@article {3423, title = {Improved Digital Quantum Simulation by Non-Unitary Channels}, year = {2023}, month = {7/24/2023}, abstract = {

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.

}, url = {https://arxiv.org/abs/2307.13028}, author = {W. Gong and Yaroslav Kharkov and Minh C. Tran and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {2859, title = {Shadow process tomography of quantum channels}, journal = {Phys. Rev. A}, volume = {107}, year = {2023}, month = {4/4/2023}, abstract = {

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

}, doi = {https://doi.org/10.1103/PhysRevA.107.042403}, url = {https://arxiv.org/abs/2110.03629}, author = {Jonathan Kunjummen and Minh C. Tran and Daniel Carney and Jacob M. Taylor} } @article {2920, title = {Clustering of steady-state correlations in open systems with long-range interactions}, year = {2021}, month = {10/28/2021}, abstract = {

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from \"reversibility\" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

}, url = {https://arxiv.org/abs/2110.15368}, author = {Andrew Y. Guo and Simon Lieu and Minh C. Tran and Alexey V. Gorshkov} } @article {2605, title = {Faster Digital Quantum Simulation by Symmetry Protection}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {2/14/2021}, type = {Report number: FERMILAB-PUB-20-240-QIS-T}, abstract = {

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply our technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, our algorithm can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that our technique can also protect simulation against other types of coherent, temporally correlated errors, such as the 1/f noise commonly found in solid-state experiments.

}, issn = {2691-3399}, doi = {http://dx.doi.org/10.1103/PRXQuantum.2.010323}, url = {https://arxiv.org/abs/2006.16248}, author = {Minh C. Tran and Yuan Su and Daniel Carney and J. M. Taylor} } @article {2759, title = {The Lieb-Robinson light cone for power-law interactions}, year = {2021}, month = {3/29/2021}, abstract = {

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α\>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α\−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

}, url = {https://arxiv.org/abs/2103.15828}, author = {Minh C. Tran and Andrew Y. Guo and Christopher L. Baldwin and Adam Ehrenberg and Alexey V. Gorshkov and Andrew Lucas} } @article {2506, title = {Theory of Trotter Error with Commutator Scaling}, journal = {Phys. Rev. X}, volume = {11}, year = {2021}, month = {2/1/2021}, pages = {49}, chapter = {011020}, abstract = {

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, k-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of 5, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011020}, url = {https://arxiv.org/abs/1912.08854}, author = {Andrew M. Childs and Yuan Su and Minh C. Tran and Nathan Wiebe and Shuchen Zhu} } @article {2514, title = {Destructive Error Interference in Product-Formula Lattice Simulation}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {6/4/2020}, abstract = {

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.\ 

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502}, url = {https://arxiv.org/abs/1912.11047}, author = {Minh C. Tran and Su-Kuan Chu and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {2577, title = {Hierarchy of linear light cones with long-range interactions}, journal = {Physical Review X}, volume = {10}, year = {2020}, month = {5/29/2020}, abstract = {

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a \"linear light cone,\" which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)\∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators \⟨ψ|[Ox(t),Oy]|ψ\⟩ are negligible in every state |ψ\⟩ when |x\−y|≳vt, where v is finite when α\>3 (Lieb-Robinson light cone); in a typical state |ψ\⟩ drawn from the infinite temperature ensemble, v is finite when α\>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α\>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

}, doi = {https://doi.org/10.1103/PhysRevX.10.031009}, url = {https://arxiv.org/abs/2001.11509}, author = {Minh C. Tran and Chi-Fang Chen and Adam Ehrenberg and Andrew Y. Guo and Abhinav Deshpande and Yifan Hong and Zhe-Xuan Gong and Alexey V. Gorshkov and Andrew Lucas} } @article {2689, title = {Optimal state transfer and entanglement generation in power-law interacting systems}, year = {2020}, month = {10/6/2020}, abstract = {

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α\>2d and a superpolynomial speedup for α\≤2d, compared to the state of the art. For all α\>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states.\ 

}, url = {https://arxiv.org/abs/2010.02930}, author = {Minh C. Tran and Abhinav Deshpande and Andrew Y. Guo and Andrew Lucas and Alexey V. Gorshkov} } @article {2403, title = {Signaling and Scrambling with Strongly Long-Range Interactions}, journal = {Physical Review A}, volume = {102}, year = {2020}, month = {7/8/2020}, abstract = {

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α\≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α\≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α\<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.\ 

}, doi = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.010401}, url = {https://arxiv.org/abs/1906.02662}, author = {Andrew Y. Guo and Minh C. Tran and Andrew M. Childs and Alexey V. Gorshkov and Zhe-Xuan Gong} } @article {2406, title = {Complexity phase diagram for interacting and long-range bosonic Hamiltonians}, year = {2019}, month = {06/10/2019}, abstract = {

Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a \"complexity phase diagram\" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.\ 

}, url = {https://arxiv.org/abs/1906.04178}, author = {Nishad Maskara and Abhinav Deshpande and Minh C. Tran and Adam Ehrenberg and Bill Fefferman and Alexey V. Gorshkov} } @article {2195, title = {Locality and digital quantum simulation of power-law interactions}, journal = {Phys. Rev. X 9, 031006}, volume = {9}, year = {2019}, month = {07/10/2019}, abstract = {

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α\>3D (where D is the number of dimensions).

