Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and scalability relative to the multi-layered, non-linear architectures of classical deep networks. We introduce superposed parameterised quantum circuits to overcome these limitations. By combining flip-flop quantum random-access memory with repeat-until-success protocols, a superposed parameterised quantum circuit embeds an exponential number of parameterised sub-models in a single circuit and induces polynomial activation functions through amplitude transformations and post-selection. We provide an analytic description of the architecture, showing how multiple parameter sets are trained in parallel while non-linear amplitude transformations broaden representational power beyond conventional quantum kernels. Numerical experiments underscore these advantages: on a 1D step-function regression a two-qubit superposed parameterised quantum circuit cuts the mean-squared error by three orders of magnitude versus a parameter-matched variational baseline; on a 2D star-shaped two-dimensional classification task, introducing a quadratic activation lifts accuracy to 81.4% and reduces run-to-run variance three-fold. These results position superposed parameterised quantum circuits as a hardware-efficient route toward deeper, more versatile parameterised quantum circuits capable of learning complex decision boundaries.

Speech Emotion Recognition (SER) is a complex and challenging task in human-computer interaction due to the intricate dependencies of features and the overlapping nature of emotional expressions conveyed through speech. Although traditional deep learning methods have shown effectiveness, they often struggle to capture subtle emotional variations and overlapping states. This paper introduces a hybrid classical-quantum framework that integrates Parameterised Quantum Circuits (PQCs) with conventional Convolutional Neural Network (CNN) architectures. By leveraging quantum properties such as superposition and entanglement, the proposed model enhances feature representation and captures complex dependencies more effectively than classical methods. Experimental evaluations conducted on benchmark datasets, including IEMOCAP, RECOLA, and MSP-Improv, demonstrate that the hybrid model achieves higher accuracy in both binary and multi-class emotion classification while significantly reducing the number of trainable parameters. While a few existing studies have explored the feasibility of using Quantum Circuits to reduce model complexity, none have successfully shown how they can enhance accuracy. This study is the first to demonstrate that Quantum Circuits has the potential to improve the accuracy of SER. The findings highlight the promise of QML to transform SER, suggesting a promising direction for future research and practical applications in emotion-aware systems.

Currently available quantum computers suffer from constraints including hardware noise and a limited number of qubits. As such, variational quantum algorithms that utilise a classical optimiser in order to train a parameterised quantum circuit have drawn significant attention for near-term practical applications of quantum technology. In this work, we take a probabilistic point of view and reformulate the classical optimisation as an approximation of a Bayesian posterior. The posterior is induced by combining the cost function to be minimised with a prior distribution over the parameters of the quantum circuit. We describe a dimension reduction strategy based on a maximum a posteriori point estimate with a Laplace prior. Experiments on the Quantinuum H1-2 computer show that the resulting circuits are faster to execute and less noisy than the circuits trained without the dimension reduction strategy. We subsequently describe a posterior sampling strategy based on stochastic gradient Langevin dynamics. Numerical simulations on three different problems show that the strategy is capable of generating samples from the full posterior and avoiding local optima.