
Gauge equivariant neural networks for quantum lattice gauge theories
Gauge symmetries play a key role in physics appearing in areas such as q...
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FiniteState Classical Mechanics
Reversible lattice dynamics embody basic features of physics that govern...
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Emergent Quantumness in Neural Networks
It was recently shown that the Madelung equations, that is, a hydrodynam...
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Quantum Adiabatic Evolution for Global Optimization in Big Data
Big Data is characterized by Volume, Velocity, Veracity and Complexity. ...
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Generative Neural Samplers for the Quantum Heisenberg Chain
Generative neural samplers offer a complementary approach to Monte Carlo...
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A Correspondence Between Random Neural Networks and Statistical Field Theory
A number of recent papers have provided evidence that practical design q...
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Phases of twodimensional spinless lattice fermions with firstquantized deep neuralnetwork quantum states
Firstquantized deep neural network techniques are developed for analyzi...
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Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models
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 realtime dynamics for a variety of models. We exactly represent the ground and excited states of the 2D and 3D toric codes, and the Xcube 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.
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