Quantum Data Compression and Quantum Cross Entropy

• URL: http://arxiv.org/abs/2106.13823v3
• Date: Sat, 11 Nov 2023 06:39:44 GMT
• Title: Quantum Data Compression and Quantum Cross Entropy
• Authors: Zhou Shangnan
• Abstract summary: We show that quantum cross entropy acts as the compression rate for sub-optimal quantum source coding. This reveals that quantum cross entropy can effectively serve as a loss function in quantum machine learning algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void persists. This paper addresses the gap by highlighting the quantum cross entropy, a pivotal counterpart to the classical cross entropy. We establish quantum cross entropy's role in quantum data compression, a fundamental machine learning task, by demonstrating that it acts as the compression rate for sub-optimal quantum source coding. Our approach involves a novel, universal quantum data compression protocol based on the quantum generalization of variable-length coding and the principle of quantum strong typicality. This reveals that quantum cross entropy can effectively serve as a loss function in quantum machine learning algorithms. Furthermore, we illustrate that the minimum of quantum cross entropy aligns with the von Neumann entropy, reinforcing its role as the optimal compression rate and underscoring its significance in advancing our understanding of quantum machine learning's theoretical framework.

Related papers

• The curse of random quantum data [62.24825255497622]
  We quantify the performances of quantum machine learning in the landscape of quantum data. We find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in qubits. Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks.
  arXiv  Detail & Related papers  (2024-08-19T12:18:07Z)
• Simulating quantum field theories on continuous-variable quantum computers [0.0]
  We develop and prove a method to reproduce the time evolution of quantum-mechanical states under arbitrary Hamiltonians. Our method centres on constructing an evolver-state, a specially prepared quantum state that induces the desired time-evolution on the target state. We propose a framework in which these methods can be extended to encode field theories in CVQC without discretising the field values.
  arXiv  Detail & Related papers  (2024-03-15T18:31:09Z)
• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory [10.708145906104205]
  We introduce the dissipaton-embedded quantum master equation in second quantization (DQME-SQ) This exact and compact theory offers two key advantages: representability by quantum circuits and universal applicability to any Gaussian environment. We demonstrate these capabilities through digital quantum simulations of non-Markovian dissipative dynamics in both bosonic and fermionic environments.
  arXiv  Detail & Related papers  (2024-01-30T18:46:30Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Unraveling the Mystery of Quantum Measurement with A New Space-Time Approach to Relativistic Quantum Mechanics [9.116661570248171]
  Quantum measurement is a fundamental concept in the field of quantum mechanics. Despite its significance, four fundamental issues continue to pose significant challenges to the broader application of quantum measurement. We employ a new space-time approach to relativistic quantum mechanics to address these issues systematically.
  arXiv  Detail & Related papers  (2023-06-01T13:25:08Z)
• Quantum Machine Learning: from physics to software engineering [58.720142291102135]
  We show how classical machine learning approach can help improve the facilities of quantum computers. We discuss how quantum algorithms and quantum computers may be useful for solving classical machine learning tasks.
  arXiv  Detail & Related papers  (2023-01-04T23:37:45Z)
• Unclonability and Quantum Cryptanalysis: From Foundations to Applications [0.0]
  Unclonability is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. We introduce new notions of unclonability in the quantum world, namely quantum physical unclonability. We discuss several applications of this new type of unclonability as a cryptographic resource for designing provably secure quantum protocols.
  arXiv  Detail & Related papers  (2022-10-31T17:57:09Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Quantum Cross Entropy and Maximum Likelihood Principle [0.0]
  Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. We define its quantum generalization, the quantum cross entropy, and investigate its relations with the quantum fidelity and the maximum likelihood principle.
  arXiv  Detail & Related papers  (2021-02-23T19:00:06Z)
• Quantum walk processes in quantum devices [55.41644538483948]
  We study how to represent quantum walk on a graph as a quantum circuit. Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
  arXiv  Detail & Related papers  (2020-12-28T18:04:16Z)
• 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.