Quantum expectation-value estimation by computational basis sampling

TL;DR

This paper introduces a quantum expectation-value estimation method using computational basis sampling, reducing measurement counts significantly for certain states, thereby potentially accelerating variational quantum algorithms.

Contribution

The paper presents a novel sampling-based algorithm that estimates expectation values with fewer measurements, especially effective for states concentrated in specific computational basis states.

Findings

Reduces measurement counts by several orders of magnitude for certain molecules.

Numerical comparisons show improved efficiency over existing methods.

Applicable to electronic ground state energy measurements in quantum chemistry.

Abstract

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision, such as chemical accuracy in the application to quantum chemistry computations. Here we propose an algorithm to estimate the expectation value based on its approximate expression as a weighted sum of classically-tractable matrix elements with some modulation, where the weight and modulation factors are evaluated by sampling appropriately prepared quantum states in the computational basis on quantum computers. Each of those states is prepared by applying a unitary transformation consisting of at most N CNOT gates, where N is the number of qubits, to a target quantum state whose expectation value is evaluated. Our algorithm is expected to require fewer measurements than conventional methods for a required statistical precision of the expectation value when the target quantum state is concentrated in particular computational basis states. We provide numerical comparisons of our method with existing ones for measuring electronic ground state energies (expectation values of electronic Hamiltonians for the lowest-energy states) of various small molecules. Numerical results show that our method can reduce the numbers of measurements to obtain the ground state energies for a targeted precision by several orders of magnitudes for molecules whose ground states are concentrated. Our results provide another route to measure expectation values of observables, which could accelerate the variational quantum algorithms.