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A Single-Gate, Single-Qubit Quantum Neural Network for All Boolean Logic Functions and the Iris Dataset

Mirza Nur Hidayat, Muhammad Faruq Nuruddinsyah

Published Nov 13, 2025• 0 citations
Publisher

Abstract

In this study, we demonstrate a single-qubit quantum neural network employing one rotation gate to implement all Boolean logic functions and to classify the Iris dataset. This rotation gate serves simultaneously as both a quantum feature map and an ansatz. The ansatz parameters are optimised using gradient descent, with the mean squared error as the loss function. Results confirm that the circuit successfully implements all Boolean logic functions and classifies the Iris dataset.

DOI
10.36227/techrxiv.176300561.14675355/v1

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In this study, we demonstrate a single-qubit quantum neural network employing one rotation gate to implement all Boolean logic functions and to classify the Iris dataset. This rotation gate serves simultaneously as both a quantum feature map and an ansatz. The ansatz parameters are optimised using gradient descent, with the mean squared error as the loss function. Results confirm that the circuit successfully implements all Boolean logic functions and classifies the Iris dataset.
In this paper, we implement a single-qubit quantum neural network to realise all Boolean logic functions. The circuit consists of four quantum rotation gates: two at the beginning as a quantum feature map of the dense angle encoding type, and the last two gates as the ansatz. The optimal parameters in the ansatz are determined using an iterative method, yielding expectation values that match the desired values and enabling Boolean output predictions. Our results demonstrate that the single-qubit parametric circuit, constructed with optimal parameter values obtained from iterative optimisation, is capable of implementing all Boolean logic functions.
This paper presents a hybrid quantum-classical machine learning model for classification tasks, integrating a 4-qubit quantum circuit with a classical neural network. The quantum circuit is designed to encode the features of the Iris dataset using angle embedding and entangling gates, thereby capturing complex feature relationships that are difficult for classical models alone. The model, which we term a Quantum Convolutional Neural Network (QCNN), was trained over 20 epochs, achievinga perfect 100% accuracy on the Iris dataset test set on 16 epoch. Our results demonstrate the potential of quantum-enhanced models in supervised learning tasks, particularly in efficiently encoding and processing data using quantum resources. We detail the quantum circuit design, parameterizedgate selection, and the integration of the quantum layer with classical neural network components.This work contributes to the growing body of research on hybrid quantum-classical models and theirapplicability to real-world datasets.
We report on a gate-based variational quantum classifier implemented with single photons and probabilistic gates, to emulate the standard quantum circuit model framework. We evaluate the expressive power of two deployable quantum neural networks (QNNs) by computing their effective dimension, a capacity measure grounded in a proven generalization-error bound, and compare them with classical artificial neural networks (ANNs) of equivalent trainable-parameter count. Supervised binary classification tasks are used to benchmark performance across photonic and superconducting QNNs, both of which exhibit superior converged (lower) cross-entropy loss and (higher) prediction accuracy relative to matched-parameter ANNs. For a nonlinearly separable task, our photonic QNN with a single pair of trainable parameters successfully converged (loss 0.04 and accuracy 100%), whereas the equivalent ANN failed to learn the decision boundary, saturating at random-guessing performance. We simulate photonic quantum circuits, training them on the XOR problem and a two-class Iris subset using gradient-free optimization, and assess their robustness to sampling errors under realistic noise processes including photon loss and phase-shifter imperfections. Circuits with comparatively high effective dimension were deployed remotely on a six-qubit photonic quantum processor, achieving classification accuracies of up to 100% in both online and offline learning settings. Notably, even the simplest QNN deployed, with just two trainable parameters, successfully solved tasks that classically require ANNs with at least quadruple the number of parameters, suggesting an emergent algorithmic advantage. Overall, these results demonstrate a clear proof-of-principle that gate-based QNNs can be realized and trained effectively on current photonic hardware, providing proof of algorithmic advantage on a gate-based photonic QNN.
In this work, we present a training method for a Fully Quantum Neural Network (FQNN) based entirely on quantum circuits. The model processes data exclusively through quantum operations, without incorporating classical neural network layers. In the proposed architecture, the roles of classical neurons and weights are assumed, respectively, by qubits and parameterized quantum gates: input features are encoded into quantum states of qubits, while the network weights correspond to the rotation angles of quantum gates that govern the system’s state evolution. The optimization of gate parameters is performed using directional gradient estimation, where gradients are numerically approximated via finite differences, eliminating the need for analytic derivation. The training objective is defined as the quantum-state fidelity, which measures the similarity between the network’s output state and a reference state representing the correct class. Experiments were conducted using the Qiskit AerSimulator, which allows for the accurate simulation of quantum circuits on a classical computer. The proposed approach was applied to the classification of the Iris dataset. The experimental results demonstrate that the FQNN is capable of effectively learning to distinguish between classes based on input features, achieving stable test accuracy across runs. These findings confirm the feasibility of constructing fully quantum classifiers without relying on hybrid quantum—classical architectures. The FQNN architecture consists of multiple quantum layers, each incorporating parameterized rotation operations and entanglement between qubits. The number of layers is determined by the ratio of quantum parameters (weights) to the number of input features. Each layer functions analogously to a hidden layer in a classical neural network, transforming the quantum-state space into a richer feature representation through controlled quantum operations. As a result, the network is capable of dynamically modeling dependencies among input features without the use of classical activation functions.
In this paper, we propose a simple neural net that requires only O(n log_2k) number of qubits and O(nk) quantum gates: Here, N is the number of input parameters, and k is the number of weights applied to these parameters in the proposed neural net. We describe the network in terms of a quantum circuit, and then draw its equivalent classical neural net which involves O(k^n) nodes in the hidden layer. Then, we show that the network uses a periodic activation function of cosine values of the linear combinations of the inputs and weights. The backpropagation is described through the gradient descent, and then iris and breast cancer datasets are used for the simulations. The numerical results indicate the network can be used in machine learning problems and it may provide exponential speedup over the same structured classical neural net.