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

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.