High-Dimensional Subspace Expansion Using Classical Shadows

TL;DR

This paper presents a classical shadow-based method that enhances ground state energy estimation by expanding the measurement subspace, achieving higher accuracy with limited quantum resources and robustness against noise.

Contribution

The authors introduce a stable, noise-resilient subspace expansion technique that improves ground state estimation from classical shadows without extra quantum resources.

Findings

Significant reduction in energy estimation errors, sometimes over tenfold.

Robust performance against coherent errors and gate noise.

Method outperforms direct energy estimation in various scenarios.

Abstract

We introduce a post-processing technique for classical shadow measurement data that enhances the precision of ground state estimation through high-dimensional subspace expansion; the dimensionality is only limited by the amount of classical post-processing resources rather than by quantum resources. Crucial steps of our approach are the efficient identification of useful observables from shadow data, followed by our regularised subspace expansion that is designed to be numerically stable even when using noisy data. We analytically investigate noise propagation within our method, and upper bound the statistical fluctuations due to the limited number of snapshots in classical shadows. In numerical simulations, our method can achieve a reduction in the energy estimation errors in many cases, sometimes by more than an order of magnitude. We also demonstrate that our performance improvements are robust against both coherent errors (bad initial state) and gate noise in the state-preparation circuits. Furthermore, performance is guaranteed to be at least as good - and in many cases better - than direct energy estimation without using additional quantum resources and the approach is thus a very natural alternative for estimating ground state energies directly from classical shadow data.