Gauge-equivariant graph neural networks embed non-Abelian local symmetries directly into message passing for lattice gauge theories, enabling learning of nonlocal observables from local operations.
Wiese, Ultracold quantum gases and lattice sys- tems: quantum simulation of lattice gauge theories, An- nalen der Physik525, 777 (2013)
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A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.
Quantum simulation on trapped ions shows that a plaquette term in a 2+1D U(1) gauge theory enables string propagation in the plane and extended matter creation, realizing genuine two-dimensional dynamics.
Deterministic QITE made gauge-invariant via commuting Pauli operators achieves relative error below 0.1 percent for ground-state preparation in 2+1D Z2 LGT on systems up to twelve plaquettes, as shown by tensor-network simulations benchmarked against DMRG.
citing papers explorer
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Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
Gauge-equivariant graph neural networks embed non-Abelian local symmetries directly into message passing for lattice gauge theories, enabling learning of nonlocal observables from local operations.
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Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.