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

TL;DR

The paper addresses the challenge of non-ideal training sets in quantum perceptrons and proposes a unitary-weights approach to enable one-iteration learning. It constructs a total weight from training data and enforces unitarity through a decomposition step, allowing implementation of universal quantum gates. The authors validate the method with gates including H, S, T, CNOT, Toffoli, and Fredkin, as well as composite gates. Compared to prior quantum perceptron models, the method claims higher availability for non-ideal training sets and broader gate applicability, with potential for scalable quantum neural networks.

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.

Figures (5)

• Figure 1: Quantum circuit for evaluating $f(0)$ and $f(1)$ simultaneously.
• Figure 2: The classical perceptron model.
• Figure 3: Quantum circuit of the Toffoli gate.
• Figure 4: Quantum circuit of the Fredkin gate.
• Figure 5: Quantum circuit of the composite gate.