EAGER-QAC-QSA: Variational Quantum Algorithms for Nonequilibrium Quantum Many-Body Systems

本奖项是根据量子算法挑战Dear Colleague Letter邀请的EAGER提案颁发的。它支持研究和教育，以开发和实现在目前存在或将在不久的将来存在的量子计算机上运行的算法。一台完美的量子计算机有望比任何传统计算机（也称为经典计算机）更快地解决某些实际问题。例子包括用肖尔算法将大数分解为质数，用劳埃德算法预测相互作用的量子系统偏离平衡的时间演变。后者可以帮助优化和设计新的生物材料、药物和功能量子材料。虽然过去几年在构建完美量子计算机方面取得了巨大进展，但目前的噪声中等规模量子（NISQ）技术距离能够在实际相关尺度上运行肖尔和劳埃德算法还有几十年的距离。潜在的原因是NISQ计算机拥有数百个量子比特，而不是完全纠正由噪声门操作引起的错误所需的数百万个量子比特。这严重限制了与NISQ硬件兼容的量子算法的复杂性，并暴露了进一步改进算法以实现实际量子优势的迫切需要。在这个项目中，pi开发了适合NISQ量子处理单元（qpu）的算法，可以解决非平衡物理中的基本挑战。具体来说，研究小组提出了新的混合量子经典变分算法来模拟非平衡动力学和高激发态的新材料，如无序量子磁体。这些算法将在IBM和Rigetti的qpu上实现，并对现有的最先进的量子和经典算法进行仔细的基准测试。除了寻找短期量子优势的机会外，该项目还将为相互作用的粒子系统如何松弛到热平衡以及它们如何响应强外场等基本问题提供新的见解。该项目的教育部分解决了教育量子劳动力的国家优先事项，并加强了STEM领域传统上代表性不足群体的参与和包容。在这个项目中，pi将教育和培训一名研究生，一名本科生和一名博士后学者，应用量子计算算法来挑战开放的科学问题。pi还将设计一个关于量子计算的实践外展研讨会，并在面向女性初高中学生的STEM职业会议“Go Further”上展示。最后，pi将为公众创建和维护一个在线博客，突出量子信息科学的职业选择，并向读者介绍量子算法的最新趋势。本奖项是根据量子算法挑战Dear Colleague Letter邀请的EAGER提案颁发的。它支持研究和教育，以开发和实现在目前存在或将在不久的将来存在的量子计算机上运行的算法。噪声中等规模量子（NISQ）计算设备具有任何经典超级计算机无法达到的计算能力，正如谷歌团队最近所证明的那样。它们是否也为物理、化学或材料科学中感兴趣的计算提供了实际的量子优势，这是一个悬而未决的问题。量子多体系统中非平衡动力学和高激发态的模拟是一个有希望但又具有挑战性的目标，因为这种模拟的经典算法受到指数复杂性和一般激发态高度纠缠性质的影响。为当前NISQ硬件开发资源高效的量子算法可以释放其潜力，以解决非平衡多体物理中的重要挑战。在此，pi提出了两种基于变分量子特征求解器（VQE）算法的新型变分量子算法，该算法已在NISQ硬件上进行了验证。与之前的工作不同，pi们提出使用不同的代价函数来探索高激发和时间演化的量子态的流形，而不是瞄准基态。经过对已知量子算法和经典算法的仔细基准测试，这两种算法将用于解决强无序和相互作用量子系统中多体定位、非线性响应和非平衡动力学领域的基本开放科学问题。该项目将提高变分算法的能力，超越探索低能态的性质。本研究结果将提供对强无序相互作用自旋链中高激发态性质的见解，并解决违反本征态热化假设的多体局域相和迁移率乳剂的存在。研究小组还将阐明在后猝灭动力学中出现的预热量子态的相关和纠缠特性，并测试它们的时间稳定性与小能量方差相关的假设，使它们近似特征态。最后，通过实施高效的NISQ量子算法来计算高阶和非时序相关函数，pi将确定这些函数是否可以解开无序和相互作用对准粒子性质的影响，并探索自旋模型中量子混沌的开始。通过解决凝聚态物理中的基本挑战，研究团队将为NISQ技术是否提供实用的量子优势这一悬而未决的问题做出贡献。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Nontechnical SummaryThis award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to develop and implement algorithms to run on quantum computers that currently exist or will exist in the near future. A perfect quantum computer is expected to solve certain problems of practical interest much faster than any conventional computer, also called a classical computer. Examples include factoring large numbers into primes with Shor's algorithm and using Lloyd's algorithm to predict the time evolution of an interacting quantum system away from equilibrium. The latter could help in optimization and design of new biomaterials, drugs, and functional quantum materials. While the past few years have brought tremendous progress in efforts to build a perfect quantum computer, the current noisy intermediate-scale quantum (NISQ) technology is potentially decades away from being able to run Shor's and Lloyd's algorithms at practically relevant scales. The underlying reason is that NISQ computers possess of the order of hundreds of qubits as opposed to the millions required to fully correct for errors that arise from noisy gate operations. This severely limits the complexity of quantum algorithms compatible with NISQ hardware and exposes a critical need for further algorithmic advancement to achieve practical quantum advantage.In this project, the PIs develop algorithms tailored to NISQ quantum processing units (QPUs) that can address fundamental challenges in nonequilibrium physics. Specifically, the research team proposes new hybrid quantum-classical variational algorithms to simulate nonequilibrium dynamics and highly excited states in novel materials such as disordered quantum magnets. The algorithms will be implemented on QPUs from IBM and Rigetti and carefully benchmarked against existing state-of-the-art quantum and classical algorithms. In addition to finding opportunities for near-term quantum advantage, this project will provide new insights into fundamental questions of how systems of interacting particles relax to