Center for Quantum Information and Control (CQuIC), University of New Mexico

The Boson sampling problem introduced by Aaronson and Arkhipov showed quantum supremacy in terms of sampling complexity for the output distribution of photons scattering from a linear optical network. We study here an analogous problem in the case of multiple boson continuous-time quantum random walkers on a lattice, e.g., Bosonic atoms in an optical lattice. Results are presented for the special case of a 1D lattice with nearest neighbor and uniform hopping amplitude. We show that the permanent of the unitary time evolution operator can be approximated in \( O \left({{2T}\choose{T}}^3 \log N \right)\) time, using an algorithm developed by M. Shwartz [1]. Thus the sampling problem is easy as long as the time of evolution (T) is constant or at least logarithmic in N. When the time of evolution passes the logarithmic scale, the algorithm takes exponential time. It is not clear if the sampling problem is hard in this regime. Periodic and hard wall boundary conditions lead to the same result when number of lattice sites are substantially larger than the number of particles. When extended to arbitrary hopping amplitudes and on-site interactions, this corresponds to sampling complexity for a general Bose-Hubbard model. 1: Moshe Schwartz, "Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices" , Linear Algebra and its Applications, Volume 430, Issue 4, 2009, Pages 1364-1374, ISSN 0024-3795, http://dx.doi.org/10.1016/j.laa.2008.10.029.

## 25. Subradiance in the emission of atoms coupled to an optical nanofiber

Austin Nar, Miami University

We investigate subradiance in the emission into an optical nanofiber of ultracold atoms trapped in a MOT surrounding the nanofiber. The atoms are coherently excited on resonance by a laser propagating orthogonally to the nanofiber. We present a classical random phase model which predicts subradiance and we also describe progress toward a quantum model which combines free space collective emission as described in Lehmberg, et. al [PRA 2 883] with the coupling to the nanofiber modes described by Le Kien, et. al [PRA 72 063815].

## 26. Quantum algorithms for Gibbs sampling and hitting-time estimation

Anirban Narayan Chowdhury, Center for Quantum Information and Control

We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time that is polylogarithmic in the precision parameter, exponentially improving the precision dependence over known quantum algorithms. It also polynomially improves dependence on parameters such as system size and inverse temperature. The second algorithm estimates the hitting time of a classical Markov chain. For a sparse stochastic matrix, it provides quadratic improvement in complexity over a natural classical algorithm to estimate the hitting time. Both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

## 27. Multipartite entanglement in stabilizer tensor networks

Sepehr Nezami, Stanford University

Tensor network models reproduce important structural features of holography, including the Ryu-Takayanagi formula for the entanglement entropy and quantum error correction in the entanglement wedge. In contrast, only little is known about their multipartite entanglement structure, which has been of considerable recent interest. In this work, we study random stabilizer tensor networks and show that here the tripartite entanglement question has a sharp answer: The average number of GHZ triples that can be extracted from a stabilizer tensor network is small, implying that the entanglement is predominantly bipartite. As a consequence, we obtain a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks and a novel formula for the third moment of random stabilizer states.

## 28. Higher moments of stabilizer states

Sepehr Nezami, Stanford University

Stabilizer states are a fundamental tool in quantum information theory. In the past years, there has been renewed interest in their statistical properties, motivated by a number of important applications. Celebrated results include a characterization of their third and fourth moments in the multiqubit case (e.g.,Zhu/Webb/Kueng&Gross, QIP 2016). In this work, we present a simple explicit expression for all higher moments of stabilizer states in odd prime power dimensions. Previously, it was only known that they form a 2-design but not a 3-design (i.e. that their second but not their third moments agree with the Haar measure). In contrast, and significantly for applications, our formula allows the computation of a t-th moment even when the stabilizer states fail to be a t-design. Our key technical result is a version of Schur-Weyl duality for the Clifford group. Whereas the commutant of the tensor power action of the unitary group is spanned by the permutation action, we show that for the Clifford group the commutant has a natural description in terms of discrete symplectic phase space, unraveling a new and surprising algebraic structure. We sketch possible applications of our result to quantum information theory and signal recovery.

