Unitary quantum perceptron as efficient universal approximator

Abstract

We demonstrate that it is possible to implement a quantum perceptron with a sigmoid activation function as an efficient, reversible many-body unitary operation. When inserted in a neural network, the perceptron's response is parameterized by the potential exerted by other neurons. We prove that such a quantum neural network is a universal approximator of continuous functions, with at least the same power as classical neural networks. While engineering general perceptrons is a challenging control problem -also defined in this work-, the ubiquitous sigmoid-response neuron can be implemented as a quasi-adiabatic passage with an Ising model. In this construct, the scaling of resources is favorable with respect to the total network size and is dominated by the number of layers. We expect that our sigmoid perceptron will have applications also in quantum sensing or variational estimation of many-body Hamiltonians. arXiv:1801.00934v2 [quant-ph]

An artificial neuron implemented on an actual quantum processor

“…As it will be shown in the following, this choice proves simultaneously very simple and effective in producing the correct result. However, it should be noticed that refined threshold functions can be applied once the inner product information is stored on the ancilla [23][24][25]. We also notice that both parallel and anti-parallel i-w vectors produce an activation of the perceptron, while orthogonal vectors always result in the ancilla being measured in the state |0 a .…”

Training Optimization for Gate-Model Quantum Neural Networks

“…In [48], the authors defined the model of a universal quantum perceptron as efficient unitary approximators. The authors studied the implementation of a quantum perceptron with a sigmoid activation function as a reversible many-body unitary operation.…”

“…Gate-based quantum computers represent an implementable way to realize experimental quantum computations on near-term quantum computer architectures [1][2][3][4][5][6][7][8][9][10][11]19,20]. In a gate-model quantum computer, the transformations are realized by quantum gates, such that each quantum gate is represented by a unitary operation [12][13][14]16,23,24,[26][27][28]30,32,47,48]. An input quantum state is evolved through a sequence of unitary gates and the output state is then assessed by a measurement operator [12][13][14]16].…”

“…A quantum neural network (QNN) is formulated by a set of quantum operations and connections between the operations with a particular weight parameter [12,[39][40][41][46][47][48]. Gate-model QNNs refer to QNNs implemented on gate-model quantum computers [12].…”

Variational Quantum Circuit Model for Knowledge Graph Embedding

“…However, one has to note that WN18RR possesses the smallest number of average links per node. Thus, questions are: Whether the quantum circuit models are only practical for modeling large and sparse datasets due to the intrinsic linearity of the circuit models; and whether applying nonlinearity activation functions on the circuit models [20,21] can further improve the performance on other dense datasets? We leave these questions for future research.…”