The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications

• URL: http://arxiv.org/abs/2212.00553v3
• Date: Wed, 6 Dec 2023 15:50:47 GMT
• Title: The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Authors: Isaac D. Smith, Marius Krumm, Lukas J. Fiderer, Hendrik Poulsen Nautrup and Hans J. Briegel
• Abstract summary: We formalise multi-round learning processes using a generalisation of classical-quantum states, called classical-quantum combs. We focus attention on an array of problems derived from measurement-based quantum computation (MBQC) and related applications.
• Score: 0.5999777817331317
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning a hidden property of a quantum system typically requires a series of interactions. In this work, we formalise such multi-round learning processes using a generalisation of classical-quantum states, called classical-quantum combs. Here, "classical" refers to a random variable encoding the hidden property to be learnt, and "quantum" refers to the quantum comb describing the behaviour of the system. The optimal strategy for learning the hidden property can be quantified by applying the comb min-entropy (Chiribella and Ebler, NJP, 2016) to classical-quantum combs. To demonstrate the power of this approach, we focus attention on an array of problems derived from measurement-based quantum computation (MBQC) and related applications. Specifically, we describe a known blind quantum computation (BQC) protocol using the combs formalism and thereby leverage the min-entropy to provide a proof of single-shot security for multiple rounds of the protocol, extending the existing result in the literature. Furthermore, we consider a range of operationally motivated examples related to the verification of a partially unknown MBQC device. These examples involve learning the features of the device necessary for its correct use, including learning its internal reference frame for measurement calibration. We also introduce a novel connection between MBQC and quantum causal models that arises in this context.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Hybrid Quantum-Classical Machine Learning with String Diagrams [49.1574468325115]
  This paper develops a formal framework for describing hybrid algorithms in terms of string diagrams. A notable feature of our string diagrams is the use of functor boxes, which correspond to a quantum-classical interfaces.
  arXiv  Detail & Related papers  (2024-07-04T06:37:16Z)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• Quantum Information Geometry and its classical aspect [0.0]
  This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations. We also demonstrate that for Gaussian states, classical analogs can be used to obtain the same mathematical results.
  arXiv  Detail & Related papers  (2023-02-21T21:39:02Z)
• Quantum advantage in temporally flat measurement-based quantum computation [0.0]
  We study the efficiency of measurement-based quantum computation with a completely flat temporal ordering of measurements. We identify a family of Boolean functions for which deterministic evaluation using non-adaptive MBQC is possible.
  arXiv  Detail & Related papers  (2022-12-07T14:34:56Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Variational Quantum Policy Gradients with an Application to Quantum Control [0.0]
  Quantum Machine Learning models are composed by Variational Quantum Circuits (VQCs) in a very natural way. In this work, we consider Policy Gradients using a hardware-efficient ansatz. We prove that the complexity of obtaining an epsilon-approximation of the gradient using quantum hardware scales only logarithmically with the number of parameters.
  arXiv  Detail & Related papers  (2022-03-20T16:14:49Z)
• Probably approximately correct quantum source coding [0.0]
  Holevo's and Nayak's bounds give an estimate of the amount of classical information that can be stored in a quantum state. We show two novel applications in quantum learning theory and delegated quantum computation with a purely classical client.
  arXiv  Detail & Related papers  (2021-12-13T17:57:30Z)
• Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
  "Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation. We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
  arXiv  Detail & Related papers  (2021-12-09T19:00:00Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.