## 29. Heuristics for machine learning in quantum compression

Jonathan Olson, Harvard University

Machine learning (ML) is a powerful technique for discovering and classifying features in large data sets. However, the somewhat ad-hoc nature of ML algorithms cultivates a heavy dependence on the heuristics of these methods. In this talk, we discuss and introduce new general heuristics for quantum machine learning in the context of data compression.

## 30. Band-limited quantum optimal control

Adrian Orozco, Center for Quantum Information and Control (CQuIC), University of New Mexico

Control of quantum systems is important for the development of quantum technology. Many researchers have explored a variety of functional analytic methods for synthesizing optimal control waveforms that evolve a quantum system from an initial state to a final target state. In particular, the GRadient Ascent Pulse Engineering (GRAPE) method has proven to be a powerful platform for synthesizing these controls. However, in the standard GRAPE algorithm controls are designed in the time domain and there is no direct way of limiting its bandwidth, which is important in practical applications. In addition, for higher dimensional Hilbert spaces GRAPE requires more time steps to completely specify the system’s state. As the total coherence time is limited, the bandwidth will increase when augmenting the number of time steps. These concerns are greatly important when implementing these designed controls in the laboratory. We circumvent these problems by expanding the control via a truncated Fourier series constraining the bandwidth through its Fourier coefficients. A gradient ascent method is used to numerically optimize the Fourier coefficients of a piecewise constant control that lead to the desired evolution of our quantum state. A weakly dressed symmetric Rydberg ensemble model is used to investigate the effect of expanding the control in this way [1]. We find that the control waveform can be designed to have two important characteristics for practical applications; a band-limited power spectrum and constrained control amplitudes during the entire evolution. Furthermore, we find that the total number of time steps (total evolution time) can be restricted for a particular range of Hilbert space dimensions without imparting additional constraints to experimental apparatus. 1. T. Keating, C. H. Baldwin, Y.-Y. Jau, J. Lee, G. W. Biedermann, and I. H. Deutsch, Phys. Rev. Lett. 117, 213601 (2016).

## 31. Quantum algorithm for linear differential equations with exponentially improved dependence on precision

Aaron Ostrander, QuICS, University of Maryland

Recently quantum algorithms for Hamiltonian simulation have been proposed which have complexity logarithmic in the inverse error. Hamiltonian simulation is just a special case of simulating the ordinary differential equation dx/dt=Ax+b where A is anti-Hermitian and b=0. For more general A, the complexity of such a simulation is less well understood. Berry proposed a quantum algorithm for ODEs using linear multistep methods that is polynomial in the inverse error. This algorithm encoded the simulation problem in a linear system and used a quantum linear systems algorithm (QLSA) to solve the system. Recently, QLSAs which scale logarithmically in the inverse error have been proposed. However, this exponential improvement in solving linear systems does not necessarily translate to an exponential improvement for algorithms that use the QLSA as a subroutine. In fact, Berry’s algorithm has polynomial scaling regardless of which QLSA is used. This is because there are other error-dependent parameters in the algorithm that contribute to the complexity. In this work, we revisit the problem of solving linear differential equations and propose a new QLSA-based algorithm that scales logarithmically in the inverse error. Our approach is based on evolving according to the propagator exp(At) by approximating it using a Taylor series.

## 32. Optimal control for quantum metrology with time-dependent Hamiltonians

Shengshi Pang, University of Rochester

Due to its importance in many areas of physics, quantum metrology has attracted a growing attention in recent years. Most of the current researches on quantum metrology were focused on systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, little has been known due to the complexity of dynamics. In this work, we study quantum metrology with general time-dependent Hamiltonians to bridge this gap. We obtain the maximum quantum Fisher information for general parameters in time-dependent Hamiltonians, and find that proper Hamiltonian control on the system is necessary to reach the maximum Fisher information. We derive the optimal Hamiltonian control in general, and show that it is generally an adaptive and feedback-based control. With a minimal example of a qubit in a rotating magnetic field, we surprisingly find that the time scaling of quantum Fisher information reaches T^4 in estimating the rotation frequency of the field, which significantly breaks the traditional limit of T^2 time scaling for quantum Fisher information with time-independent Hamiltonians. This suggests a dramatic difference between quantum metrology with time-dependent Hamiltonians and time-independent Hamiltonians, and also shows the advantage of quantum control in enhancing quantum metrology. We conclude by considering the effect of level crossings in the derivative of the Hamiltonian with respect to the parameter of interest, and point out that additional control on the Hamiltonian is necessary for that case.

