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QI: Fachverband Quanteninformation
QI 24: Verification and Benchmarking of Quantum Systems
QI 24.9: Talk
Thursday, March 21, 2024, 12:00–12:15, HFT-TA 441
Stability of classical shadows under gate-dependent noise — •Raphael Brieger1,3, Markus Heinrich1, Ingo Roth2, and Martin Kliesch1,3 — 1Heinrich Heine University Düsseldorf, Faculty of Mathematics and Natural Sciences, Germany — 2Quantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE — 3Hamburg University of Technology, Institute for Quantum Inspired and Quantum Optimization, Germany
Expectation values of observables are routinely estimated using so-called classical shadows---the outcomes of randomized bases measurements on a repeatedly prepared quantum state. In order to trust the accuracy of shadow estimation in practice, it is crucial to understand the behavior of the estimators under realistic noise. In this work, we prove that any shadow estimation proto- col involving Clifford unitaries is stable under gate-dependent noise for observables with bounded stabilizer norm---originally introduced in the context of simulating Clifford circuits. For these ob- servables, we also show that the protocol's sample complexity is essentially identical to the noiseless case. In contrast, we demonstrate that estimation of "magic" observables can suffer from a bias that scales exponentially in the system size. We further find that so-called robust shadows, aiming at mitigating noise, can introduce a large bias in the presence of gate-dependent noise compared to unmitigated classical shadows. On a technical level, we identify average noise channels that affect shadow estimators and allow for a more fine-grained control of noise-induced biases.
Keywords: Estimation; Shadows; Randomized; Measurements; Noise