Optimising quantum tomography via shadow inversion

• URL: http://arxiv.org/abs/2402.06727v4
• Date: Mon, 16 Sep 2024 14:22:51 GMT
• Title: Optimising quantum tomography via shadow inversion
• Authors: Andrea Caprotti, Joshua Morris, Borivoje Dakić,
• Abstract summary: This work introduces a novel technique for estimating such objects, leveraging an underutilised resource in the inversion map of classical shadows. A generalised framework for computing is given that may be adapted to a variety of near-term problems.
• Score: 0.393259574660092
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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