Learning ground states of gapped quantum Hamiltonians with Kernel Methods

• URL: http://arxiv.org/abs/2303.08902v2
• Date: Thu, 10 Aug 2023 06:44:54 GMT
• Title: Learning ground states of gapped quantum Hamiltonians with Kernel Methods
• Authors: Clemens Giuliani, Filippo Vicentini, Riccardo Rossi, Giuseppe Carleo
• Abstract summary: We introduce a statistical learning approach that makes the optimization trivial by using kernel methods. Our scheme is an approximate realization of the power method, where supervised learning is used to learn the next step of the power.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel methods. Our scheme is an approximate realization of the power method, where supervised learning is used to learn the next step of the power iteration. We show that the ground state properties of arbitrary gapped quantum hamiltonians can be reached with polynomial resources under the assumption that the supervised learning is efficient. Using kernel ridge regression, we provide numerical evidence that the learning assumption is verified by applying our scheme to find the ground states of several prototypical interacting many-body quantum systems, both in one and two dimensions, showing the flexibility of our approach.

Related papers

• Learning and Verifying Maximal Taylor-Neural Lyapunov functions [0.4910937238451484]
  We introduce a novel neural network architecture, termed Taylor-neural Lyapunov functions. This architecture encodes local approximations and extends them globally by leveraging neural networks to approximate the residuals. This work represents a significant advancement in control theory, with broad potential applications in the design of stable control systems and beyond.
  arXiv  Detail & Related papers  (2024-08-30T12:40:12Z)
• ShadowNet for Data-Centric Quantum System Learning [188.683909185536]
  We propose a data-centric learning paradigm combining the strength of neural-network protocols and classical shadows. Capitalizing on the generalization power of neural networks, this paradigm can be trained offline and excel at predicting previously unseen systems. We present the instantiation of our paradigm in quantum state tomography and direct fidelity estimation tasks and conduct numerical analysis up to 60 qubits.
  arXiv  Detail & Related papers  (2023-08-22T09:11:53Z)
• A Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design [1.03590082373586]
  In this work, we combine interpretable circuit designs with an effective basis approach to optimize a multiconfigurational bond wavefunction. Based on selected model systems, we show how this leads to explainable performance. We demonstrate that the developed methodology outperforms related methods in terms of the size of the effective basis as well as individual quantum resources for the involved circuits.
  arXiv  Detail & Related papers  (2023-02-21T13:23:51Z)
• Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics [96.9177297872723]
  We present a novel method for guaranteeing linear momentum in learned physics simulations. We enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional layers. In combination, the proposed method allows us to increase the physical accuracy of the learned simulator substantially.
  arXiv  Detail & Related papers  (2022-10-12T09:12:59Z)
• Modern applications of machine learning in quantum sciences [51.09906911582811]
  We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms. We discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.
  arXiv  Detail & Related papers  (2022-04-08T17:48:59Z)
• High-accuracy Hamiltonian learning via delocalized quantum state evolutions [0.0]
  We show that the accuracy of the learning process is maximized for states that are delocalized in the Hamiltonian eigenbasis. This implies that delocalization is a quantum resource for Hamiltonian learning, that can be exploited to select optimal initial states for learning algorithms.
  arXiv  Detail & Related papers  (2022-04-08T11:06:07Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• Certificates of quantum many-body properties assisted by machine learning [0.0]
  We propose a novel approach combining the power of relaxation techniques with deep reinforcement learning. We illustrate the viability of the method in the context of finding the ground state energy of many transfer systems. We provide tools to generalize the approach to other common applications in the field of quantum information processing.
  arXiv  Detail & Related papers  (2021-03-05T17:47:26Z)
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation [5.668795025564699]
  We present an approach for tackling open quantum system dynamics. We compactly represent quantum states with autoregressive transformer neural networks. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-09-11T18:00:00Z)
• Efficient construction of tensor-network representations of many-body Gaussian states [59.94347858883343]
  We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems.
  arXiv  Detail & Related papers  (2020-08-12T11:30:23Z)
• Quantum Geometric Machine Learning for Quantum Circuits and Control [78.50747042819503]
  We review and extend the application of deep learning to quantum geometric control problems. We demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
  arXiv  Detail & Related papers  (2020-06-19T19:12:14Z)

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.