Adaptive Pauli Shadows for Energy Estimation

TL;DR

This paper introduces Adaptive Pauli Shadows, a modified classical shadow technique that combines classical computing resources with locally-biased shadows to achieve state-of-the-art energy estimation accuracy for quantum Hamiltonians.

Contribution

It proposes a novel hybrid approach that enhances classical shadows with adaptivity, improving energy estimation accuracy without excessive classical resource costs.

Findings

Adaptive Pauli Shadows outperform previous methods in energy estimation accuracy.

Adding classical resources to locally-biased shadows improves results.

The method is practical and enhances quantum energy estimation techniques.

Abstract

Locally-biased classical shadows allow rapid estimation of energies of quantum Hamiltonians. Recently, derandomised classical shadows have emerged claiming to be even more accurate. This accuracy comes at a cost of introducing classical computing resources into the energy estimation procedure. This present note shows, by adding a fraction of this classical computing resource to the locally-biased classical shadows setting, that the modified algorithm, termed Adaptive Pauli Shadows is state-of-the-art for energy estimation.