EAGER: QSA: Approximating the Ground States of Non-Stoquastic Hamiltonians Using the Variational Quantum Eigensolver

量子算法利用量子物理的独特特性来执行计算任务，对于某些任务，它们比受经典物理定律限制的算法更有效。可以实现这种算法的量子计算机现在已经公开可用，但是这些设备在它们可以执行的计算的大小和长度方面仍然有限，使得具有量子优势的量子算法遥不可及。已经提出了使用量子和经典硬件的混合算法作为解决这一挑战的一种方法，该项目旨在通过与最先进的经典算法进行系统的计算成本比较，研究混合方法在提供量子优势方面的可行性。如果近期使用量子计算机有可能带来优势，它将极大地提高我们理解和预测物理科学领域复杂系统的能力。该项目突出了量子计算的多学科性质，并将培养学生拥有多样化的工具箱来应对该领域的新挑战。这种方法是该项目开发新课程的核心，旨在培养“量子就绪”的劳动力，以应对2018年《国家量子倡议法案》的呼吁。近似多体非随机哈密顿量基态的任务，是一类描述许多相关模型系统的量子哈密顿量，如费米子哈密顿量和有符号问题的哈密顿量，在从高能物理到量子化学的一系列学科中都有体现。目前解决这一问题的经典方法在相关系统规模上是计算上的限制，克服或减轻这一计算瓶颈将使重要模型系统的新模拟成为可能，对物理科学产生深远的影响。目前的量子硬件能在多大程度上实现这一目标仍然是一个悬而未决的问题。本项目通过对混合量子经典变分算法和最先进的经典算法的计算成本进行并排比较来解决这种可能性，该算法使用定义良好的不同难度的非随机哈密顿算子问题类。该评估的一个关键目标是了解混合方法和纯经典方法的优化景观之间的差异和相似之处，这可能有助于深入了解混合方法可以实现优势的条件。该研究结合了自旋玻璃理论、哈密顿复杂性、数值模拟和严格的基准测试经验，以评估在近期量子硬件上实现量子优势的可行性。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。

Quantum algorithms utilize the unique properties of quantum physics to perform computational tasks, and for certain tasks they can do so more efficiently than algorithms restricted to the laws of classical physics. Quantum computers that can implement such algorithms are now publicly available, but these devices remain limited in the size and length of computations they can perform, keeping quantum algorithms with proven quantum advantages out of reach. Hybrid algorithms that use both quantum and classical hardware have been proposed as one approach to address this challenge, and this project aims to study the viability of hybrid approaches in delivering a quantum advantage by performing a systematic computational cost comparison with state-of-the-art classical algorithms. If advantages are possible using near-term quantum computers, it would dramatically enhance our ability to understand and predict complex systems across the physical sciences. The project highlights the multi-disciplinary nature of quantum computing and will train students to have a diverse toolbox to tackle emerging challenges in the field. This approach is at the heart of the project's efforts to develop a new curriculum to prepare a 'quantum-ready' workforce to address the call of the National Quantum Initiative Act of 2018.The task of approximating the ground state of many-body non-stoquastic Hamiltonians, a class of quantum Hamiltonians that describes many relevant model systems such as fermionic and sign-problematic Hamiltonians, manifests itself in a range of disciplines, from high energy physics to quantum chemistry. Current classical approaches for tackling this problem are computationally prohibitive at relevant system sizes, and overcoming or mitigating this computational bottleneck would enable new simulations of important model systems with far-reaching impacts across the physical sciences. To what degree present quantum hardware can achieve this remains an open question. This project addresses this possibility by performing a side-by-side comparison of the computational cost of hybrid quantum-classical variational algorithms and state-of-the-art classical algorithms using well-defined problem classes of non-stoquastic Hamiltonians of varying difficulty. A key objective of this assessment is to understand the differences and similarities between the optimization landscapes of the hybrid and purely-classical approaches, which may provide insight into the conditions under which the hybrid approach can achieve an advantage. The research combines lessons from spin glass theory, Hamiltonian complexity, numerical simulations, and rigorous benchmarking experience in order to make an assessment of the viability of achieving a quantum advantage on near-term quantum hardware.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.