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Neural Network Quantum States
Neural Network Quantum States (NQS or NNQS) is a general class of Variational method (quantum mechanics), variational quantum states parameterized in terms of an artificial neural network. It was first introduced in 2017 by the physicists Giuseppe Carleo and Matthias Troyer to approximate wave functions of many-body quantum systems. Given a many-body quantum state , \Psi\rangle comprising N degrees of freedom and a choice of associated quantum numbers s_1 \ldots s_N , then an NQS parameterizes the wave-function amplitudes \langle s_1 \ldots s_N , \Psi; W \rangle = F(s_1 \ldots s_N; W), where F(s_1 \ldots s_N; W) is an artificial neural network of parameters (weights) W , N input variables ( 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. Learning the Ground-State Wave Function One common app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Method (quantum Mechanics)
In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals. The basis for this method is the variational principle. The method consists of choosing a "trial wavefunction" depending on one or more parameters, and finding the values of these parameters for which the expectation value of the energy is the lowest possible. The wavefunction obtained by fixing the parameters to such values is then an approximation to the ground state wavefunction, and the expectation value of the energy in that state is an upper bound to the ground state energy. The Hartree–Fock method, density matrix renormalization group, and Ritz method apply the variational method. Description Suppose we are given a Hilbert space and a Hermitian operator over it called the Hamiltonian H . Ignoring complications about continuous spectr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |