A stochastic quantum Krylov protocol with double factorized Hamiltonians

• URL: http://arxiv.org/abs/2211.08274v1
• Date: Tue, 15 Nov 2022 16:27:41 GMT
• Title: A stochastic quantum Krylov protocol with double factorized Hamiltonians
• Authors: Nicholas H. Stair, Cristian L. Cortes, Robert M. Parrish, Jeffrey Cohn, Mario Motta
• Abstract summary: 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, $e-ihatH tau$, as a linear combination of unitaries and subsequently uses a sampling procedure to reduce circuit depth requirements.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, $e^{-i\hat{H} \tau}$, 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.

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