thermal equilibrium and how they respond to strong external fields.The educational component of this project addresses the national priorities of educating a quantum-enabled workforce and enhancing the participation and inclusion of traditionally underrepresented groups in STEM areas. Within this project, the PIs will educate and train one graduate student, one undergraduate student, and one postdoctoral scholar in applying quantum computing algorithms to challenging open scientific questions. The PIs will also design a hands-on outreach workshop on quantum computing and present it at "Go Further," a STEM career conference aimed at female middle- and high-school students. Finally, the PIs will create and maintain an online blog for the general public that highlights career options in quantum information science and informs readers about recent trends in quantum algorithms.Technical SummaryThis award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to develop and implement algorithms to run on quantum computers that currently exist or will exist in the near future. Noisy intermediate-scale quantum (NISQ) computing devices have computing capabilities that are beyond the reach of any classical supercomputer, as has recently been demonstrated by the Google team. Whether they also offer a practical quantum advantage for calculations of interest in physics, chemistry or materials science is an open question. Simulations of nonequilibrium dynamics and highly excited states in quantum many-body systems are a promising yet challenging target, since classical algorithms for such simulations suffer from the exponential complexity and highly entangled nature of generic excited states. The development of resource-efficient quantum algorithms for current NISQ hardware can unlock their potential to address important challenges in nonequilibrium many-body physics.Here, the PIs propose two novel variational quantum algorithms that are based on the variational quantum eigensolver (VQE) algorithm, which has been demonstrated on NISQ hardware. Instead of targeting ground states as in previous works, the PIs propose to use different cost functions to explore the manifold of highly excited and time-evolved quantum states. After careful benchmarking against known quantum and classical algorithms, both algorithms will be used to address fundamental open scientific questions in the fields of many-body localization, nonlinear response and nonequilibrium dynamics in strongly disordered and interacting quantum systems.The project will advance the capabilities of variational algorithms beyond exploring properties of low-energy states. Results of this research will provide insights into the properties of highly excited states in strongly disordered interacting spin chains, and address the existence of many-body localized phases and mobility emulsions, which violate the eigenstate thermalization hypothesis. The research team will also shed light on the correlation and entanglement properties of prethermal quantum states that emerge in post-quench dynamics and test the hypothesis that their temporal stability is related to a small energy variance, making them approximate eigenstates. Finally, by implementing efficient NISQ quantum algorithms for the computation of higher-order and out-of-time-ordered correlation functions, the PIs will determine whether these functions can disentangle effects of disorder and interactions on quasiparticle properties and explore the onset of quantum chaos in spin models. By addressing fundamental challenges in condensed matter physics, the research team will contribute to the open question of whether NISQ technology offers a practical quantum advantage.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.