Convergence of sample-based quantum diagonalization on a variable-length cuprate chain

TL;DR

This paper investigates the convergence of sample-based quantum diagonalization (SQD) for simulating small copper oxide molecules on NISQ devices, highlighting hardware and algorithmic strategies to improve performance and the unexpected beneficial role of noise.

Contribution

It demonstrates how connectivity, expansion order, and basis choices affect SQD convergence and reveals noise can enhance energy accuracy on real quantum hardware.

Findings

All-to-all connectivity improves convergence.

Higher expansion order aids in overcoming sampling bottlenecks.

Noise on quantum hardware can unexpectedly improve energy estimates.

Abstract

Sample-based quantum diagonalization (SQD) is an algorithm for hybrid quantum-classical molecular simulation that has been of broad interest for application with noisy intermediate scale quantum (NISQ) devices. However, SQD does not always converge on a practical timescale. Here, we explore scaling of the algorithm for a variable-length molecule made up of 2 to 6 copper oxide plaquettes with a minimal molecular orbital basis. The results demonstrate that enabling all-to-all connectivity, instituting a higher expansion order for the SQD algorithm, and adopting a non-Hartree-Fock molecular orbital basis can all play significant roles in overcoming sampling bottlenecks, though with tradeoffs that need to be weighed against the capabilities of quantum and classical hardware. Additionally, we find that noise on a real quantum computer, the Quantinuum H2 trapped ion device, can improve energy convergence beyond expectations based on noise-free statevector simulations.