A Unitary Weights Based One-Iteration Quantum Perceptron Algorithm for Non-Ideal Training Sets

TL;DR

This paper introduces a novel quantum perceptron algorithm that uses unitary weights to efficiently learn from non-ideal training sets in a single iteration, demonstrating high accuracy and applicability.

Contribution

The paper presents a new quantum perceptron algorithm based on unitary weights that effectively handles non-ideal training sets with one iteration, improving upon previous methods.

Findings

Accurately implements arbitrary quantum gates within one iteration

Demonstrates advantages in applicability, accuracy, and availability over existing algorithms

Validates with quantum gates and composite quantum gates

Abstract

In order to solve the problem of non-ideal training sets (i.e., the less-complete or over-complete sets) and implement one-iteration learning, a novel efficient quantum perceptron algorithm based on unitary weights is proposed, where the singular value decomposition of the total weight matrix from the training set is calculated to make the weight matrix to be unitary. The example validation of quantum gates {H, S, T, CNOT, Toffoli, Fredkin} shows that our algorithm can accurately implement arbitrary quantum gates within one iteration. The performance comparison between our algorithm and other quantum perceptron algorithms demonstrates the advantages of our algorithm in terms of applicability, accuracy, and availability. For further validating the applicability of our algorithm, a quantum composite gate which consists of several basic quantum gates is also illustrated.