Quantum Neural Estimation of Entropies

• URL: http://arxiv.org/abs/2307.01171v2
• Date: Mon, 5 Feb 2024 13:15:39 GMT
• Title: Quantum Neural Estimation of Entropies
• Authors: Ziv Goldfeld, Dhrumil Patel, Sreejith Sreekumar, and Mark M. Wilde
• Abstract summary: entropy measures quantify the amount of information and correlation present in a quantum system. We propose a variational quantum algorithm for estimating the von Neumann and R'enyi entropies, as well as the measured relative entropy and measured R'enyi relative entropy.
• Score: 20.12693323453867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and R\'enyi entropies, as well as the measured relative entropy and measured R\'enyi relative entropy. Our approach first parameterizes a variational formula for the measure of interest by a quantum circuit and a classical neural network, and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it as a promising approach for usage in downstream tasks.

Related papers

• Natural gradient and parameter estimation for quantum Boltzmann machines [3.9134031118910264]
  We establish formulas for the basic geometry of parameterized thermal states. We delineate quantum algorithms for estimating the values of these formulas. Results have applications in developing a natural gradient descent algorithm for quantum Boltzmann machine learning.
  arXiv  Detail & Related papers  (2024-10-31T15:56:06Z)
• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states. It is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• Disentanglement Provides a Unified Estimation for Quantum Entropies and Distance Measures [2.14566083603001]
  This paper introduces a unified approach using Disentangling Quantum Neural Networks (DEQNN) for estimating quantum entropies and distances. Our mathematical proof demonstrates that DEQNN can preserve quantum entropies and distances in smaller partial states. This method is scalable to an arbitrary number of quantum states and is particularly effective for less complex quantum systems.
  arXiv  Detail & Related papers  (2024-01-15T14:33:03Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Commutation simulator for open quantum dynamics [0.0]
  We propose an innovative method to investigate directly the properties of a time-dependent density operator $hatrho(t)$. We can directly compute the expectation value of the commutation relation and thus of the rate of change of $hatrho(t)$. A simple but important example is demonstrated in the single-qubit case and we discuss extension of the method for practical quantum simulation with many qubits.
  arXiv  Detail & Related papers  (2022-06-01T16:03:43Z)
• An Introduction to Quantum Machine Learning for Engineers [36.18344598412261]
  Quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. This book provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra.
  arXiv  Detail & Related papers  (2022-05-11T12:10:52Z)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• Quantum algorithms for estimating quantum entropies [6.211541620389987]
  We propose quantum algorithms to estimate the von Neumann and quantum $alpha$-R'enyi entropies of an fundamental quantum state. We also show how to efficiently construct the quantum entropy circuits for quantum entropy estimation using single copies of the input state.
  arXiv  Detail & Related papers  (2022-03-04T15:44:24Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule [0.0]
  We study the problem of estimating the gradient of the function to be optimized directly from quantum measurements. We derive a mathematically exact formula that provides an algorithm for estimating the gradient of any multi-qubit parametric quantum evolution. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy.
  arXiv  Detail & Related papers  (2020-05-20T18:24:11Z)

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.