Non-binary artificial neuron with phase variation implemented on a quantum computer

TL;DR

The paper proposes a non-binary, phase-variational artificial neuron implemented on quantum hardware by encoding inputs and weights as phase-modulated amplitudes in $m=2^N$-dimensional quantum states. It presents two unitary construction strategies—phase-rotation blocks and Hypergraph States Generation Subroutine (HSGS)—to compute the inner product $|\langle \psi_w|\psi_i\rangle|^2 = \frac{|\vec w\cdot\vec i|^2}{m^2}$ and supports training via gradient descent with a cost $C = \frac{1}{2n}\sum_k (s_k - |\langle \psi_w|\psi_i\rangle|_k^2)^2$, updating weights by $\vec w' = \vec w - \eta \nabla_w C$. Experiments on IBM quantum hardware (N=2) compare the two methods and show small mean discrepancies, while simulations demonstrate successful learning for a 3-input sigmoid-like neuron; real devices reveal notable noise, limiting practical learning but highlighting the approach’s viability on near-term quantum devices.

Abstract

The first artificial quantum neuron models followed a similar path to classic models, as they work only with discrete values. Here we introduce an algorithm that generalizes the binary model manipulating the phase of complex numbers. We propose, test, and implement a neuron model that works with continuous values in a quantum computer. Through simulations, we demonstrate that our model may work in a hybrid training scheme utilizing gradient descent as a learning algorithm. This work represents another step in the direction of evaluation of the use of artificial neural networks efficiently implemented on near-term quantum devices.

Figures (7)

• Figure 1: General scheme of the quantum algorithm that calculates the inner product.
• Figure 2: Example of a circuit utilizing the rotation blocks algorithm.
• Figure 3: Example of one circuit utilizing the HSGS algorithm.
• Figure 4: Affinity $\times$ number of steps in the quantum device.
• Figure 5: Behavior of the cost function for the sigmoid in the simulator.