Variational Phase Estimation with Variational Fast Forwarding

TL;DR

This paper introduces a circuit-based implementation of Variational Quantum Phase Estimation (VQPE) for molecular systems and proposes Variational Fast Forwarding (VFF) to reduce quantum circuit depth, demonstrating effective Hamiltonian diagonalization.

Contribution

It presents a practical implementation of VQPE for molecules and introduces VFF to lower quantum circuit depth, maintaining efficiency even with approximate states.

Findings

VQPE successfully applied to H2, H3+, and H6 molecules.

VFF reduces quantum circuit depth while preserving diagonalization accuracy.

Approximate unitaries enable efficient Hamiltonian diagonalization with low fidelity states.

Abstract

Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained by a quantum computer. The recently proposed Variational Quantum Phase Estimation (VQPE) algorithm uses a basis of real time-evolved states, for which the energy eigenvalues can be obtained directly from the unitary matrix U = exp(-iHt), which can be computed with cost linear in the number of states used. In this paper, we report a circuit-based implementation of VQPE for arbitrary molecular systems and assess its performance and costs for the H2, H3+ and H6 molecules. We also propose using Variational Fast Forwarding (VFF) to decrease to quantum depth of time-evolution circuits for use in VQPE. We show that the approximation provides a good basis for Hamiltonian diagonalisation even when its fidelity to the true time evolved states is low. In the high fidelity case, we show that the approximate unitary U can be diagonalised instead, preserving the linear cost of exact VQPE.