Simulations of Many-Body Quantum Systems by a Quantum Computer
Stephen Wiesner
我们认为，量子计算机可以解决量子多体问题是不切实际的解决一个经典的计算机。
We suggest that quantum computers can solve quantum many-body problems that are impracticable to solve on a classical computer.
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Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
我们提供了一个通用的量子计算机上模拟多体费米系统的快速算法。第一和第二量化的描述被认为是，并在每种情况下确定的相对计算复杂度。为了用第一量子化的哈密顿量来容纳费米子，给出了一种有效的反对称化量子算法。最后，详细讨论了哈伯德模型的模拟。
We estimate the resources required to prepare the ground state of a quantum many-body system on a quantum computer of intermediate size. This estimate is made possible using a combination of quantum many-body methods and analytic upper bounds. Our routine can also be used to optimize certain design parameters for specific problem instances. Lastly, we propose and benchmark an improved quantum state preparation procedure. We find that it reduces the circuit T-depth by a factor as large as $10^6$ for intermediate-size lattices.
Quantum simulation of a three-body interaction Hamiltonian on an NMR quantum computer
将平均哈密顿量理论扩展到量子计算，可以设计任意的哈密顿量，允许在一个大的希尔伯特空间中旋转。这样，任何量子系统的运动学和动力学都可以通过量子计算机来模拟。系统之间的基映射决定了在模拟系统中实现所需哈密顿量所需的量子计算机中的平均哈密顿量。该程序的灵活性说明与13-C标记的丙氨酸的NMR通过创建对应于三体相互作用的非物理哈密顿量ZZZ。
Three and Four-Body Interactions in Spin-Based Quantum Computers
在设计和构建量子计算机的努力中，几个领先的提议利用了基于自旋的量子比特。这些设计通常假设自旋经历成对的相互作用。我们指出，当几个自旋相互从事成对相互作用，相互作用的定量强度可以改变和定性新的条款可以出现在哈密顿量，包括四体相互作用。在实验感兴趣的参数制度，这些相干效应是大到足以干扰计算，并可能需要新的纠错或避免技术。
Preparing ground states of quantum many-body systems on a quantum computer
制备相互作用经典粒子系统的基态是一个NP难问题。因此，一般来说，没有更好的算法来解决这个问题，而不是穷尽地通过系统的所有N个配置来确定具有最低能量的一个，需要与N成比例的运行时间。量子计算机，如果可以建造的话，可以在时间sqrt（N）内解决这个问题。在这里，我们提出了一个强有力的扩展，这一结果的情况下，相互作用的量子粒子，证明了量子计算机可以准备的基态的量子系统，因为它的经典系统一样有效。
Quantum flow algorithms for simulating many-body systems on quantum computers
本文提出量子流（QFlow）算法，通过降维活性空间中的耦合特征值问题采样希尔伯特空间，在保持恒定电路深度和量子比特数的同时显著降低电路复杂度并优化波函数参数数量。
Detection of many-body entanglement partitions in a quantum computer
本文提出基于系统固有对称性、结合弱Schur采样的多体纠缠划分检测方法，可在量子计算机实现，覆盖多类纠缠结构，还推导了相关矩阵不等式新结论。
Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
本研究提出量子计算机上多体系统模拟的有限对称性统一框架，通过高效量子线路实现对称群不可约表示的适配投影，经资源估算与含噪硬件小分子实验验证，为利用对称性实现容错量子计算的实用量子优势奠定基础。
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled pr…
Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polyn…
We show that current noisy quantum computers are ideal platforms for the simulation of quantum many-body dynamics in generic open systems. We demonstrate this using the IBM Quantum Computer as an experimental platform for confirming the theoretical prediction from [Phys. Rev. Lett.124, 100604 (2020)] of an emergent hierarchy of relaxation timescales of many-body observables involving different numbers of qubits. Using different protocols, we leverage the intrinsic dissipation of the machine responsible for gate errors, to implement a quantum simulation of generic (i.e. structureless) local dis…
Starting from the Quantum-Phase-Estimate (QPE) algorithm, a method is proposed to construct entangled states that describe correlated many-body systems on quantum computers. Using operators for which the discrete set of eigenvalues is known, the QPE approach is followed by measurements that serve as projectors on the entangled states. These states can then be used as inputs for further quantum or hybrid quantum-classical processing. When the operator is associated to a symmetry of the Hamiltonian, the approach can be seen as a quantum--computer formulation of symmetry breaking followed by symm…
Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics -- we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small …
Machine learning on quantum experimental data toward solving quantum many-body problems
该研究将经典机器学习与量子实验数据结合，在127量子比特硬件上降噪后，成功预测基态性质并分类量子相，验证了方法在44量子比特系统中的可扩展性。
A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spec…
Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
我们提出了一个基于地面码测量的量子计算机方案，它具有两个主要优点。首先，每个逻辑量子比特被编码在具有最近邻两体相互作用的自旋为1的链的带隙简并基态子空间中，使得它具有对噪声的内置鲁棒性。第二，通过沿着按需动态耦合的多个链的单自旋测量来处理计算，以便在关闭与要测量的自旋的相互作用之后保持仅将逻辑信息传送到剩余链的间隙保护的基态。我们描述了在光晶格中使用被捕获的原子或极性分子的实现方式，其中期望间隙分别大到0.2 kHz或4.8 kHz。
Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
本文回顾了超导量子模拟的基本概念及实验进展，探讨其在模拟强相互作用多体系统非平衡量子现象（如多体局域化等）中的应用，并展望了解决非平衡多体物理开放问题的前景。
Quantum pathology of static internal imperfections in flawed quantum computers
即使在没有外部影响的情况下，量子计算机（QC）的可操作性也不能得到保证，因为残余的单体和两体缺陷的影响。在这里，我们研究这些内部缺陷如何影响量子控制非（CNOT）门在一个孤立的缺陷QC的性能。首先，我们发现当两体缺陷很强时，CNOT门的性能要好得多。其次，我们发现最大的误差源是由于相干位移，而不是退相干或耗散。我们的研究结果表明，内部缺陷的问题，应给予更多的关注，在设计可扩展的QC架构。
Many-body thermal states on a quantum computer: a variational approach
提出一种混合量子-经典变分算法制备量子XY模型的Gibbs态，利用系统对称性减少变分参数，模拟显示其与精确Gibbs态保真度接近1。
The negative hydrogen ion is the first three body quantum problem whose ground state energy is calculated using the `Chandrasekhar Wavefunction' that accounts for the electron-electron correlation. Solving multi-body systems is a daunting task in quantum mechanics as it includes choosing a trial wavefunction and the calculation of integrals for the system that becomes almost impossible for systems with three or more particles. This difficulty can be addressed by quantum computers. They have emerged as a tool to address different electronic structure problems with remarkable efficiency. They ha…
We explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer followed by additional post-processing. The final goal is to develop configuration interaction techniques based on many-body trial states pre-optimized on a quantum computer. We show how the projection method used for symmetry restoration can prepare optimized states that could then be employed as initial states for quantum or hybrid quantum-classical algorithms. We use the quantum phase estimation and quantum Krylov approaches for the post-processing. The latter metho…
Perturbative Analysis of Quasi-periodic Patterning of Transmon Quantum Computers: Enhancement of Many-Body Localization
本研究提出利用超周期模式替代随机性以增强转子量子计算机的多体局域化，通过微扰理论分析验证其有效性。
We present MISTIQS, a Multiplatform Software for Time-dependent Quantum Simulations. MISTIQS delivers end-to-end functionality for simulating the quantum many-body dynamics of systems governed by time-dependent Heisenberg Hamiltonians across multiple quantum computing platforms. It provides high-level programming functionality for generating intermediate representations of quantum circuits which can be translated into a variety of industry-standard representations. Furthermore, it offers a selection of circuit compilation and optimization methods and facilitates execution of the quantum circui…
Quantum Statistical Mechanics on a Quantum Computer
本文描述了一种计算量子多体系统态密度和热平衡性质的量子算法。我们目前的情况下，反铁磁海森堡模型的三角晶格上的不同大小的21量子位量子计算机的软件实现上运行该算法所获得的结果。
Quantum Simulation of Simple Many-Body Dynamics
本文提出模拟三维非相对论库仑多体系统时间演化的通用量子算法，基于离散 Schrödinger 模型实现 Wiesner-Zalka 方案，并通过小规模数值验证其与解析解一致。
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the results of such simulations will also become classically intractable as system sizes increase. In this work, we introduce and implement a coherent imaging spectroscopic technique to validate a quantum simulation, much as magnetic resonance imaging exposes structure in condensed matter. We use this method to determine the energy levels and interaction strengt…
Calculating the many-body density of states on a digital quantum computer
本文提出并实现了一种受核多项式方法启发的量子算法，在Quantinuum H1-1离子阱芯片上利用18量子比特受控寄存器估计不可积哈密顿量的态密度，展示了量子硬件上多体热力学性质计算的最新水平。
