EAGER: QSA: Approximating the Ground States of Non-Stoquastic Hamiltonians Using the Variational Quantum Eigensolver

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.