Quantum Dynamics of Machine Learning

• URL: http://arxiv.org/abs/2407.19890v1
• Date: Sun, 7 Jul 2024 16:30:46 GMT
• Title: Quantum Dynamics of Machine Learning
• Authors: Peng Wang, Maimaitiniyazi Maimaitiabudula,
• Abstract summary: The quantum dynamic equation (QDE) of machine learning is obtained based on Schr"odinger equation and potential energy equivalence relationship. The relationship between quantum dynamics and thermodynamics is also established in this paper.
• Score: 3.567107449359775
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum dynamic equation (QDE) of machine learning is obtained based on Schr\"odinger equation and potential energy equivalence relationship. Through Wick rotation, the relationship between quantum dynamics and thermodynamics is also established in this paper. This equation reformulates the iterative process of machine learning into a time-dependent partial differential equation with a clear mathematical structure, offering a theoretical framework for investigating machine learning iterations through quantum and mathematical theories. Within this framework, the fundamental iterative process, the diffusion model, and the Softmax and Sigmoid functions are examined, validating the proposed quantum dynamics equations. This approach not only presents a rigorous theoretical foundation for machine learning but also holds promise for supporting the implementation of machine learning algorithms on quantum computers.

Related papers

• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential [0.0]
  The Schr"odinger equation is a fundamental equation in quantum mechanics. Over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems.
  arXiv  Detail & Related papers  (2024-08-04T13:11:52Z)
• Fourier Neural Differential Equations for learning Quantum Field Theories [57.11316818360655]
  A Quantum Field Theory is defined by its interaction Hamiltonian, and linked to experimental data by the scattering matrix. In this paper, NDE models are used to learn theory, Scalar-Yukawa theory and Scalar Quantum Electrodynamics. The interaction Hamiltonian of a theory can be extracted from network parameters.
  arXiv  Detail & Related papers  (2023-11-28T22:11:15Z)
• 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)
• TeD-Q: a tensor network enhanced distributed hybrid quantum machine learning framework [59.07246314484875]
  TeD-Q is an open-source software framework for quantum machine learning. It seamlessly integrates classical machine learning libraries with quantum simulators. It provides a graphical mode in which the quantum circuit and the training progress can be visualized in real-time.
  arXiv  Detail & Related papers  (2023-01-13T09:35:05Z)
• Fluctuation theorems for genuine quantum mechanical regimes [0.0]
  We look for corrections to work fluctuations theorems when the acting system is allowed to enter the quantum domain. For some specific processes, we derive several fluctuation theorems within both the quantum and classical statistical arenas.
  arXiv  Detail & Related papers  (2022-11-29T13:14:30Z)
• Machine learning for excitation energy transfer dynamics [0.0]
  We use the hierarchical equations of motion (HEOM) to simulate open quantum dynamics in the biological regime. We generate a set of time dependent observables that depict the coherent propagation of electronic excitations through the light harvesting complexes. We demonstrate the capability of convolutional neural networks to tackle this research problem.
  arXiv  Detail & Related papers  (2021-12-22T14:11:30Z)
• 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)
• 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 advantage for differential equation analysis [13.39145467249857]
  We show how the output of quantum differential equation solving can serve as the input for quantum machine learning. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods.
  arXiv  Detail & Related papers  (2020-10-29T17:19:04Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)
• Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit [0.0]
  We introduce a method that reconstructs the dynamical equation of open quantum systems, directly from a set of expectation values of selected observables. We benchmark our technique both by a simulation and experimentally, by measuring the dynamics of a trapped $88textSr+$ ion under spontaneous photon scattering.
  arXiv  Detail & Related papers  (2020-03-10T13:09:00Z)

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.