Optimising quantum tomography via shadow inversion

TL;DR

This paper presents a new quantum tomography method that enhances observable estimation accuracy by optimizing the shadow inversion process, significantly reducing sample complexity without extra costs.

Contribution

It introduces a generalized framework for optimizing shadow inversion in quantum tomography, achieving exponential sample complexity improvements and matching global measurement efficiencies.

Findings

Exponential reduction in sample complexity for local measurement strategies.

Feasible optimization of post-processing in local measurements.

Achieves efficiency comparable to global Clifford shadows.

Abstract

In quantum information theory, the accurate estimation of observables is pivotal for quantum information processing, playing a crucial role in compute and communication protocols. This work introduces a novel technique for estimating such objects, leveraging an underutilised resource in the inversion map of classical shadows that greatly refines the estimation cost of target observables without incurring any additional overhead. A generalised framework for computing and optimising additional degrees of freedom in the homogeneous space of the shadow inversion is given that may be adapted to a variety of near-term problems. In the special case of local measurement strategies we show feasible optimisation leading to an exponential separation in sample complexity versus the standard approach and in an exceptional case we give non-trivial examples of optimised post-processing for local measurements, achieving the same efficiency as the global Cliffords shadows.