We investigate many-body localization of interacting spinless fermions in a one-dimensional disordered and tilted lattice. The fermions undergo energy-dependent transitions from ergodic to Stark many-body localization driven by the tilted potential, which are manifested by the appearance of mobility edges between delocalized states and Stark many-body localized states even when the disorder is weak. We can concretely diagnose these transitions rather than crossovers by finite-size scaling of energy-level statistics. Moreover, in the Stark many-body localization, the entanglement entropy obeys …
We study a spin-gas model, where N_S system qubits are interacting with N_B bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decohenerce induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between baths that are coupled to different individual system qubit and compare Markovian with non-Markovian interactions. As examples we co…
Digital quantum simulation uses the capabilities of quantum computers to determine the dynamics of quantum systems, which are beyond the computability of modern classical computers. A notoriously challenging task in this field is the description of non-equilibrium dynamics in quantum many-body systems. Here we use the IBM quantum computers to simulate the non-equilibrium dynamics of few spin and fermionic systems. Our results reveal, that with a combination of error mitigation, noise extrapolation and optimized initial state preparation, one can tackle the most important drawbacks of modern qu…
Schrieffer-Wolff transformation (SWT) has been extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It provides a perturbative method to comprehend the renormalization effects of strong correlations in the quantum many-body models. The generator for Schrieffer-Wolff transformation is calculated usually by heuristic methods. Recently, a systematic and elegant method for the calculation of this extremely significant transformation has been reported [1]. Given the huge significance of SWT for many areas including quantum condensed matter physics, quantu…
Towards few-body QCD on a quantum computer
本文针对少体QCD量子模拟问题，提出一种寄存器与粒子对应的紧凑编码方案，实现低粒子数、高自由度系统的指数级存储压缩，并在双寄存器上验证了反对称化与指数化算法。
Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in practice. Nevertheless, they are always very heavy to treat numerically. The envelope theory, also known as the auxiliary field method, is a very efficient technique to obtain approximate, but reliable, solutions of many-body systems interacting via one- or two-body forces. It is adapted here to allow the treatment of a special form of many-body forces. In the most …
About mathematical apparatus of many body quantum dynamics
我们讨论了修改多体希尔伯特量子形式主义的可能性，这是必要的量子系统动力学的表示。有效经典算法的概念和量子动力学的可视化起着关键作用。
An optical realization of the phenomenon of many-body coherent destruction of tunneling, recently predicted for interacting many-boson systems by Gong, Molina and Haenggi [Phys. Rev. Lett. 103, 133002 (2009)], is proposed for light transport in engineered waveguide arrays. The optical system enables a direct visualization in Fock space of the many-body tunneling control process
Robust Finite-Temperature Many-Body Scarring on a Quantum Computer
该研究利用IBM Kolkata量子处理器，发现PXP模型中的量子多体疤痕在有限温热吉布斯系综下具备出人意料的鲁棒性，而其他含严格量子多体疤痕的模型无此特性，揭示了模型代数结构对有限温鲁棒性的影响。
Geometric phases induced in auxiliary qubits by many-body systems near its critical points
计算和讨论了多体系统在辅助量子比特中诱导的几何相位。考虑了辅助量子比特与多体系统之间的两种耦合，分别导致量子比特中的退相和耗散。作为例子，我们考虑XY自旋链与量子比特的退相耦合，给出并讨论了量子比特中的几何相位。结果表明，几何相位可以用来表征多体系统的临界点，并且随着多体系统参数远离临界点，几何相位趋于零。
Comment on a letter to Nature Physics, where Sakmann and Kasevich claim to solve the many-body time dependent Schrödinger equation to simulate single experimental runs of interacting quantum systems.
