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.
- Score: 0.0
- 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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