Log In Sign Up

Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

by   Di Luo, et al.

Gauge invariance plays a crucial role in quantum mechanics from condensed matter physics to high energy physics. We develop an approach to constructing gauge invariant autoregressive neural networks for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries. We variationally optimize our gauge invariant autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We exactly represent the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We simulate the dynamics of the quantum link model of U(1) lattice gauge theory, obtain the phase diagram for the 2D ℤ_2 gauge theory, determine the phase transition and the central charge of the SU(2)_3 anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.


page 3

page 5

page 14

page 15


Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation

Gauge Theory plays a crucial role in many areas in science, including hi...

Gauge equivariant neural networks for quantum lattice gauge theories

Gauge symmetries play a key role in physics appearing in areas such as q...

Finite-State Classical Mechanics

Reversible lattice dynamics embody basic features of physics that govern...

Emergent Quantumness in Neural Networks

It was recently shown that the Madelung equations, that is, a hydrodynam...

Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it...

Quantum Adiabatic Evolution for Global Optimization in Big Data

Big Data is characterized by Volume, Velocity, Veracity and Complexity. ...

Simulating first-order phase transition with hierarchical autoregressive networks

We apply the Hierarchical Autoregressive Neural (HAN) network sampling a...