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  • Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  (11)
  • 2020-2024  (11)
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  • Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  (11)
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  • 2020-2024  (11)
Year
  • 1
    Online Resource
    Online Resource
    Encoding-dependent generalization bounds for parametrized quantum circuits
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2021
    In:  Quantum Vol. 5 ( 2021-11-17), p. 582-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 5 ( 2021-11-17), p. 582-
    Abstract: A large body of recent work has begun to explore the potential of parametrized quantum circuits (PQCs) as machine learning models, within the framework of hybrid quantum-classical optimization. In particular, theoretical guarantees on the out-of-sample performance of such models, in terms of generalization bounds, have emerged. However, none of these generalization bounds depend explicitly on how the classical input data is encoded into the PQC. We derive generalization bounds for PQC-based models that depend explicitly on the strategy used for data-encoding. These imply bounds on the performance of trained PQC-based models on unseen data. Moreover, our results facilitate the selection of optimal data-encoding strategies via structural risk minimization, a mathematically rigorous framework for model selection. We obtain our generalization bounds by bounding the complexity of PQC-based models as measured by the Rademacher complexity and the metric entropy, two complexity measures from statistical learning theory. To achieve this, we rely on a representation of PQC-based models via trigonometric functions. Our generalization bounds emphasize the importance of well-considered data-encoding strategies for PQC-based models.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2021-11-17-582
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2021
    detail.hit.zdb_id: 2931392-2
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  • 2
    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
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  • 3
    Online Resource
    Online Resource
    Correcting non-independent and non-identically distributed errors with surface codes
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2023
    In:  Quantum Vol. 7 ( 2023-09-26), p. 1123-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 7 ( 2023-09-26), p. 1123-
    Abstract: A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern multi-qubit devices are typically neither independent nor identical across qubits. In this work, we develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates when compared to the standard surface code. Furthermore, we study the behaviour of the tailored surface code under local two-qubit noise and show the role that code degeneracy plays in correcting such noise. The proposed methods do not require additional overhead in terms of the number of qubits or gates and use a standard matching decoder, hence come at no extra cost compared to the standard surface-code error correction.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2023-09-26-1123
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2023
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  • 4
    Online Resource
    Online Resource
    Stochastic gradient descent for hybrid quantum-classical optimization
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2020
    In:  Quantum Vol. 4 ( 2020-08-31), p. 314-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 4 ( 2020-08-31), p. 314-
    Abstract: Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore the consequences of the prior observation that estimation of these quantities on quantum hardware results in a form of s t o c h a s t i c gradient descent optimization. We formalize this notion, which allows us to show that in many relevant cases, including VQE, QAOA and certain quantum classifiers, estimating expectation values with k measurement outcomes results in optimization algorithms whose convergence properties can be rigorously well understood, for any value of k . In fact, even using single measurement outcomes for the estimation of expectation values is sufficient. Moreover, in many settings the required gradients can be expressed as linear combinations of expectation values -- originating, e.g., from a sum over local terms of a Hamiltonian, a parameter shift rule, or a sum over data-set instances -- and we show that in these cases k -shot expectation value estimation can be combined with sampling over terms of the linear combination, to obtain ``doubly stochastic'' gradient descent optimizers. For all algorithms we prove convergence guarantees, providing a framework for the derivation of rigorous optimization results in the context of near-term quantum devices. Additionally, we explore numerically these methods on benchmark VQE, QAOA and quantum-enhanced machine learning tasks and show that treating the stochastic settings as hyper-parameters allows for state-of-the-art results with significantly fewer circuit executions and measurements.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2020-08-31-314
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2020
    detail.hit.zdb_id: 2931392-2
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  • 5
    Online Resource
    Online Resource
    Randomizing multi-product formulas for Hamiltonian simulation
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2022
    In:  Quantum Vol. 6 ( 2022-09-19), p. 806-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 6 ( 2022-09-19), p. 806-
    Abstract: Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of quantum simulation algorithms are deterministic, a recent surge of ideas has shown that randomization can greatly benefit algorithmic performance. In this work, we introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multi-product formulas, as they are used for example in linear-combination-of-unitaries (LCU) algorithms or quantum error mitigation, on the other hand. In doing so, we propose a framework of randomized sampling that is expected to be useful for programmable quantum simulators and present two new multi-product formula algorithms tailored to it. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification required by the implementation of multi-product formulas using standard LCU methods, rendering it especially useful for early quantum computers used to estimate the dynamics of quantum systems instead of performing full-fledged quantum phase estimation. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth. To corroborate their functioning, we prove rigorous performance bounds as well as the concentration of the randomized sampling procedure. We demonstrate the functioning of the approach for several physically meaningful examples of Hamiltonians, including fermionic systems and the Sachdev–Ye–Kitaev model, for which the method provides a favorable scaling in the effort.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2022-09-19-806
