Excitation Amplitude Sampling for Low Variance Electronic Structure on Quantum Computers

TL;DR

This paper introduces a sampling method combining classical heuristics and shadow tomography to efficiently extract electronic structure information on quantum computers, significantly reducing measurement shots and noise sensitivity.

Contribution

It proposes a novel excitation amplitude sampling technique that reduces measurement requirements and enhances noise resilience in quantum electronic structure calculations.

Findings

Achieved nearly two orders of magnitude reduction in shots needed for energy estimation.

Demonstrated linear scaling with system size for the proposed protocol.

Showed increased noise tolerance on real quantum devices.

Abstract

We combine classical heuristics with partial shadow tomography to enable efficient protocols for extracting information from correlated ab initio electronic systems encoded on quantum devices. By proposing the use of a correlation energy functional and sampling of a polynomial set of excitation amplitudes of the quantum state, we can demonstrate an almost two order of magnitude reduction in required number of shots for a given statistical error in the energy estimate, as well as observing a linear scaling to accessible system sizes. Furthermore, we find a high-degree of noise resilience of these estimators on real quantum devices, with up to an order of magnitude increase in the tolerated noise compared to traditional techniques. While these approaches are expected to break down asymptotically, we find strong evidence that these large system arguments do not prevent algorithmic advantage from these simple protocols in many systems of interest. We further extend this to consider the extraction of beyond-energetic properties by mapping to a coupled cluster surrogate model, as well as a natural combination within a quantum embedding framework. This embedding framework avoids the unstable self-consistent requirements of previous approaches, enabling application of quantum solvers to realistic correlated materials science, where we demonstrate the volume-dependence of the spin gap of Nickel Oxide.