Probably approximately correct quantum source coding

• URL: http://arxiv.org/abs/2112.06841v1
• Date: Mon, 13 Dec 2021 17:57:30 GMT
• Title: Probably approximately correct quantum source coding
• Authors: Armando Angrisani, Brian Coyle and Elham Kashefi
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Information-theoretic lower bounds are often encountered in several branches of computer science, including learning theory and cryptography. In the quantum setting, Holevo's and Nayak's bounds give an estimate of the amount of classical information that can be stored in a quantum state. Previous works have shown how to combine information-theoretic tools with a counting argument to lower bound the sample complexity of distribution-free quantum probably approximately correct (PAC) learning. In our work, we establish the notion of Probably Approximately Correct Source Coding and we show two novel applications in quantum learning theory and delegated quantum computation with a purely classical client. In particular, we provide a lower bound of the sample complexity of a quantum learner for arbitrary functions under the Zipf distribution, and we improve the security guarantees of a classically-driven delegation protocol for measurement-based quantum computation (MBQC).

Related papers

• Quantum delegated and federated learning via quantum homomorphic encryption [0.5939164722752263]
  We present a general framework that enables quantum delegated and federated learning with atheoretical data privacy guarantee. We show that learning and inference under this framework feature substantially lower communication complexity compared with schemes based on blind quantum computing.
  arXiv  Detail & Related papers  (2024-09-28T14:13:50Z)
• 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)
• Separable Power of Classical and Quantum Learning Protocols Through the Lens of No-Free-Lunch Theorem [70.42372213666553]
  The No-Free-Lunch (NFL) theorem quantifies problem- and data-independent generalization errors regardless of the optimization process. We categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2024-05-12T09:05:13Z)
• 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)
• Information-theoretic generalization bounds for learning from quantum data [5.0739329301140845]
  We propose a general mathematical formalism for describing quantum learning by training on classical-quantum data. We prove bounds on the expected generalization error of a quantum learner in terms of classical and quantum information-theoretic quantities. Our work lays a foundation for a unifying quantum information-theoretic perspective on quantum learning.
  arXiv  Detail & Related papers  (2023-11-09T17:21:38Z)
• Quantum variational learning for entanglement witnessing [0.0]
  This work focuses on the potential implementation of quantum algorithms allowing to properly classify quantum states defined over a single register of $n$ qubits. We exploit the notion of "entanglement witness", i.e., an operator whose expectation values allow to identify certain specific states as entangled. We made use of Quantum Neural Networks (QNNs) in order to successfully learn how to reproduce the action of an entanglement witness.
  arXiv  Detail & Related papers  (2022-05-20T20:14:28Z)
• Machine learning applications for noisy intermediate-scale quantum computers [0.0]
  We develop and study three quantum machine learning applications suitable for NISQ computers. These algorithms are variational in nature and use parameterised quantum circuits (PQCs) as the underlying quantum machine learning model. We propose a variational algorithm in the area of approximate quantum cloning, where the data becomes quantum in nature.
  arXiv  Detail & Related papers  (2022-05-19T09:26:57Z)
• A Theoretical Framework for Learning from Quantum Data [15.828697880068704]
  We propose a theoretical foundation for learning classical patterns from quantum data. We present a quantum counterpart of the well-known PAC framework. We establish upper bounds on the quantum sample complexity quantum concept classes.
  arXiv  Detail & Related papers  (2021-07-13T21:39:47Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Quantum Federated Learning with Quantum Data [87.49715898878858]
  Quantum machine learning (QML) has emerged as a promising field that leans on the developments in quantum computing to explore large complex machine learning problems. This paper proposes the first fully quantum federated learning framework that can operate over quantum data and, thus, share the learning of quantum circuit parameters in a decentralized manner.
  arXiv  Detail & Related papers  (2021-05-30T12:19:27Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)

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.