Neural network quantum states

Neural Network Quantum States (NQS or NNQS) is a general class of <a href="/facts/Variational_method_(quantum_mechanics)/vGHjImQT">variational</a> <a href="/facts/Quantum_states/7jbxd7Dx">quantum states</a> parameterized in terms of an <a href="/facts/Artificial_neural_network/6V1jMlkx">artificial neural network</a>. It was first introduced in 2017 by the <a href="/facts/Physicists/cQcgvSIm">physicists</a> Giuseppe Carleo and <a href="/facts/Matthias_Troyer/hCgaDmhG">Matthias Troyer</a> to approximate <a href="/facts/Wave_functions/KgM5ykjY">wave functions</a> of <a href="/facts/Many-body/n2rIxgwv">many-body</a> <a href="/facts/Quantum/4x5QTxGB">quantum</a> systems.
Given a many-body quantum state 
 
 
 
 
 |
 
 Ψ
 ⟩
 
 
 {\displaystyle |\Psi \rangle }
 
 comprising 
 
 
 
 N
 
 
 {\displaystyle N}
 
 degrees of freedom and a choice of associated quantum numbers 
 
 
 
 
 s
 
 1
 
 
 …
 
 s
 
 N
 
 
 
 
 {\displaystyle s_{1}\ldots s_{N}}
 
, then an NQS parameterizes the wave-function amplitudes

 
 
 
 ⟨
 
 s
 
 1
 
 
 …
 
 s
 
 N
 
 
 
 |
 
 Ψ
 ;
 W
 ⟩
 =
 F
 (
 
 s
 
 1
 
 
 …
 
 s
 
 N
 
 
 ;
 W
 )
 ,
 
 
 {\displaystyle \langle s_{1}\ldots s_{N}|\Psi ;W\rangle =F(s_{1}\ldots s_{N};W),}

where 
 
 
 
 F
 (
 
 s
 
 1
 
 
 …
 
 s
 
 N
 
 
 ;
 W
 )
 
 
 {\displaystyle F(s_{1}\ldots s_{N};W)}
 
 is an <a href="/facts/Artificial_neural_network/6V1jMlkx">artificial neural network</a> of parameters (weights) 
 
 
 
 W
 
 
 {\displaystyle W}
 
, 
 
 
 
 N
 
 
 {\displaystyle N}
 
 input variables (
 
 
 
 
 s
 
 1
 
 
 …
 
 s
 
 N
 
 
 
 
 {\displaystyle s_{1}\ldots s_{N}}
 
) and one complex-valued output corresponding to the wave-function amplitude.
This variational form is used in conjunction with specific stochastic learning approaches to approximate quantum states of interest.

Neural network quantum states open-in-new

Neural network quantum states