Parametrized constant-depth quantum neuron : framework, conception, and applications

Abstract

Quantum computing has been revolutionizing the development of algorithms, which in- cludes remarkable advances in artificial neural networks. The exploration of inherently quantum phenomena holds the promise of transcending classical computing. However, only noisy intermediate-scale quantum devices are available currently. To demonstrate advantages in this quantum era, the development of quantum algorithms needs to satisfy several software requirements due to the insufficiency of quantum computing resources. In this research, we propose a kernel-based framework of quantum neurons that not only contemplates existing quantum neurons but also makes room to define countless others, including quantum neurons that comply with the present hardware restrictions. For exam- ple, we propose here a quantum neuron that is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. Existing quantum neurons are im- plemented by exponentially expensive circuits, even using complex multi-qubit gates. We improve the proposed quantum neuron through a parametrization that can change its ac- tivation function shape in order to fit underlying patterns that existing quantum neurons cannot fit. As an initial demonstration, we show the proposed quantum neuron producing optimal solutions for six classification problems that an existing quantum neuron can solve only two of them. After, we benchmark classical and quantum neurons in several classifi- cation problems. As a result, in the majority of the cases, the proposed quantum neuron is the best over all neurons, which solidly confirms its superiority. The parametrization offers flexibility to not only fit a wide range of problems but also to optimize the margin between classes, at least better than the classical neurons and existing quantum ones. In light of those advantages, this research paves the way to develop quantum neural networks that can demonstrate a practical quantum advantage in the current quantum era already.