Neural network representations of quantum many-body states

Approximating Ground States by Neural Network Quantum States

“…To start with, let us recall the concept and the related properties of NNQSs introduced in [20]. Let Q 1 , Q 2 , .…”

“…In this paper, based on the NNQSs introduced in [20], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian H. The remainder part of this paper are organized as follows. In Section 2, we recall the concept and the related properties of NNQSs introduced in [20].…”

“…In this paper, based on the NNQSs introduced in [20], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian H. The remainder part of this paper are organized as follows. In Section 2, we recall the concept and the related properties of NNQSs introduced in [20]. In Section 3, we explore the NNQS approximation of the unknown ground state of a given Hamiltonian H in terms of the best relative error and consider the influence of sum, tensor product, local unitary of Hamiltonian on the best relative error.…”

Approximating Ground States by Neural Network Quantum States

“…Despite such exciting developments, it is unknown whether a general state can be expressed by neural networks efficiently. Recently, by generalizing the idea of [ 26 ], we introduced in [ 38 ] neural networks quantum states (NNQSs) based on general input observables and explored some related properties about NNQSs. Secondly, we established some necessary and sufficient conditions for a general graph state to be represented by an NNQS.…”

“…In this paper, based on the NNQSs introduced in [ 38 ], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian H . The remaining part of this paper is organized as follows.…”