A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

TL;DR

The paper presents a multireference quantum Krylov algorithm for simulating strongly correlated electrons, offering a low-cost alternative to quantum phase estimation that constructs target states from non-orthogonal Krylov bases.

Contribution

It introduces a novel multireference quantum Krylov method that avoids parameter optimization and efficiently constructs orthogonal reference bases for better quantum simulations.

Findings

Accurately predicts energies of H6, H8, and BeH2 with compact bases.

Provides an efficient algorithm for overlap and Hamiltonian matrix element evaluation.

Demonstrates the method's potential for strongly correlated electron systems.

Abstract

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H$_6$, H$_8$, and BeH$_2$ indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.