Revising measurement process in the variational quantum eigensolver: Is it possible to reduce the number of separately measured operators?

TL;DR

This paper proposes a novel partitioning method for the VQE measurement process that reduces the number of separately measured operators by grouping terms with simple eigenstates and applying multi-qubit transformations, demonstrated on small molecules.

Contribution

It introduces a new partitioning scheme for the VQE Hamiltonian that decreases measurement complexity by fewer parts and less entanglement, improving efficiency.

Findings

Significant reduction in measured terms for H2 and LiH molecules.

Enhanced measurement efficiency through new partitioning scheme.

Potential for scalable improvements in quantum chemistry simulations.

Abstract

Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit subspaces. The number of such parts rapidly grows with the size of the molecule, this increases the uncertainty in the measurement of the energy expectation value because elements from different parts need to be measured independently. To address this problem we introduce a more efficient partitioning of the qubit Hamiltonian using fewer parts that need to be measured separately. The new partitioning scheme is based on two ideas: 1) grouping terms into parts whose eigenstates have a single-qubit product structure, and 2) devising multi-qubit unitary transformations for the Hamiltonian or its parts to produce less entangled operators. The first condition allows the new parts to be measured in the number of involved qubit consequential one-particle measurements. Advantages of the new partitioning scheme resulting in several-fold reduction of separately measured terms are illustrated on the H2 and LiH problems.