Collaborative Research: EAGER-QSA: Variational Monte-Carlo-Inspired Quantum Algorithms for Many-Body Systems and Combinatorial Optimization

多体量子系统的模拟是一个极具挑战性的科学问题，它推动了现有和可预见的经典计算能力的极限。有效模拟这种系统的能力将为解决高温超导中长期存在的科学问题以及促进新药物和新材料的设计提供可能。大于一个空间维度的量子系统的通用求解器超出了经典硬件的范围，是开发量子资源的自然候选问题。该项目研究了变分蒙特卡罗模拟的最新进展如何用于激发新的量子模拟技术。该项目还将开展与研究工作相结合的教育、指导和外联活动。该项目将利用最近在变分量子算法、变分蒙特卡罗方法和量子信息几何领域之间形成的知识桥梁。它包括三个研究重点：费米子系统模拟、组合优化和量子信息几何。具体来说，该项目将设计变分量子算法，通过利用费米子系统的第一量子化和规范理论重新表述来避免非局部费米子-量子位映射。在组合优化问题的量子启发解算器中施加约束的有效方法将被探索。在经典数值分析工具的基础上，利用黎曼度规的高阶不变性来开发量子自然梯度的加速技术。由于物理状态根据薛定谔方程演化的实时演化过程至关重要，因此该项目将进一步研究量子自然梯度从虚数到实时的泛化。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。

Simulation of many-body quantum systems is an extremely challenging scientific problem that pushes the limits of existing and foreseeable classical computing capabilities. The ability to simulate such systems efficiently would open the possibility of resolving longstanding scientific questions in high-temperature superconductivity as well as facilitating the design of new drugs and materials. General-purpose solvers for quantum systems in greater than one spatial dimension are beyond the reach of classical hardware and are natural candidate problems for exploiting quantum resources. This project investigates how recent progress in variational Monte Carlo simulation can be used to inspire new quantum simulation techniques. The project will also undertake educational, mentoring, and outreach activities that are integrated with the research effort. This project will capitalize on recent intellectual bridges formed between the fields of variational quantum algorithms, variational Monte Carlo methods, and quantum information geometry. It consists of three research thrusts focused on fermionic systems simulation, combinatorial optimization, and quantum information geometry. Specifically, this project will design variational quantum algorithms that avoid nonlocal fermion-qubit mappings by exploiting first-quantized and gauge-theoretic reformulations of fermionic systems. Efficient methods for imposing constraints in quantum-inspired solvers for combinatorial optimization problems will be explored. Building upon classical numerical analysis tools, acceleration techniques for the quantum natural gradient will be developed by exploiting higher-order invariance of the Riemannian metric. Because the real-time evolution process by which physical states evolve according to the Schrodinger equation is of fundamental importance, the project will furthermore investigate generalization of the quantum natural gradient from imaginary to real time.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.