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2022
    detail.hit.zdb_id: 2931392-2
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  • 6
    Online Resource
    Online Resource
    Anonymous conference key agreement in linear quantum networks
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2023
    In:  Quantum Vol. 7 ( 2023-09-21), p. 1117-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 7 ( 2023-09-21), p. 1117-
    Abstract: Sharing multi-partite quantum entanglement between parties allows for diverse secure communication tasks to be performed. Among them, conference key agreement (CKA) - an extension of key distribution to multiple parties - has received much attention recently. Interestingly, CKA can also be performed in a way that protects the identities of the participating parties, therefore providing a n o n y m i t y . In this work, we propose an anonymous CKA protocol for three parties that is implemented in a highly practical network setting. Specifically, a line of quantum repeater nodes is used to build a linear cluster state among all nodes, which is then used to anonymously establish a secret key between any three of them. The nodes need only share maximally entangled pairs with their neighbours, therefore avoiding the necessity of a central server sharing entangled states. This linear chain setup makes our protocol an excellent candidate for implementation in future quantum networks. We explicitly prove that our protocol protects the identities of the participants from one another and perform an analysis of the key rate in the finite regime, contributing to the quest of identifying feasible quantum communication tasks for network architectures beyond point-to-point.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2023-09-21-1117
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2023
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  • 7
    Online Resource
    Online Resource
    Non-Pauli topological stabilizer codes from twisted quantum doubles
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2021
    In:  Quantum Vol. 5 ( 2021-02-17), p. 398-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 5 ( 2021-02-17), p. 398-
    Abstract: It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group cohomological data sitting at the heart of these lattice models, we transmute the terms of these Hamiltonians into full-rank, pairwise commuting operators, defining commuting stabilizers. The resulting codes are defined by non-Pauli commuting stabilizers, with local systems that can either be qubits or higher dimensional quantum systems. Thus, this work establishes a new connection between condensed matter physics and quantum information theory, and constructs tools to systematically devise new topological quantum error correcting codes beyond toric or surface code models.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2021-02-17-398
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2021
    detail.hit.zdb_id: 2931392-2
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  • 8
    Online Resource
    Online Resource
    Tensor network models of AdS/qCFT
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2022
    In:  Quantum Vol. 6 ( 2022-02-03), p. 643-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 6 ( 2022-02-03), p. 643-
    Abstract: The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error correction, are constructed on regular time-slice discretizations of AdS. In this work, we show that the symmetries of these models are well suited for approximating CFT states, as their geometry enforces a discrete subgroup of conformal symmetries. Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity. We discuss holographic code states and their renormalization group flow as specific implementations of a qCFT with fractional central charges and argue that their behavior generalizes to a large class of existing and future models. Beyond approximating CFT properties, we show that these can be best understood as belonging to a paradigm of discrete holography.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2022-02-03-643
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2022
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  • 9
    Online Resource
    Online Resource
    By-passing fluctuation theorems
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2020
    In:  Quantum Vol. 4 ( 2020-02-20), p. 231-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 4 ( 2020-02-20), p. 231-
    Abstract: Fluctuation theorems impose constraints on possible work extraction probabilities in thermodynamical processes. These constraints are stronger than the usual second law, which is concerned only with average values. Here, we show that such constraints, expressed in the form of the Jarzysnki equality, can be by-passed if one allows for the use of catalysts---additional degrees of freedom that may become correlated with the system from which work is extracted, but whose reduced state remains unchanged so that they can be re-used. This violation can be achieved both for small systems but also for macroscopic many-body systems, and leads to positive work extraction per particle with finite probability from macroscopic states in equilibrium. In addition to studying such violations for a single system, we also discuss the scenario in which many parties use the same catalyst to induce local transitions. We show that there exist catalytic processes that lead to highly correlated work distributions, expected to have implications for stochastic and quantum thermodynamics.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2020-02-20-231
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2020
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  • 10
    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
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