A stochastic quantum Krylov protocol with double factorized Hamiltonians

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.

References in corpus (2)

• Compilation by stochastic Hamiltonian sparsification
• Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Cited by in corpus (8)

• Early Fault-Tolerant Quantum Computing
• Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers
• Sampling Error Analysis in Quantum Krylov Subspace Diagonalization
• Measurement-efficient quantum Krylov subspace diagonalisation
• Solving lattice gauge theories using the quantum Krylov algorithm and qubitization
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions