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  • Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  (3)
  • Hangleiter, Dominik  (3)
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  • Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  (3)
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  • 1
    Online Resource
    Online Resource
    Semi-device-dependent blind quantum tomography
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2023
    In:  Quantum Vol. 7 ( 2023-07-11), p. 1053-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 7 ( 2023-07-11), p. 1053-
    Abstract: Extracting tomographic information about quantum states is a crucial task in the quest towards devising high-precision quantum devices. Current schemes typically require measurement devices for tomography that are a priori calibrated to high precision. Ironically, the accuracy of the measurement calibration is fundamentally limited by the accuracy of state preparation, establishing a vicious cycle. Here, we prove that this cycle can be broken and the dependence on the measurement device & apos;s calibration significantly relaxed. We show that exploiting the natural low-rank structure of quantum states of interest suffices to arrive at a highly scalable `blind & apos; tomography scheme with a classically efficient post-processing algorithm. We further improve the efficiency of our scheme by making use of the sparse structure of the calibrations. This is achieved by relaxing the blind quantum tomography problem to the de-mixing of a sparse sum of low-rank matrices. We prove that the proposed algorithm recovers a low-rank quantum state and the calibration provided that the measurement model exhibits a restricted isometry property. For generic measurements, we show that it requires a close-to-optimal number of measurement settings. Complementing these conceptual and mathematical insights, we numerically demonstrate that robust blind quantum tomography is possible in a practical setting inspired by an implementation of trapped ions.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2023-07-11-1053
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2023
    detail.hit.zdb_id: 2931392-2
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  • 2
    Online Resource
    Online Resource
    Anticoncentration theorems for schemes showing a quantum speedup
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2018
    In:  Quantum Vol. 2 ( 2018-05-22), p. 65-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 2 ( 2018-05-22), p. 65-
    Abstract: One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum speedup, or sometimes "quantum computational supremacy". The known schemes heavily rely on mathematical assumptions that are plausible but unproven, prominently results on anticoncentration of random prescriptions. In this work, we aim at closing the gap by proving two anticoncentration theorems and accompanying hardness results, one for circuit-based schemes, the other for quantum quench-type schemes for quantum simulations. Compared to the few other known such results, these results give rise to a number of comparably simple, physically meaningful and resource-economical schemes showing a quantum speedup in one and two spatial dimensions. At the heart of the analysis are tools of unitary designs and random circuits that allow us to conclude that universal random circuits anticoncentrate as well as an embedding of known circuit-based schemes in a 2D translation-invariant architecture.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2018-05-22-65
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2018
    detail.hit.zdb_id: 2931392-2
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  • 3
    Online Resource
    Online Resource
    On the Quantum versus Classical Learnability of Discrete Distributions
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2021
    In:  Quantum Vol. 5 ( 2021-03-23), p. 417-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 5 ( 2021-03-23), p. 417-
    Abstract: Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown discrete probability distribution, output with high probability an efficient algorithm for generating new samples from a good approximation of the original distribution. Our primary result is the explicit construction of a class of discrete probability distributions which, under the decisional Diffie-Hellman assumption, is provably not efficiently PAC learnable by a classical generative modelling algorithm, but for which we construct an efficient quantum learner. This class of distributions therefore provides a concrete example of a generative modelling problem for which quantum learners exhibit a provable advantage over classical learning algorithms. In addition, we discuss techniques for proving classical generative modelling hardness results, as well as the relationship between the PAC learnability of Boolean functions and the PAC learnability of discrete probability distributions.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2021-03-23-417
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2021
    detail.hit.zdb_id: 2931392-2
    Location Call Number Limitation Availability
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    Online Resource
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