Simulation of quantum many
-body physics\, such as looking for ground state properties and real time
dynamics\, plays an important role in the study of condensed matter physic
s\, high energy physics and quantum information science. The recent advanc
ement of machine learning provides new opportunities for tackling challeng
es in simulating quantum many-body physics. In this talk\, I will first di
scuss a class of wave functions via neural network transformation\, neural
network backflow\, \; which can fulfill the anti-symmetry property an
d capture the correlation and the sign structure for strongly-interacting
fermionic physics. Next\, I will talk about recent progress of simulating
continuum quantum field theories with neural quantum field state [2]\, and
lattice gauge theories such as 2+1D quantum electrodynamics with finite d
ensity dynamical fermions using gauge symmetric neural networks [3\,4]. Fi
nally\, I will present a neural network representation based on positive-v
alue-operator measurements for quantum circuit and open quantum system dyn
amics simulation [5].

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\nReference:

\n[1] Di Luo\, Bryan
K. Clark\, Backflow Transformations via Neural Networks for Quantum Many-B
ody WaveFunctions\, Phys. Rev. Lett. 122\, 226401.

\n[2] John M. Mart
yn\, Khadijeh Najafi\, Di Luo\, Variational Neural-Network Ansatz for Cont
inuum Quantum Field Theory\, https://arxiv.org/abs/2212.00
782.

\n[3] \; Di Luo\, Giuseppe Carleo\, Bryan K. Clark\, Jam
es Stokes\, Gauge Equivariant Neural Networks for Quantum Lattice Gauge Th
eories\, Phys. Rev. Lett. 127\, 276402.

\n[4] Zhuo Chen&dagger\;\, Di
Luo&dagger\;\, Kaiwen Hu\, Bryan K. Clark\, Simulating 2+1D Lattice Quant
um Electrodynamics at Finite Density with Neural Flow Wavefunctions\, https://arxiv.org/abs/2212.06835.

\n[5] Di Luo&dagger
\;\, Zhuo Chen&dagger\;\, Juan Carrasquilla\, Bryan K. Clark\, Autoregress
ive Neural Network for Simulating Open Quantum Systems via a Probabilistic
Formulation\, Phys. Rev. Lett. 128\, 090501.

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