Using the properties of quantum superposition, we propose a quantum classification algorithm to efficiently perform multi-class classification tasks, where the training data are loaded into parameterized operators which are applied to the basis of the quantum state in quantum circuit composed by \emph{sample register} and \emph{label register}, and the parameters of quantum gates are optimized by a hybrid quantum-classical method, which is composed of a trainable quantum circuit and a gradient-based classical optimizer. After several quantum-to-class repetitions, the quantum state is optimal that the state in \emph{sample register} is the same as that in \emph{label register}. %A structure of loading data many times is performed as a quantum version of neural network to improve the expression ability of quantum circuit. For a classification task of
L-class, the analysis shows that the space and time complexity of the quantum circuit are
O(L∗logL) and
O(logL), respectively. The numerical simulation results of 2-class task and 5-class task show that the proposed algorithm has a higher classification accuracy, faster convergence and higher expression ability. The classification accuracy and the speed of converging can also be improved by increasing the number times of applying multi-qubit controlled operators on the quantum circuit, especially for multiple classes classification.
We propose a Quantum Machine Learning (QML) framework that applies the core design principle of quantum algorithms–superposition, oracle, and interference–to accelerate training. Building on the structural analogy between feature extraction in foundational quantum algorithms and parameter optimization in QML, we reformulate the training process to leverage quantum parallelism: all training samples are encoded into a quantum superposition, processed through a parameterized quantum circuit, and classified via an interferometer module that implements quantum interference across the dataset. This architectural reformulation reduces the theoretical complexity of loss function evaluation from
O(N2) in conventional QML training to O ( N ), where N is the dataset size. Numerical simulations on multiple binary and multi-class classification datasets (with up to
N=128 samples) demonstrate that our method achieves classification accuracies comparable to conventional circuits while reducing the number of quantum circuit executions per cost function evaluation from N to 1. This represents a near N -fold reduction in quantum overhead per training iteration, reducing the required circuit executions without loss of accuracy. These results highlight the potential of quantum algorithmic design principles as a scalable pathway to efficient QML implementations.
We introduce here a supervised quantum machine learning algorithm for multi-class classification on NISQ architectures. A parametric quantum circuit is trained to output a specific bit string corresponding to the class of the input datapoint. We train and test it on an IBMq 5-qubit quantum computer and the algorithm shows good accuracy - compared to a classical machine learning model - for ternary classification of the Iris dataset and an extension of the XOR problem. Furthermore, we evaluate with simulations how the algorithm fares for a binary and a quaternary classification on resp. a known binary dataset and a synthetic dataset.