We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator, e−iH^τ, as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorized electronic-structure Hamiltonian. To demonstrate the potential of the proposed rQKD algorithm, we provide numerical benchmarks for a variety of molecular systems with circuit-based statevector simulators, achieving ground state energy errors of less than 1~kcal~mol−1 with circuit depths orders of magnitude shallower than those required for low-rank deterministic Trotter-Suzuki decompositions.
@article{arxiv.2211.08274,
title = {A stochastic quantum Krylov protocol with double factorized Hamiltonians},
author = {Nicholas H. Stair and Cristian L. Cortes and Robert M. Parrish and Jeffrey Cohn and Mario Motta},
journal= {arXiv preprint arXiv:2211.08274},
year = {2023}
}