## 33. Open quantum systems with arbitrary initial conditions

Gerardo Paz-Silva, Griffith University (Australia)

The theory of Open Quantum Systems is concerned with the prediction and control of the dynamics of a quantum system in the presence of interactions with external degrees of freedom. This is a highly non-trivial problem, and in its study two assumptions are usually made: (A1) the state of system and bath is factorizable at time t=0, and (A2) certain knowledge of the bath, e.g., of the bath correlations, is assumed despite (by definition) not being fully accessible. Seeking to replace the assumption character of (A2) by measurable information, recent years have seen the emergence of the so-called Quantum Noise Spectroscopy protocols. These, provided (A1) holds, use the measurable response of a quantum system to its bath and different control scenarios, in order to extract information regarding the bath correlations (with respect to the reduced density matrix of the bath). In this talk, by introducing a new universal density matrix decomposition we show how (A1) can be naturally removed from current calculations methods, such as master equations, and, additionally, how the notion of Quantum Noise Spectroscopy can be extended to the case where system and bath are initially correlated. Thus, we show how (A1) and (A2) can in principle be simultaneously discarded from the set of assumptions made in the theory of Open Quantum Systems. We further discuss consequences and applications of our decomposition method to quantum steering and to the understanding of quantum channels.

## 34. Performance of quantum annealers on hard scheduling problems

Bibek Pokharel, University of New Mexico

Quantum annealers have been employed to attack a variety of optimization problems. We compared the performance of the current D-Wave 2X quantum annealer to that of the previous generation D-Wave Two quantum annealer on scheduling-type planning problems. Further, we compared the effect of different anneal times, embeddings of the logical problem, and different settings of the ferromagnetic coupling across the logical vertex-model on the performance of the D-Wave 2X quantum annealer. Our results show that at the best settings, the scaling of expected anneal time to solution for D-WAVE 2X is better than that of the DWave Two, but still inferior to that of state of the art classical solvers on these problems. We discuss the implication of our results for the design and programming of future quantum annealers.

## 35. Random quantum circuits with varying topologies and gate sets

Anthony Polloreno, Rigetti Quantum Computing

We build on recent results using sampling from the output of random unitary matrices as a metric for quantum supremacy. We first investigate the relationship between the choice of gate set and the circuit depth required to converge to the Porter-Thomas distribution. In particular, we note that convergence is possible using iSWAP gates in place of CZ gates. Next we explore the effects of varying qubit connectivity on the convergence behavior of random circuits. We address the feasibility of these schemes with near-term superconducting qubit hardware.

## 36. Pump-probe spectroscopy in near-resonance optical lattices

Anthony Rapp, Miami University

We observe vibrational and Brillouin resonances in the transmission spectrum of a weak light beam probing a near-resonance optical lattice. We discuss future measurements on novel Brownian ratchets in our lab.

## 37. Investigations of quantum heuristics for optimization

Eleanor Rieffel, NASA Ames Research Center

We explore the design of quantum heuristics for optimization, focusing on the quantum approximate optimization algorithm, a metaheuristic developed by Farhi, Goldstone, and Gutmann. We develop specific instantiations of the of quantum approximate optimization algorithm for a variety of challenging combinatorial optimization problems. Through theoretical analyses and numeric investigations of select problems, we provide insight into parameter setting and Hamiltonian design for quantum approximate optimization algorithms and related quantum heuristics, and into their implementation on hardware realizable in the near term.

