Deep learning lattice gauge theories

• URL: http://arxiv.org/abs/2405.14830v1
• Date: Thu, 23 May 2024 17:46:49 GMT
• Title: Deep learning lattice gauge theories
• Authors: Anuj Apte, Anthony Ashmore, Clay Cordova, Tzu-Chen Huang,
• Abstract summary: We use neural network quantum states to accurately compute the ground state of lattice gauge theories in $2+1$ dimensions. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.

Related papers

• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation [39.20075231137991]
  We address the computation of the cumulative distribution function (CDF) of the spectral measure of the Hamiltonian. We introduce a signal processing technique for identifying the inflection point of the CDF. We conduct numerical experiments on a 26-qubit fully-connected Heisenberg model using a truncated density-matrix renormalization group (DMRG) initial state of low bond dimension.
  arXiv  Detail & Related papers  (2024-05-06T18:00:03Z)
• Hamiltonian truncation tensor networks for quantum field theories [42.2225785045544]
  We introduce a tensor network method for the classical simulation of continuous quantum field theories. The method is built on Hamiltonian truncation and tensor network techniques. One of the key developments is the exact construction of matrix product state representations of global projectors.
  arXiv  Detail & Related papers  (2023-12-19T19:00:02Z)
• A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theories [44.99833362998488]
  Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators. We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT. We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
  arXiv  Detail & Related papers  (2023-11-28T13:01:24Z)
• 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)
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories [0.0]
  We introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. Our proposal simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. Our work gives a new perspective for the application of tensor network methods to high-energy physics.
  arXiv  Detail & Related papers  (2023-04-05T15:49:20Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term [0.0]
  We show that the quantum theory is massless in the strong-coupling regime. We also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices.
  arXiv  Detail & Related papers  (2022-10-07T16:35:03Z)
• Tuning the Topological $\theta$-Angle in Cold-Atom Quantum Simulators of Gauge Theories [3.4075669047370125]
  We show how a tunable topological $theta$-term can be added to a prototype theory with gauge symmetry. The model can be realized experimentally in a single-species Bose--Hubbard model in an optical superlattice with three different spatial periods. This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.
  arXiv  Detail & Related papers  (2022-04-13T18:00:01Z)
• Topological fracton quantum phase transitions by tuning exact tensor network states [1.0753191494611891]
  Gapped fracton phases of matter generalize the concept of topological order. We employ an exact 3D quantum tensor-network approach to study a prototypical X cube fracton model.
  arXiv  Detail & Related papers  (2022-02-28T19:00:01Z)
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations [0.0]
  We derive the (3+1)D topological $theta$-term for Abelian and non-Abelian lattice gauge theories. We study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory.
  arXiv  Detail & Related papers  (2021-05-13T01:10:42Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)

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.