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Item type:Publication, Access status: without files , Stability of Classical Shadows under Gate-Dependent Noise(American Physical Society (APS), 2025-03-04); ; ; 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 Letter, we prove that any shadow estimation protocol involving Clifford unitaries is stable under gate-dependent noise for observables with bounded stabilizer norm—originally introduced in the context of simulating Clifford circuits. In contrast, we demonstrate with concrete examples that estimation of “magic” observables can lead to highly misleading results in the presence of miscalibration errors and a worst case bias scaling 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. Nevertheless, we guarantee the functioning of robust shadows for a more general noise setting than in previous works. On a technical level, we identify average noise channels that affect shadow estimators and allow for a more fine-rained control of noise-induced biases.Publicationtype: Journal Article24 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Closed-form analytic expressions for shadow estimation with brickwork circuits(2023-09); ; ; Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.Publicationtype: Journal Article56 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Compressive gate set tomographyFlexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. Obtaining such a detailed picture of the experimental implementation is associated with high requirements on the number of sequences and their design, making gate set tomography a challenging task even for only two qubits. In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them randomly. Such tomographic information is needed for the crucial task of dealing with coherent noise. To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem. We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics by using second-order geometrical optimization methods on the complex Stiefel manifold. Besides the reduction in sequences, we demonstrate numerically that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography. Therefore, it is more flexible than traditional approaches.Publicationtype: Journal ArticleScopus© Citations 6 46 119