## 38. Practical transmission matrix of a multimode fiber

Nate Ristoff, Center for Quantum Information and Control (CQuIC), University of New Mexico

Transmission of information through multimode fibers can provide a path to achieving higher capacity than what is currently possible with single mode fibers. However, cross talk between different spatial modes makes information transmission challenging. Therefore a method to reverse intermodal cross talk is required to ensure information transmission with high fidelity. States of light with spatial structure in Laguerre Gaussian (LG) modes are an ideal basis to investigate experimentally the communication capacity of such multimode fibers due to the orthogonality between modes and the infinite size of the basis. The mode structure of LG beams have radial and orbital angular momentum (OAM) degrees of freedom and thus both must be included in a modal decomposition. We investigate a protocol previously used to characterize the output of a few mode fiber and extend it to the study the transmission of light through a fiber with many modes (highly multi-mode fiber) with the goal of increasing information transmission. This protocol allows for a fast determination of the transmission matrix of a multi-mode fiber with a modest number of measurements. In addition, this method does not require a second beam to act as a local oscillator to retrieve inter-modal phase information. This protocol could in principle allow for implementing real time tracking of the transmission matrix of the fiber so that a disturbance in the fiber can be detected and corrected to avoid loss of information.

## 39. Entanglement from topology in Chern-Simons theory

Grant Salton, Stanford University

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary 3-manifolds with a fixed number of torus boundaries in both abelian U(1) and non-abelian SO(3) Chern-Simons theory. For the abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the nonabelian theory, we find a notion of "state universality", namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multi-boundary wormholes in AdS/CFT.

## 40. Scalable macromodeling for superconducting circuits

Michael Scheer, Rigetti Quantum Computing

Modeling and simulation tools enable more rapid exploration of the superconducting quantum circuit parameter space than would be possible with fabrication and measurement alone. A variety of promising modeling schemes for these circuits have been proposed but their scalability and validity for many qubit systems has not been demonstrated. We give a detailed discussion of a superconducting circuit modeling technique that allows for rapid simulation of several qubits. We compare the predictions made by this and several other models to the measured parameters of many qubits. We evaluate these models in terms of their accuracy and resource requirements and discuss their utility for designing many-qubit systems.

## 41. Determining the effective dimension of a quantum state space

Travis Scholten, Sandia National Labs

Quantum state tomography of multiple qubits or optical modes usually relies on techniques to reduce the number of parameters being fit. For example, quantum compressed sensing searches for low-rank estimates, and in optical tomography, the (formally infinite-dimensional) Hilbert space is truncated in some physically- motivated manner. Is it possible to reduce the number of parameters in some other way, using maximum likelihood estimation? Under the assumptions of local asymptotic normality, we have found two useful ways of doing so. The first uses model selection based on the loglikelihood ratio statistic, and allows one to choose the best Hilbert space dimension directly. The second uses the idea of the statistical dimension of the quantum state space to calculate its "effective" dimension. Surprisingly, both results imply that tomography of low-rank true states almost always yields estimates whose dimension is small, even when the estimator does not explicitly impose that constraint.

## 42. Quantum effects in vibrational energy harvesting

John Scott, Carleton College

Vibrational energy harvesting is a promising means of recovering energy from random external excitation by coupling these to an electrical harvesting circuit via a mechanical oscillator. We have explored a model bistable vibrational energy harvester in detail to elucidate the dynamical mechanisms which lead to the best performance, especially as it relates to higher energy orbits and chaos. Further, recent advances in nanoelectromechanical systems engineering indicate that such systems could operate at a scale where quantum mechanical effects are non-trivial. Using a semiclassical approximation to quantum state diffusion model, we explore the effects of these quantum effects and find that these can lead to a substantial increase in the efficiency with which the harvester is able to convert energy.

## 43. Flux-noise insensitive and flux-tunable superconducting qubit

Eyob Sete, Rigetti Quantum Computing

Fast high-fidelity two-qubit gates are an essential component of a universal quantum computer. Tunable qubits are promising candidates to realize such gates. However, tunability often comes at the expense of increased noise-sensitivity for a qubit, thus degrading gate performance. We propose a superconducting circuit that mitigates a dominant noise source for a class of tunable qubits. The circuit consists of a SQUID with asymmetric junctions and shunted using a superinductor. We show that flux ‘sweet spots’ can be engineered at the frequency of operation by varying the junction asymmetry and the applied magnetic flux. This device coupled with a fixed frequency qubit allows a realization of fast high-fidelity two-qubit gates.

