Optimising quantum tomography via shadow inversion

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.

6 pages, 2 figures

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Cited by in corpus (5)

• Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation
• Low variance estimations of many observables with tensor networks and informationally-complete measurements
• Improving shadow estimation with locally-optimal dual frames
• Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates
• Classical Shadows with Improved Median-of-Means Estimation