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学的独特性质来执行计算任务，对于某些任务，它们可以比局限于经典物理定律的算法更有效地执行。 可以实现这种算法的量子计算机现在已经公开可用，但这些设备在它们可以执行的计算的大小和长度方面仍然受到限制，从而使具有已证明的量子优势的量子算法无法实现。使用量子和经典硬件的混合算法已被提出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。 如果使用近期量子计算机的优势是可能的，它将大大提高我们理解和预测物理科学中复杂系统的能力。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，以应对该领域的新挑战。这种方法是该项目努力开发新课程的核心，以准备一个“量子就绪”的劳动力，以应对2018年国家量子倡议法案的要求。在一系列学科中表现出来，从高能物理到量子化学。目前解决这个问题的经典方法在相关系统规模上是计算上禁止的，克服或减轻这种计算瓶颈将使重要模型系统的新模拟在物理科学中具有深远的影响。目前的量子硬件能在多大程度上实现这一点仍然是一个悬而未决的问题。该项目解决了这种可能性，通过执行并行比较的计算成本的混合量子经典变分算法和国家的最先进的经典算法，使用定义良好的问题类的非随机哈密顿的不同难度。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，这可能会提供对混合方法可以实现优势的条件的洞察。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NSF的法定使命，并通过使用基金会的智力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.