Storage Capacity Evaluation of the Quantum Perceptron using the Replica Method

TL;DR

This paper evaluates the storage capacity of a quantum perceptron implemented on a quantum circuit, demonstrating it has higher capacity than classical perceptrons due to its nonlinear activation function, using the replica method.

Contribution

It introduces a method to assess quantum perceptron capacity via the replica method, revealing enhanced capacity compared to classical models.

Findings

Quantum perceptron has larger capacity than classical perceptron.

The replica method effectively evaluates quantum model capacity.

Quantum perceptron exhibits a highly nonlinear activation function.

Abstract

We investigate a quantum perceptron implemented on a quantum circuit using a repeat until method. We evaluate this from the perspective of capacity, one of the performance evaluation measures for perceptions. We assess a Gardner volume, defined as a volume of coefficients of the perceptron that can correctly classify given training examples using the replica method. The model is defined on the quantum circuit. Nevertheless, it is straightforward to assess the capacity using the replica method, which is a standard method in classical statistical mechanics. The reason why we can solve our model by the replica method is the repeat until method, in which we focus on the output of the measurements of the quantum circuit. We find that the capacity of a quantum perceptron is larger than that of a classical perceptron since the quantum one is simple but effectively falls into a highly nonlinear form of the activation function.