Estimating quantum relative entropies on quantum computers

• URL: http://arxiv.org/abs/2501.07292v1
• Date: Mon, 13 Jan 2025 13:00:24 GMT
• Title: Estimating quantum relative entropies on quantum computers
• Authors: Yuchen Lu, Kun Fang,
• Abstract summary: We propose the first quantum algorithm for estimating quantum relative entropy and Petz R'enyi divergence from two unknown quantum states on quantum computers. This is achieved by combining quadrature approximations of relative entropies, variational representation of quantum f-divergences, and a new technique for parameterizing Hermitian operators. We validate our algorithm through numerical simulations, laying the groundwork for its future deployment on quantum hardware devices.
• Score: 5.552464954935806
• License:
• Abstract: Quantum relative entropy, a quantum generalization of the well-known Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science. Despite its importance, efficiently estimating quantum relative entropy between two quantum states on quantum computers remains a significant challenge. In this work, we propose the first quantum algorithm for estimating quantum relative entropy and Petz R\'{e}nyi divergence from two unknown quantum states on quantum computers, addressing open problems highlighted in [Phys. Rev. A 109, 032431 (2024)] and [IEEE Trans. Inf. Theory 70, 5653-5680 (2024)]. This is achieved by combining quadrature approximations of relative entropies, the variational representation of quantum f-divergences, and a new technique for parameterizing Hermitian polynomial operators to estimate their traces with quantum states. Notably, the circuit size of our algorithm is at most 2n+1 with n being the number of qubits in the quantum states and it is directly applicable to distributed scenarios, where quantum states to be compared are hosted on cross-platform quantum computers. We validate our algorithm through numerical simulations, laying the groundwork for its future deployment on quantum hardware devices.

Related papers

• Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization [0.6512657417859998]
  We introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces. We prove that our algorithm converges under working assumptions of Krylov quantum diagonalization and sparseness of ground state. We then show numerical investigations of lattice Hamiltonians, which indicate that our method can outperform existing Krylov quantum diagonalization in presence of shot noise.
  arXiv  Detail & Related papers  (2025-01-16T17:56:19Z)
• Quantum computing topological invariants of two-dimensional quantum matter [0.0]
  We present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. First algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. Second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits.
  arXiv  Detail & Related papers  (2024-04-09T06:22:50Z)
• Review on Quantum Walk Computing: Theory, Implementation, and Application [0.30723404270319693]
  The quantum walk is proposed as an important theoretical model for quantum computing. Quantum walks and their variety have been extensively studied for achieving beyond classical computing power. Recent progress has been achieved in implementing a wide variety of quantum walks and quantum walk applications.
  arXiv  Detail & Related papers  (2024-04-05T15:45:35Z)
• 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)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Optimal Stochastic Resource Allocation for Distributed Quantum Computing [50.809738453571015]
  We propose a resource allocation scheme for distributed quantum computing (DQC) based on programming to minimize the total deployment cost for quantum resources. The evaluation demonstrates the effectiveness and ability of the proposed scheme to balance the utilization of quantum computers and on-demand quantum computers.
  arXiv  Detail & Related papers  (2022-09-16T02:37:32Z)
• A thorough introduction to non-relativistic matrix mechanics in multi-qudit systems with a study on quantum entanglement and quantum quantifiers [0.0]
  This article provides a deep and abiding understanding of non-relativistic matrix mechanics. We derive and analyze the respective 1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density operators. We also address the fundamental concepts of quantum nondemolition measurements, quantum decoherence and, particularly, quantum entanglement.
  arXiv  Detail & Related papers  (2021-09-14T05:06:47Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• 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 Phases of Matter on a 256-Atom Programmable Quantum Simulator [41.74498230885008]
  We demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms. We benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation.
  arXiv  Detail & Related papers  (2020-12-22T19:00:04Z)

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.