Liquid state NMR simulations of quantum many-body problems
最近开发的量子算法表明，原则上，量子计算机可以比经典计算机更有效地解决物理系统模拟等问题。要将这些概念性的想法应用到实际的量子计算机中，还有很多工作要做。作为一个小规模的演示他们的能力，我们模拟了一个简单的多费米子问题，Fano-Anderson模型，使用液态核磁共振（NMR）。我们仔细设计了我们的实验，以便资源需求将随着要模拟的量子系统的大小而多项式地增加。实验结果使我们能够评估在这类实验中达到的量子控制程度的极限。对具有不同粒子统计的其它物理系统的模拟也进行了讨论。
Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the critical exponents. Numerically calculating these results for systems in new universality classes is complicated due to critical slowing down, requiring increasing resources near the critical point. An alternative approach analytically continues the calculation onto the complex plane and determines the partition function via its zeros. Here we show how to robustly…
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed. After briefly discussing some of the standard symmetries relevant for many-particle systems, we discuss the advantage of encoding some symmetries directly in quantum ansätze, especially to reduce the quantum register size. It is, however, well-known that the use of symmetry-breaking states can also be a unique way to incorporate specific internal …
Quantum Computation, Complexity, and Many-Body Physics
最近开发的量子算法表明，量子计算机可以比传统计算机更有效地解决某些问题并执行某些任务。除其他原因外，这是由于可能产生非经典关联，或量子纠缠，这是一种很难或不可能通过经典信息方法再现的现象。在这篇论文中，我首先研究在由二能级量子元或量子比特构成的量子计算机上模拟量子系统。为此，我提出了代数映射，允许一个获得的物理性质和计算关联函数的费米子，任意子，玻色子系统与这样的计算机。结果表明，制备包含计算所需信息的量子态的复杂性是至关重要的。其次，我提出了一个广泛的量子计算，其中可能涉及纠缠态，可以在两种类型的计算机上以相同的效率进行模拟。广义量子纠缠的概念自然就出现了。这种对纠缠的概括是基于这样一种想法，即纠缠是一个依赖于粒子的概念，也就是说，相对于一组优选的可观测量。
The generating function of a Hamiltonian $H$ is defined as $F(t)=\langle e^{-itH}\rangle$, where $t$ is the time and where the expectation value is taken on a given initial quantum state. This function gives access to the different moments of the Hamiltonian $\langle H^{K}\rangle$ at various orders $K$. The real and imaginary parts of $F(t)$ can be respectively evaluated on quantum computers using one extra ancillary qubit with a set of measurement for each value of the time $t$. The low cost in terms of qubits renders it very attractive in the near term period where the number of qubits is li…
Preparing quantum many-body scar states on quantum computers
本研究针对受扰量子多体疤痕态难以用经典计算研究的问题，提出了多种适配量子计算机的态制备协议，并在超导量子硬件上完成了原理性演示，为疤痕态相关研究提供了量子计算路径。
Quantum lattice-gas models for the many-body Schrodinger equation
本文描述了一类一般的离散么正模型，其在连续极限的行为对应于一个多体薛定谔方程。在量子计算机上，这些模型可以用来模拟量子多体系统，与经典计算机上的类似模拟相比，其加速率为指数级。在经典计算机上，这些模型给出了离散薛定谔方程的显式酉和局部处方。结果表明，这种类型的模型可以构建为任意数量的粒子在任意数量的维度与任意粒子间的相互作用。
Quantum many-body Jarzynski equality and dissipative noise on a digital quantum computer
该研究在囚禁离子和超导量子计算机上对最多十六个相互作用自由度的系统验证量子多体 Jarzynski 等式与 Crooks 关系，并揭示快速幺正驱动可补偿能量耗散。
Quantum circuit algorithm for topological invariants of second order topological many-body quantum magnets
研究二阶拓扑多体量子磁体拓扑不变量计算难题，提出基于量子电路绝热演化的算法，可利用量子计算机表征多体拓扑量子物质，并发现隐藏拓扑不变量。
Time dynamics in chaotic many-body systems: can chaos destroy a quantum computer?
量子系统（原子核、原子、量子点、自旋系统、量子计算机）中的高激发多粒子态可以是平均场基态（斯莱特行列式、自旋或量子比特态的乘积）的“混沌”叠加。这是由于多体状态的非常高的能级密度，其可以通过粒子之间的残余相互作用容易地混合。我们考虑了这种混沌系统中波函数的时间动力学和熵的增加。作为一个例子，我们提出了一个封闭的量子计算机中的时间演化。熵S（t）增加的时间尺度是t_c =t_0/（n log_2{n}），其中t_0是量子比特的“寿命”，n是量子比特的数量，S（0）=0并且S（t_c）=1。在t << t_c时，熵很小：S= n t^2 J^2 log_2（1/t^2 J^2），其中J是量子比特间的相互作用强度。在t > t_c时，"错误“状态的数量以2^{S（t）}的形式呈指数增长。因此，t_c可以被解释为量子计算机运行的最大时间，因为在t > t_c时，人们必须与热力学第二定律作斗争。当t >>t_c时，系统熵接近混沌本征态熵.
