Fig. 3
From: Efficient representation of quantum many-body states with deep neural networks
Representation of universal quantum computational states by DBMs. a Gadget is a complex function of binary variables represented by port neurons, a short-hand notation after encapsulation of hidden neurons. b Two elementary gadgets for representation of quantum circuits: the Hadamard gadget with weight W H given by Eq. (1) and the phase gadget with weight W θ given by Eq. (3). c Two types of fusion rules for gadgets: rule I and rule II and their neural network representation. d Fusion with Hadamard or phase gadgets with rule I or rule II simulates application of three elementary quantum gates: the Hadamard gate, the phase gate, and the controlled phase flip gate, which together make universal quantum computation. The figure illustrates evolution of the wave function from step t to step t + 1. e Representation of an example quantum circuits with elementary gadgets. To represent circuits of depths T, we need to apply T steps of fusions with elementary gadgets, and gadget fusions in the same step can be applied in parallel. The identity gadget is a special phase gadget with θ = 0. After the last step of computation, port neurons become visible neurons to represent the index of physical qubits, and we get a DBM representation of the output state
