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

量子模拟采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导致指数障碍，这将经典模拟的范围限制为小系统尺寸和短持续时间。原则上，使用量子模拟器可以避免这些障碍，但仍然存在挑战。已经有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，这些数字量子设备中会出现噪声和错误，限制了整体性能。这项研究将利用物理知识，如小系统尺寸或近似的结果，并采用技术来减轻噪声和误差的影响，以提高目前有噪声的量子器件模拟理论建模的量子系统的能力。 其中一些系统表现出非常规的对称性和拓扑性质，理解它们扩展了物理科学的进步。这些量子模拟技术可以潜在地导致在当前经典计算机难以实现的机制中实现物理模型的模拟。因此，该项目也有助于推进量子信息科学和技术，这是国家量子计划和后续路线图的战略方向。它还培训研究生和本科生，并为他们提供量子科学和技术职业发展所必需的技能，以及有助于材料和活动的量子教育水平适当的高，该项目将从量子模拟的角度研究各种物理模型，利用一些物理知识设计数字量子模拟方案，创建基态并研究经历时间演化的初始状态的动力学。将被考虑的物理模型包括自旋1/2 XXZ自旋模型，XXZ-Heisenberg模型的Half-phase，Affleck-Kennedy-Lieb-Tasaki模型，伊辛规范模型，和一个超对称模型。基态将近似使用变分ansatzes，这是基于物理动机的绝热连接从一个适当的简单的哈密顿量的最终哈密顿量。动力学将与离散的特罗特演化和本地观测和纠缠特性进行研究将被探讨。在基于云的量子计算机上的某些实现将通过噪声和错误缓解来执行，作为原理证明演示。结果将与理论和数值分析进行比较，以基准性能，并进一步用作改进实现的反馈。一些模型具有拓扑秩序（无论是内在的或受保护的），这些基态的实现，甚至近似，提供了一个潜在的游乐场来探测物质的非平凡相。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前沿技术的研究培训。该奖项将研究成果纳入斯托尼布鲁克大学新开发的量子信息科学与技术硕士课程的教材中，进一步加强了对高中学生和教师的量子教育。该奖项反映了NSF的法定使命，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 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.