Dynamical simulations of many-body quantum chaos on a quantum computer
本研究利用量子计算机模拟双幺正电路，展示其在误差缓解下的量子模拟能力，用于探索新涌现的量子许多体相。
Error-Mitigated Simulation of Quantum Many-Body Scars on Quantum Computers with Pulse-Level Control
本文在至多19格点的混合场伊辛链上模拟量子多体疤痕动力学，结合零噪声外推、动力学解耦等误差缓解与脉冲级控制，实现长达40个Trotter步的相干演化。
Quantum computer-based simulation of Stark many-body localization in a 1D Fermi-Hubbard model
研究人员借助IBM超导量子计算机，通过多步电路优化实现12量子比特一维费米-哈伯德模型的斯塔克多体局域化模拟，验证了弱场倾斜下热化、大倾斜下强局域化的动力学交叉，结果与精确模拟吻合。
Probing Entanglement Dynamics in the SYK Model using Quantum Computers
本文利用量子计算机研究SYK模型的纠缠熵，通过优化协议和误差缓解技术验证了其在探索复杂量子系统混沌动力学中的能力。
Thermodynamics of quantum systems and quantum thermal machines are rapidly developing fields, which have already delivered several promising results, as well as raised many intriguing questions. Many-body quantum machines present new opportunities stemming from many-body effects. At the same time, they pose new challenges related to many-body physics. In this short review we discuss some of the recent developments on technologies based on many-body quantum systems. We mainly focus on many-body effects in quantum thermal machines. We also briefly address the role played by many-body systems in …
Simulation of Higher Dimensional Discrete Time Crystals on a Quantum Computer
本研究在量子计算机上模拟了高维离散时间晶体，证明将其推广到2维可降低热噪声并扩大多体局域态的工作范围。
Automatic generation of vacuum amplitude many-body perturbation series
本文给出了计算具有两体相互作用的基态能量多体微扰级数的Hugenholtz图表示的算法和程序。输出的形式适合于后处理，如自动代码生成。一个特定的应用程序，生成LaTeX代码绘制图表的结果，显示。
Ultra-cold atoms in optical lattices provide an ideal platform for exploring many-body physics of a large system arising from the coupling among a series of small identical systems whose few-body dynamics is exactly solvable. Using Landau-Zener (LZ) transition of bosonic atoms in double well optical lattices as an experimentally realizable model, we investigate such few to many body route by exploring the relation and difference between the small few-body (in one double well) and the large many-body (in double well lattice) non-equilibrium dynamics of cold atoms in optical lattices. We find th…
We show how coherences between identical constituents of a many-body quantum state can be interrogated by suitable correlation functions, and identify sufficient conditions under which low-order correlators fully characterize many-body coherences, as controlled by the constituents' mutual distinguishability. Comparison of correlators of different order detects many-body entanglement.
Symmetry breaking and restoration for many-body problems treated on quantum computers
本研究将对称性破缺/恢复方法与VQE结合用于多体问题基态能量近似，开发了基于量子相位估计等的多种恢复技术，还提出了数种量子-经典混合的低能谱分析方法。
A highly anticipated application for quantum computers is as a universal simulator of quantum many-body systems, as was conjectured by Richard Feynman in the 1980s. The last decade has witnessed the growing success of quantum computing for simulating static properties of quantum systems, i.e., the ground state energy of small molecules. However, it remains a challenge to simulate quantum many-body dynamics on current-to-near-future noisy intermediate-scale quantum computers. Here, we demonstrate successful simulation of nontrivial quantum dynamics on IBM's Q16 Melbourne quantum processor and R…
Quantum magnets are never short of novel and fascinating dynamics, yet its simulation by classical computers requires exponentially-scaled computation resources, which renders the research on large-scale many-body dynamics fiendishly difficult. In this letter, we explore the dynamic behavior of 2D large-scale ferromagnetic J1-J2 Heisenberg model both theoretically and experimentally. First, the analytical solution of magnon dynamics is obtained to show an obvious ballistic propagation of magnon, which is typical for quantum walk. Then, we verify the dynamic behavior of the system through numer…
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