Applications and resource reductions in measurement-based variational quantum eigensolvers

TL;DR

This paper explores measurement-based quantum algorithms, focusing on resource reduction techniques for variational quantum eigensolvers, demonstrating their effectiveness on photonic systems with promising near-term applications.

Contribution

It introduces resource-efficient measurement-based implementations of VQE and shows they can be shallow, highly expressive, and feasible with current technology.

Findings

Measurement-based VQE can be resource-efficient and shallow.

Native measurement-based gates outperform standard gates in this context.

The approach is promising for near-term photonic quantum computing.

Abstract

We discuss the procedure for obtaining measurement-based implementations of quantum algorithms given by quantum circuit diagrams and how to reduce the required resources needed for a given measurement-based computation. This forms the foundation for quantum computing on photonic systems in the near term. To demonstrate that these ideas are well grounded we present three different problems which are solved by employing a measurement-based implementation of the variational quantum eigensolver algorithm (MBVQE). We show that by utilising native measurement-based gates rather than standard gates, such as the standard CNOT, MBQCs may be obtained that are both shallow and have simple connectivity while simultaneously exhibiting a large expressibility. We conclude that MBVQE has promising prospects for resource states that are not far from what is already available today.