Quantum annealing eigensolver as a NISQ era tool for probing strong correlation effects in quantum chemistry

TL;DR

This paper explores the quantum annealing eigensolver (QAE) as a promising NISQ-era alternative to the variational quantum eigensolver (VQE) for quantum chemistry, demonstrating its effectiveness in strongly correlated systems and analyzing its scaling properties.

Contribution

It introduces QAE as a viable NISQ-era quantum chemistry tool, providing numerical evidence and scaling analysis comparing it to VQE.

Findings

QAE achieves results within 1.2% of full CI for H4 molecule.

QAE shows promising scaling behaviour relative to VQE.

Numerical analysis of shot number, anneal time, and Lagrange multiplier effects.

Abstract

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is arguably the most popular noisy intermediate-scale quantum (NISQ) era approach to quantum chemistry. We consider the underexplored quantum annealing eigensolver (QAE) algorithm as a worthy alternative. We use a combination of numerical calculations for a system where strong correlation effects dominate, and conclusions drawn from our preliminary scaling analysis for QAE and VQE to make the case for QAE as a NISQ era contender to VQE for quantum chemistry. For the former, we pick the representative example of computing avoided crossings in the H4 molecule in a rectangular geometry, and demonstrate that we obtain results to within about 1.2% of the full configuration interaction value on the D-Wave Advantage system 4.1 hardware. We carry out analyses on the effect of the number of shots, anneal time, and the choice of Lagrange multiplier on our obtained results. Following our numerical results, we carry out a detailed yet preliminary analysis of the scaling behaviours of both the QAE and the VQE algorithms. We analyze the non-recurring and recurring costs involved in both the algorithms and arrive at their net scaling behaviours.