Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver

TL;DR

This paper introduces a method to reduce measurement variance in quantum chemistry simulations by optimally repartitioning fermionic fragments, significantly decreasing the number of measurements needed in the variational quantum eigensolver.

Contribution

It presents a novel approach to lower fragment variances by exploiting fermionic operator properties, enhancing measurement efficiency in quantum electronic structure calculations.

Findings

Repartitioning fragments reduces measurement count by over tenfold.

The method maintains accurate Hamiltonian expectation values.

Numerical tests confirm improved efficiency across multiple molecules.

Abstract

Measuring the expectation value of the molecular electronic Hamiltonian is one of the challenging parts of the variational quantum eigensolver. A widely used strategy is to express the Hamiltonian as a sum of measurable fragments using fermionic operator algebra. Such fragments have an advantage of conserving molecular symmetries that can be used for error mitigation. The number of measurements required to obtain the Hamiltonian expectation value is proportional to a sum of fragment variances. Here, we introduce a new method for lowering the fragments' variances by exploiting flexibility in the fragments' form. Due to idempotency of the occupation number operators, some parts of two-electron fragments can be turned into one-electron fragments, which then can be partially collected in a purely one-electron fragment. This repartitioning does not affect the expectation value of the Hamiltonian but has non-vanishing contributions to the variance of each fragment. The proposed method finds the optimal repartitioning by employing variances estimated using a classically efficient proxy for the quantum wavefunction. Numerical tests on several molecules show that repartitioning of one-electron terms lowers the number of measurements by more than an order of magnitude.