}, doi = {https://doi.org/10.1103/PhysRevX.9.031006}, url = {https://arxiv.org/abs/1808.05225}, author = {Minh C. Tran and Andrew Y. Guo and Yuan Su and James R. Garrison and Zachary Eldredge and Michael Foss-Feig and Andrew M. Childs and Alexey V. Gorshkov} } @article {2458, title = {Locality and Heating in Periodically Driven, Power-law Interacting Systems}, journal = {Phys. Rev. A }, volume = {100}, year = {2019}, month = {2019/11/12}, abstract = {

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α\>D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α\>2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.\ 

}, doi = {https://doi.org/10.1103/PhysRevA.100.052103}, url = {https://arxiv.org/abs/1908.02773}, author = {Minh C. Tran and Adam Ehrenberg and Andrew Y. Guo and Paraj Titum and Dmitry A. Abanin and Alexey V. Gorshkov} } @article {2133, title = {Bell monogamy relations in arbitrary qubit networks}, year = {2018}, month = {2018/01/09}, abstract = {

Characterizing trade-offs between simultaneous violations of multiple Bell inequalities in a large network of qubits is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for multipartite inequalities can be obtained with our method as shown in explicit examples.

}, doi = {https://doi.org/10.1103/PhysRevA.98.052325}, url = {https://arxiv.org/abs/1801.03071}, author = {Minh C. Tran and Ravishankar Ramanathan and Matthew McKague and Dagomir Kaszlikowski and Tomasz Paterek} } @article {2132, title = {Blind quantum computation using the central spin Hamiltonian}, year = {2018}, month = {2018/01/11}, abstract = {

Blindness is a desirable feature in delegated computation. In the classical setting, blind computations protect the data or even the program run by a server. In the quantum regime, blind computing may also enable testing computational or other quantum properties of the server system. Here we propose a scheme for universal blind quantum computation using a quantum simulator capable of emulating Heisenberg-like Hamiltonians. Our scheme is inspired by the central spin Hamiltonian in which a single spin controls dynamics of a number of bath spins. We show how, by manipulating this spin, a client that only accesses the central spin can effectively perform blind computation on the bath spins. Remarkably, two-way quantum communication mediated by the central spin is sufficient to ensure security in the scheme. Finally, we provide explicit examples of how our universal blind quantum computation enables verification of the power of the server from classical to stabilizer to full BQP computation.

}, url = {https://arxiv.org/abs/1801.04006}, author = {Minh C. Tran and J. M. Taylor} } @article {2210, title = {Dynamical phase transitions in sampling complexity}, journal = {Phys. Rev. Lett.}, volume = {121}, year = {2018}, pages = {12 pages, 4 figures. v3: published version}, abstract = {

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time\ t\ due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of\ t\ with the number of bosons\ n\ for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of\ t\ with\ n\ for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC \&$\#$39;11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.030501}, url = {https://arxiv.org/abs/1703.05332}, author = {Abhinav Deshpande and Bill Fefferman and Minh C. Tran and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1990, title = {Genuine N -partite entanglement without N -partite correlation functions}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/06/26}, pages = {062331}, abstract = {

A genuinely\ N-partite entangled state may display vanishing\ N-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd\ N\ is to design an \“antistate\” in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its antistate then produces a mixed state with no\ N-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of \“entanglement without correlations\” involve an\ odd\ number of particles. Here we further develop the idea of antistates, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no antistate to any pure even-N-party entangled state making the simple construction scheme unfeasible. However, as we prove by construction, higher-rank examples of entanglement without correlations for arbitrary even\ N\ indeed exist. These classes of states exhibit genuine entanglement and even violate an\ N-partite Bell inequality, clearly demonstrating the nonclassical features of these states as well as showing their applicability for quantum information processing.

}, doi = {doi.org/10.1103/PhysRevA.95.062331}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.062331}, author = {Minh C. Tran and Margherita Zuppardo and Anna de Rosier and Lukas Knips and Wieslaw Laskowski and Tomasz Paterek and Harald Weinfurter} } @article {2277, title = {Lieb-Robinson bounds on n-partite connected correlation functions}, journal = {Phys. Rev. A 96, 052334}, year = {2017}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {https://doi.org/10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1987, title = {Lieb-Robinson bounds on n-partite connected correlations}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/11/27}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an\ n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an\ n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {2102, title = {Quantum simulation of ferromagnetic Heisenberg model}, year = {2017}, month = {2017/12/14}, abstract = {

Large quantum simulators, with sufficiently many qubits to be impossible to simulate classically, become hard to experimentally validate. We propose two tests of a quantum simulator with Heisenberg interaction in a linear chain of spins. In the first, we propagate half of a singlet state through a chain of spin with a ferromagnetic interaction and subsequently recover the state with an antiferromagnetic interaction. The antiferromagnetic interaction is intrinsic to the system while the ferromagnetic one can be simulated by a sequence of time-dependent controls of the antiferromagnetic interaction and Suzuki-Trotter approximations. In the second test, we use the same technique to transfer a spin singlet state from one end of a spin chain to the other. We show that the tests are robust against parametric errors in operation of the simulator and may be applicable even without error correction.

}, url = {https://arxiv.org/abs/1712.05282}, author = {Yiping Wang and Minh C. Tran and J. M. Taylor} }