Robust shadow estimation

Abstract

Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many such tasks, near-term devices are prone to noise that will generally reduce the accuracy of such estimates. Here we show how to mitigate errors in the shadow estimation protocol recently proposed by Huang, Kueng, and Preskill. By adding an experimentally friendly calibration stage to the standard shadow estimation scheme, our robust shadow estimation algorithm can obtain an unbiased estimate of the classical shadow of a quantum system and hence extract many useful properties in a sample-efficient and noise-resilient manner given only minimal assumptions on the experimental conditions. We give rigorous bounds on the sample complexity of our protocol and demonstrate its performance with several numerical experiments.

39 pages, 10 figures. We add numerical experiments with practical gate-dependent noise models to justify the wide application of our robust protocol

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• Probing many-body quantum chaos with quantum simulators
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• Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors
• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
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• Optimising shadow tomography with generalised measurements
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• Hamiltonian-Driven Shadow Tomography of Quantum States
• Operator relaxation and the optimal depth of classical shadows
• Classical shadows with Pauli-invariant unitary ensembles
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• Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices
• Robust estimation of the Quantum Fisher Information on a quantum processor
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• Closed-form analytic expressions for shadow estimation with brickwork circuits
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• Efficient Characterizations of Multiphoton States with an Ultra-thin Optical Device
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• Estimating many properties of a quantum state via quantum reservoir processing
• Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation
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• Quantum noise modeling through Reinforcement Learning
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• Mitigation of correlated readout errors without randomized measurements
• Holographic Classical Shadow Tomography
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