Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows

TL;DR

This paper introduces a locally-optimized classical shadow estimator for quantum Hamiltonian measurements that reduces variance without increasing circuit depth, improving the efficiency of variational quantum algorithms.

Contribution

It presents a novel locally-biased classical shadow estimator tailored for molecular Hamiltonians, enhancing measurement precision without additional circuit complexity.

Findings

Significant variance reduction in Hamiltonian expectation estimates.

Estimator does not increase quantum circuit depth.

Effective for molecular Hamiltonians of varying sizes.

Abstract

Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer. We propose a novel estimator for this task, which is locally optimised with knowledge of the Hamiltonian and a classical approximation to the underlying quantum state. Our estimator is based on the concept of classical shadows of a quantum state, and has the important property of not adding to the circuit depth for the state preparation. We test its performance numerically for molecular Hamiltonians of increasing size, finding a sizable reduction in variance with respect to current measurement protocols that do not increase circuit depths.