Implementation of Measurement Reduction for the Variational Quantum Eigensolver

TL;DR

This paper presents two circuit methods for reducing measurement steps in the variational quantum eigensolver, demonstrating their effectiveness through simulations and the first experimental implementation of LCU on quantum hardware.

Contribution

It introduces and compares two circuit constructions for measurement reduction in VQE, including the first experimental use of LCU on quantum hardware.

Findings

Both methods successfully reduce measurement overhead.

The rotation-based method outperforms LCU in noisy conditions.

First experimental demonstration of LCU on quantum hardware.

Abstract

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.