Quantum computed moments correction to variational estimates

TL;DR

This paper introduces a quantum moments correction method that improves variational ground-state energy estimates by using quantum-computed Hamiltonian moments, reducing circuit depth and enhancing robustness on noisy quantum devices.

Contribution

The authors develop a novel approach that leverages quantum-computed Hamiltonian moments and the infinum theorem to correct variational estimates, demonstrated on 2D quantum magnetism models.

Findings

Infinum estimates outperform standard variational results.

Method shows stability against quantum noise and trial-state variations.

Effective on up to 25-qubit systems on IBM quantum hardware.

Abstract

The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor - Hamiltonian moments, $\langle H^n\rangle$. From these quantum computed moments, estimates of the ground-state energy are obtained using the "infinum" theorem from Lanczos cumulant expansions which manifestly correct the associated variational calculation. With system dynamics encoded in the moments the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5 $\times$ 5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infinum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.