Mathematical Methods for Quantum Subspace Diagonalization Algorithms
Quantum mechanical systems form the foundational makeup of matter. Simulating a composition of many interacting quantum systems is classically intractable due to the long-range entanglement present across an exponentially large space of states. However, for many practical applications, such as in the optimization of lithium-ion batteries, and the development of novel materials for superconductors and fusion energy, the ability to simulate quantum many-body systems is of critical importance. Quantum computation has been proposed for the efficient simulation of quantum many-body systems, and a variety of quantum algorithms have been developed for solving the ground state problem. This project is focused on the quantum subspace diagonalization (QSD) algorithms that are a family of hybrid quantum-classical algorithms and may be suitable for deployment on near-term noisy quantum computers. The objective of this project is to develop mathematical methods for QSD algorithms; focusing on understanding and improving robustness, efficiency, and scalability of these algorithms. We acknowledge support from the U.S. Department of Energy, Office of Science, ASCR, DE-SC0023398.