Digital Quantum Simulations of Ground States and Dynamics: Analysis and Realizations

量子模拟使用一个控制良好的量子系统来模拟另一个量子系统的低能量行为或动力学。人们已经认识到，使用经典计算机来模拟多体相互作用的量子系统将会遇到指数级的障碍，这将把经典模拟的范围限制在小系统规模和短持续时间内。使用量子模拟器原则上避免了这样的障碍，但仍然存在挑战。已经有了各种数字量子计算机的实现，它们比模拟量子模拟器更灵活和可编程。本研究的重点是数字量子模拟的方法。然而，目前的现状是，这些数字量子器件中存在噪声和错误，限制了整体性能。这项研究将利用物理知识，如来自小系统尺寸或近似的结果，并使用技术来减轻噪声和误差的影响，以增强当前有噪声的量子设备模拟理论模型量子系统的能力。其中一些系统表现出非常规的对称性和拓扑性，对它们的理解促进了物理科学的进步。这些量子模拟技术可能会在当前经典计算机难以实现的情况下实现物理模型的模拟。因此，该项目还有助于推进量子信息科学和技术，这是国家量子倡议和随后的路线图中的一个战略方向。它还培训研究生和本科生，使他们掌握在量子科学和技术方面的职业发展所必需的技能，并为适合高中生的量子教育材料和活动做出贡献。该项目将从量子模拟的角度研究各种物理模型，利用一些物理知识来设计数字量子模拟方案，以创建基态并研究经历时间演化的初始态的动力学。将考虑的物理模型包括自旋1/2的XXZ自旋模型、霍尔丹相的XXZ-Heisenberg模型、Affleck-Kennedy-Lieb-Tasaki模型、伊辛规范模型和超对称模型。基态将使用变分变换来近似，变分变换基于从适当的简单哈密顿量到最终哈密顿量的物理激励的绝热连接。我们将用离散化的Trotter演化来研究动力学，并探讨局域可观测量和纠缠性质。在基于云的量子计算机上的某些实现将被执行，作为原理证明的噪声和误差缓解。结果将与理论和数值分析进行比较，以对性能进行基准测试，并进一步用作改进实现的反馈。一些模型具有拓扑有序(要么是固有的，要么是对称保护的)，这些基态的实现，甚至是近似，为探索物质的非平凡相提供了一个潜在的游乐场。该项目的成果还将为在当前和未来的量子处理器上进行更大规模的量子模拟铺平道路。该项目为研究生和本科生提供量子模拟尖端技术方面的研究培训。它将研究成果纳入石溪大学新开发的量子信息科学与技术硕士项目的课程材料中，并进一步加强了针对高中生和教师的量子教育努力。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum simulation employs a well-controlled quantum system to emulate either the low-energy behavior or the dynamics of another quantum system. It has been recognized that using classical computers to simulate many-body interacting quantum systems will incur an exponential barrier that limits the scope of classical simulation to small system sizes and short duration. Using quantum simulators, in principle, avoids such obstacles, but there are still challenges. There have been realizations of various digital quantum computers and they are more flexible and programmable than analog quantum simulators. This research focuses on the approach of digital quantum simulations. However, the current status is that noise and errors occur in these digital quantum devices, limiting the overall performance. This research will exploit physics knowledge, such as results from small system sizes or approximations, and employ techniques to mitigate the effect of noise and errors so as to enhance the capability of current noisy quantum devices for simulating theoretically modeled quantum systems. Some of these systems demonstrate symmetry and topological properties that are not conventional and understanding them extends the progress of physical science. These quantum simulation techniques can potentially lead to realizations of simulations of physical models in a regime that is difficult for current classical computers. This project thus also contributes to advancing quantum information science and technology, a strategic direction in the National Quantum Initiative and subsequent roadmaps. It also trains graduate and undergraduate students and equips them with skills that will be essential for career advancement in quantum science and technology, as well as contributes to materials and activities for quantum education at the level appropriate for high-school students.This project will investigate various physical models from the perspective of quantum simulations that will exploit some physics knowledge to design digital quantum simulation schemes for creating ground states and studying the dynamics of an initial state undergoing time evolution. Physics models that will be considered include the spin-1/2 XXZ spin model, the XXZ-Heisenberg models for the Haldane phase, the Affleck-Kennedy-Lieb-Tasaki models, the Ising gauge model, and a supersymmetric one. Ground states will be approximated using variational ansatzes, which are based on physics-motivated adiabatic connection from an appropriate simple Hamiltonian to the final Hamiltonian. Dynamics will be studied with discretized Trotter evolution and local observables and entanglement properties will be probed. Certain realizations on cloud-based quantum computers will be performed with noise and error mitigation as proof-of-principle demonstration. The results will be compared with theoretical and numerical analysis to benchmark the performance and further used as feedback for improving implementations. Some models possess topological order (either intrinsic or symmetry-protected), and realizations of these ground states, even approximate, provide a potential playground to probe nontrivial phases of matter. The outcomes of this project will also pave the road for making larger-scale quantum simulations more feasible on current and future quantum processors. This project offers research training to graduate and undergraduate students in cutting-edge techniques in quantum simulations. It incorporates research findings in course materials for the newly developed master’s program in Quantum Information Science and Technology at Stony Brook University and further strengthens efforts in quantum education for high-school students and teachers.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.