## 44. Distribution of Bell inequality violation vs. multiparty quantum correlation measures

Kunal Sharma, Louisiana State University

Violation of a Bell inequality guarantees the existence of quantum correlations in a quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states. For a shared multipartite quantum state, we establish a connection between the monogamy of Bell inequality violation and genuine multi-site entanglement as well as monogamy-based multiparty quantum correlation measures. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family states which we refer to as the "special Greenberger-Horne-Zeilinger" states have the status of extremal states in such relations.

## 45. Measurement of correlations in a symmetric many-body quantum state via continuous measurement

Ezad Shojaee, Center for Quantum Information and Control (CQuIC), University of New Mexico

Continuous measurement on an ensemble of quantum systems in the presence of dynamical control is a fast and robust way to reconstruct the one-body reduced density matrix of a many-body quantum state [1-4]. We expand this protocol in order to reconstruct the correlations in a symmetric many-body state of multiple qubits. In this continuous weak measurement, the many-body system is probed collectively, weakly enough not to erase the initial conditions over the duration of the measurement, but strongly enough to map the information about the initial state in the measurement outcome. This can be achieved by subjecting the system to an external control which differentiate states with different initial correlations. The problem of extracting the correlation from this record is an inverse problem which is tricky in the strong back-action regime because the measurement back-action on the state disturbs it in a way which depends on the correlations. The conditions and requirements for reconstruction of correlations and the information-gain/disturbance tradeoff are the subject of the present work. [1] Andrew Silberfarb, Poul S. Jessen, and Ivan H. Deutsch, Phys. Rev. Lett. 95, 030402 (2005) [2] Greg A. Smith, Andrew Silberfarb, Ivan H. Deutsch, and Poul S. Jessen Phys. Rev. Lett. 97, 180403 (2006) [3] Carlos A Riofrío, Poul S Jessen and Ivan H Deutsch, Journal of Physics B: Atomic, Molecular and Optical Physics, 44, 15 (2011) [4] A. Smith, C. A. Riofrío, B. E. Anderson, H. Sosa-Martinez, I. H. Deutsch, and P. S. Jessen, Phys. Rev. A 87, 030102(R) (2013)

## 46. Entanglement detection on an NMR quantum-information processor using random local measurements

Amandeep Singh, Indian Institute of Science Education and Research, Mohali, Punjab, INDIA

Random local measurements have recently been proposed to construct entanglement witnesses and thereby detect the presence of bipartite entanglement. We experimentally demonstrate the efficacy of one such scheme on a two-qubit NMR quantum information processor. We show that a set of three random local measurements suffices to detect the entanglement of a general two-qubit state. We experimentally generate states with different amounts of entanglement, and show that the scheme is able to clearly witness entanglement. We perform complete quantum state tomography for each state and compute state fidelity to validate our results. Further, we extend previous results and perform a simulation using random local measurements to optimally detect bipartite entanglement in a hybrid system of 2⊗3 dimensionality.

## 47. Attainability of the quantum information bound in pure state models

Fabricio Toscano, Instituto de Fisica, Universidade Federal do Rio de Janeiro (UFRJ), Brasil

