Implementing An Artificial Quantum Perceptron

TL;DR

The paper addresses implementing a quantum perceptron to enable quantum-enhanced pattern classification. It presents a quantum architecture built from two unitaries that encode inputs and weights into states $|\psi_i\rangle$ and $|\psi_w\rangle$, with the output determined by the overlap $\langle \psi_w|\psi_i\rangle$, and it introduces a dataset-generation scheme via a fixed weight $w_0$ and a training loop that updates weights when misclassifications occur. The authors demonstrate pattern classification on simple inputs and report faster convergence relative to classical perceptrons, including experiments with up to four qubits. They discuss limitations such as using a single perceptron and omitting bias terms, and they propose extending the work to interconnected quantum networks and more complex datasets. The work provides a concrete, reproducible workflow (code available) for simulating and training a quantum perceptron on a quantum simulator.

Abstract

A Perceptron is a fundamental building block of a neural network. The flexibility and scalability of perceptron make it ubiquitous in building intelligent systems. Studies have shown the efficacy of a single neuron in making intelligent decisions. Here, we examined and compared two perceptrons with distinct mechanisms, and developed a quantum version of one of those perceptrons. As a part of this modeling, we implemented the quantum circuit for an artificial perception, generated a dataset, and simulated the training. Through these experiments, we show that there is an exponential growth advantage and test different qubit versions. Our findings show that this quantum model of an individual perceptron can be used as a pattern classifier. For the second type of model, we provide an understanding to design and simulate a spike-dependent quantum perceptron. Our code is available at https://github.com/ashutosh1919/quantum-perceptron

Figures (7)

• Figure 1: A classical perceptron used in deep learning systems. The perceptron takes multiple input values $\{i_0, i_1, \hdots, i_{n-1}\}$. Internally, it initializes random weight values $\{w_0, w_1, \hdots, w_{n-1}\}$ corresponding to each of the input values. The perceptron computes the dot product of the input and weight vector i.e. $\vec{i} \cdot \vec{w} = \sum_{j=0}^{n-1} i_jw_j$. This dot product result is passed through a non-linear sigmoid sigmoid_fn function which computes the probability. This probability can be used to compute the loss using the supervised label. The computed loss can then be used to train the perceptron by backpropagating gradients backpropagation and updating the weights.
• Figure 2: A Quantum Version of Perceptron.
• Figure 3: Generating dataset using single perceptron
• Figure 4: Training procedure for the generated data
• Figure 5: Simulation of perceptron on all combinations of input and weight values