Gauge equivariant neural networks for quantum lattice gauge theories

Abstract

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wavefunction for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining/deconfining phase transition of the Wilson loop order parameter.

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• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
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• Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Homogeneous vector bundles and $G$-equivariant convolutional neural networks
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• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
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• Accurate neural quantum states for interacting lattice bosons
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• Approximately-symmetric neural networks for quantum spin liquids
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• Geometric quantum thermodynamics: A fibre bundle approach
• Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
• Learning quantum symmetries with interactive quantum-classical variational algorithms
• Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice
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