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Item type:Publication, Access status: with files , Randomized quantum measurements beyond the Clifford group(2026); Randomized quantum measurements with the multi-qubit Clifford group can reconstruct many properties from the same experimental data. However, their implementation is beyond the capabilities of near-term devices. This thesis analyzes randomized protocols beyond group designs, with a focus on shadow estimation and randomized benchmarking. We provide an analytic characterization of shadow estimation with short random quantum circuits, and extend randomized benchmarking to photonic platforms to benchmark passive Gaussian transformations.Publicationtype: Doctoral Thesis39 31 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Classical certification of quantum gates under the dimension assumption(Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2025-08-08); ; ; The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not guarantee that only a correctly functioning quantum device can pass the test. We introduce a certification method for quantum gates tailored for a practical server-user scenario, where a classical user tests the results of exact quantum computations performed by a quantum server. This method is free from the systematic state preparation and measurement (SPAM) errors. For single-qubit gates, including those that form a universal set for single-qubit quantum computation, we demonstrate that our approach offers soundness guarantees based solely on the dimension assumption. Additionally, for a highly-relevant phase gate – which corresponds experimentally to a π/2-pulse – we prove that the method’s sample complexity scales as O(ε<sup>−1</sup>) relative to the average gate infidelity ε. By combining the SPAM-error-free and sound notion of certification with practical applicability, our approach paves the way for promising research into efficient and reliable certification methods for full-scale quantum computation.Publicationtype: Journal Article31 9 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Information causality as a tool for bounding the set of quantum correlations(American Physical Society (APS), 2024-10-18); ; Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously shown to imply the Uffink inequality that approximates the set of quantum correlations and rederives Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality. This result found limited generalizations due to the difficulty of deducing implications of the information causality principle on the set of nonlocal correlations. In this Letter, we present a simple technique for obtaining polynomial inequalities from information causality bounding the set of physical correlations in any bipartite Bell scenario. This result makes information causality an efficient tool for approximating the set of quantum correlations. To demonstrate our method, we derive a family of inequalities which nontrivially constrains the set of nonlocal correlations in Bell scenarios with binary outcomes and equal number of measurement settings. Finally, we propose an improved statement of the information causality principle and obtain a tighter constraint for the simplest Bell scenario that goes beyond the Uffink inequality and recovers a part of the boundary of the quantum set.Publicationtype: Journal Article26 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Classical certification of quantum computation under the dimension assumption(2024-01-30); ; ; Certification of quantum computing components can be crucial for quantum hardware improve- ments and the calibration of quantum algorithms. In this work, we propose an efficient method for certifying single-qubit quantum computation in a black-box scenario under the dimension as- sumption. The method is based on testing deterministic outcomes of quantum computation for predetermined gate sequences. Quantum gates are certified based on input-output correlations, with no auxiliary systems required. We show that a single-qubit universal gate set can be certified and analyze in detail certification of the S gate, for which the required sample complexity grows as O(e-1) with respect to the average gate infidelity e. Our approach takes a first step in bridg- ing the gap between strong notions of certification from self-testing and practically highly relevant approaches from quantum system characterization.Publicationtype: Preprint55 15 - 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: without files , Learning logical quantum noise in quantum error correction(2023-05-19); ; ; The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical post-processing. Therefore, it is desirable to measure only the information that is relevant for specific applications and develop protocols that require little additional effort. In this work, we focus on the characterization of quantum computers in the context of stabilizer quantum error correction. Our main result is that the logical error channel induced by Pauli noise can be estimated from syndrome data under minimal conditions. More precisely, we show that the estimation is possible as long as the code can correct the noise.Publicationtype: Journal Article87 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Distance-based resource quantification for sets of quantum measurements(Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2023-05-15); ; ; The advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum states have successfully been used to quantify resources like entanglement and coherence. Perhaps surprisingly, such a distance-based approach has not been adopted to study resources of quantum measurements, where other geometric quantifiers are used instead. Here, we define distance functions between sets of quantum measurements and show that they naturally induce resource monotones for convex resource theories of measurements. By focusing on a distance based on the diamond norm, we establish a hierarchy of measurement resources and derive analytical bounds on the incompatibility of any set of measurements. We show that these bounds are tight for certain projective measurements based on mutually unbiased bases and identify scenarios where different measurement resources attain the same value when quantified by our resource monotone. Our results provide a general framework to compare distance-based resources for sets of measurements and allow us to obtain limitations on Bell-type experiments.Publicationtype: Journal Article46 10 - 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 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Fast gradient estimation for variational quantum algorithms(2022-10-12); ; Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is a crucial bottleneck of the whole approach. We propose a new gradient estimation method to mitigate this measurement challenge and reduce the required measurement rounds. Within a Bayesian framework and based on the generalized parameter shift rule, we use prior information about the circuit to find an estimation strategy that minimizes expected statistical and systematic errors simultaneously. We demonstrate that this approach can significantly outperform traditional gradient estimation methods, reducing the required measurement rounds by up to an order of magnitude for a common QAOA setup. Our analysis also shows that an estimation via finite differences can outperform the parameter shift rule in terms of gradient accuracy for small and moderate measurement budgets.Publicationtype: Preprint51