The attainability of the quantum Cramer-Rao bound, that is the fundamental limit of precision in quantum parameter estimation, involves two steps. The first step is the saturation of the classical Cramer-Rao bound (CCR) associated with the Fisher information associated with the probabilities distributions of a particular positive-operator valued measure (POVM). This saturation depends on the nature of the estimator used to process the data drawn from the set of probabilities in order to estimate the true value of the parameter. Those estimators that saturates the CCR bound are called efficient estimators or asymptotically efficient estimators when the saturation only occurs in the limit of a very large number of measured data (a typical example of this type is the maximum likelihood estimator). The second step is independent on the nature of the estimator and consists in the saturation of the so called quantum information bound (QIB), that occurs when the Fisher information of a suitable POVM coincide with quantum Fisher information associated with the final quantum state where the parameter was imprinted. Braunstein and Caves [1] have shown that the QIB can be always be achieved if the suitable quantum measurement is a von Neumann projective measurement in the eigenvectors basis of an observable called symmetric logarithmic derivative. The problem is that this measurement require the knowledge of the value of the parameter to be estimated. Mainly two approaches have been adopted in order to deal with the fact that the optimal POVM depends on the true value of the parameter. The first one relies on adaptive quantum estimation schemes that could, in principle, asymptotically achieve the QCR bound. The second one looks for the families of density operators where the parameter is imprinted, for which the use of an specific POVM that does not depend on the true value of the parameter leads to the saturation of the QIB. This is known as the search for the global optimal POVM that saturates the QIB independently of the true value of the parameter. For full-rank density operators, Nagaoka [2] showed that saturation of the quantum information bound by using a POVM that does not depend on the true value of the parameter is only possible for the so called quasi-classical family of density operators. He also presented complete characterisation of the quantum measurements that guarantee the saturation for this family. Therefore, the problem of finding the states and the corresponding optimal measurements that lead to the saturation of the QIB, independently of the true value of the parameter, in the case of one-parameter families of full-rank density operators has been already solved. However, for the opposite case of pure states (rank-one density operators), the complete characterisation of the families of states and the corresponding measurements that lead to the saturation of the QIB, independently of the true value of the parameter, is still an open question in the case of arbitrary Hilbert spaces. It is important to remark that inside the families of pure states the QFI reaches its largest values. Here, we consider quantum state families of pure density operators in which the true value of the parameter is imprinted by a unitary evolution whose generator is arbitrary but with discrete spectrum and independent of the true value of the parameter. Thus, we present the complete solution to the problem of which are all the initial states and the corresponding families of global projective measurements that allow the saturation of the QIB, within the pure quantum state families considered. Also, we show that within all the states that saturate the quantum information bound those corresponding to the Heisenberg limit allow the maximum retrieval of information of the parameter in the final state. [1] S. L. Braunstein and C. M. Caves, Physical Review Letters 72, 3439 (1994). [2] H. Nagaoka, in Chapter 9 of ``Asymptotic Theory of Quantum Statistical Inference: Selected Papers'' (2005).

## 48. Quantum process tomography of optical unitaries

Kevin Valson Jacob, Louisiana State University

Characterizing quantum evolutions are of prime importance in quantum information. In the emerging area of photonic quantum technologies, this amounts to determining the unitary matrix which transforms the mode operators of a linear optical circuit. We propose a loss-tolerant method to fully characterize such unitaries by using only single photons. By inputting a single photon in a given input mode and finding the probability for it to be detected in all output modes, we find the moduli of all the matrix elements of the unitary. To find the phases of the matrix elements, we need the matrix elements to 'interfere' with each other. This is found by measuring the phase difference between two different paths taken by a photon. To implement this, we can either send in a photon superposed between any two input modes, or measure the output photon in a different mode basis. The former can be implemented by placing a 50:50 beamsplitter before the unknown unitary while the latter can be implemented by placing a beamsplitter after the unitary. We develop a scheme which optimizes the number of experimental configurations necessary for the full tomography of a `d' dimensional unitary. Although the Hilbert space is exponentially large in the dimension, only \(O(d^2)\) measurements suffice.

## 49. Quantum approximate optimization algorithm on a one-dimensional model

Zhihui Wang, NASA Ames Research Center (QuAIL)

A recently proposed class of quantum algorithm, the Quantum Approximate Optimization Algorithm (QAOA), holds great potential in tackling challenging combinatorial optimization problems on a gate model quantum computer. In QAOA, the problem Hamiltonian and a non-commuting driving Hamiltonian are applied alternatively. With an optimized time sequence for each piece, the optimal output of the problem Hamiltonian is approximated. We study QAOA on the model of a ring of disagreement. We provide analysis of QAOA for any level. Through transformation to the Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of a noisy spin ensemble. We show that the optimal controls lie within a defined subspace as a result of the symmetry in the system and hence the search effort can be focused on a lower-dimensional space. A well-known result of quantum control is that the control landscape admits only global optima. That result relies on the controllability of the system, i.e., given time, the set of provided controls can drive the system between any two states. In QAOA, however, at a finite level, the structure of the controls is constrained and does not guarantee full control over the system. We show that, nevertheless, the search space is still trap-free. While this is a study of a simple model, it may reveal underlying structure of the algorithm and inspire more efficient variants of QAOA.

