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arXiv:2404.14785

Storage Capacity Evaluation of the Quantum Perceptron using the Replica Method

Mitsuru Urushibata, Masayuki Ohzeki

Published Apr 23, 2024• 0 citations

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.

DOI: 10.48550/arxiv.2404.14785

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Driven by growing computational power and algorithmic developments, machine learning methods have become valuable tools for analyzing vast amounts of data. Simultaneously, the fast technological progress of quantum information processing suggests employing quantum hardware for machine learning purposes. Recent works discuss different architectures of quantum perceptrons, but the abilities of such quantum devices remain debated. Here, we investigate the storage capacity of a particular quantum perceptron architecture by using statistical mechanics techniques and connect our analysis to the theory of classical spin glasses. Specifically, we focus on one concrete quantum perceptron model and explore its storage properties in the limit of a large number of inputs.

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