## 50. Oscillatory localization of quantum walks

Thomas Wong, University of Texas at Austin

We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance implies oscillatory localization of the quantum walk. This reveals that oscillatory localization occurs on a large variety of regular graphs, including edge-transitive, expander, and high-degree graphs. As a corollary, high edge connectivity also implies localization of these states, since it is closely related to electric resistance.

## 51. Bell nonlocality vs. EPR steering in polarization-entangled photons

Chen Jie Xin, Harvey Mudd College

Violation of a Bell inequality, or Bell nonlocality, is a signature of only a restricted class of two-qubit entangled states. States with too little entanglement to be Bell nonlocal may nevertheless be EPR steerable: measurements performed on one subsystem can influence probabilities of measurement outcomes on the other subsystem, thus ‘steering’ the second subsystem. Surprisingly, given the mutual nature of bipartite entanglement, certain two-qubit entangled states are actually one-way steerable, with only one subsystem able to steer the other. 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. We study EPR-steerable states of photon pairs entangled in polarization, produced via spontaneous parametric down-conversion. By varying the entanglement purity, we map out a range of entangled states that may be Bell nonlocal and steerable, Bell local but steerable, or Bell local and not EPR steerable. The simplicity of the experimental approach makes it suitable for an undergraduate advanced laboratory.

## 52. Universal fault-tolerant computing with Bacon-Shor codes

Theodore Yoder, Massachusetts Institute of Technology

We present an optimized universal gate set, consisting of Hadamard and controlled-controlled-Z (CCZ), on Bacon-Shor subsystem codes. For concatenated Bacon-Shor codes, our gates possess a provably high asymptotic threshold under adversarial noise. For topological Bacon-Shor codes, our gates do not possess a threshold, but fail to do so only to the extent that a Bacon-Shor topological memory also fails. The smallest Bacon-Shor code has particularly simple implementations of our universal gates with the smallest space-time footprint of any known universal scheme by nearly 50% while also using no postselected state creation. We discuss possible implementation in ion trap architectures, where we find our CCZ is roughly three times faster than a magic-state version, a difference that translates to implementations of Shor's algorithm.

## 53. Multiparameter estimation with single photons

Chenglong You, Louisiana State University

It was suggested in [Phys. Rev. Lett. 111, 070403] that optical networks with relatively simple preparation and measurement devices – single photon Fock states and on-off detectors -- can show significant improvements over classical strategies for multiparameter estimation when the number of modes in the network is small. This was further developed in [arXiv:1610.07128] for the case of single parameter estimation, and shown to be sub-shotnoise only for n<7. In this paper, we show that this simple strategy can give asymptotically post-classical sensitivity for multiparameter estimation even when the number of modes is large. Additionally, we consider the effects of several other measurement techniques that can increase the efficiency of this device.

## 54. Quantum digital simulator interacting with a bath

Yi-Cong Zheng, Centre for Quantum Technologies, Yale-NUS college

For a quantum digital simulator simulating a closed many-body quantum system, we ask the following questions: if both systems interacting with the same bath in the same way, will the dynamics of the target system and simulator behave somewhat close to each other? In this paper, we study the open system dynamics of both target system and their digital simulator by solving their time-convolutionless non-Markovian master equations and comparing their density matrices every simulation cycle. We give conditions when their stroboscopic behavior are close to each other analytically: that is, the gate period needs to be much smaller than both bath correlation time and the simulation cycle; meanwhile, the simulation cycle needs to be either much longer or much shorter than the bath correlation time. Numerical simulation of the open system dynamics for a simplified Kitaev toric code model in a thermal boson bath is carried out to verify the validity of these conditions, surprisingly, the fast speed of gate sequence alone is not enough to keep the nature of decoherence process. This result may shed light on developing new methods of quantum error correction and Gibbs state preparation.^{1}