Scalable parameterized quantum circuits for machine learning face three obstacles: barren plateaus, no guarantee the learned function class is classically hard, and prohibitive circuit evaluations per gradient step. We propose the unitary brick-wall: a
k-particle fermionic architecture for nearest-neighbor hardware, combining Reconfigurable Beam Splitters with interleaved single-qubit phases and a non-Gaussian magic-state encoding, where
k trades classical hardness against training cost.
Trainable. The brick-wall has dynamical Lie algebra
u(n) and is surjective onto
U(n) via Givens rotations, enabling Haar initialization. Two-body correlator readouts achieve gradient variance
Θ(k3/n5), polynomial in
n throughout
n−2k=Ω(n).
Expressive. Hardness is controlled by
k: best-known classical sampling runs in time
2Θ(k), worst-case #P-hardness holds from
k=nε, and the average-case machinery of Fermion Sampling applies at
k=Θ(n). The sampler is input-dependent, so costs are paid per query: at our operating point
k=100 one query needs
∼1015 operations, beyond commercial query rates, and at
k=120 an exascale machine sustains under one query per second.
Efficient. A multi-layer parallel parameter-shift rule computes all
O(n2) gradients from
4kn circuit evaluations per step, a factor
n/k reduction over the standard rule's
4n2, growing linearly with
n at fixed
k.
The unitary butterfly targets all-to-all hardware, with
2logn layers of parallel gates and
(3/2)nlogn parameters, similar hardness guarantees, and
4klogn evaluations per step -- the same factor-
n/k reduction. Its trainability holds at two levels: absence of exponential barren plateaus is unconditional, while the sharp
Θ(k3/n5) rate needs a conjectured scalar comparison with the two-particle Haar second moment.
Quantum machine learning (QML) is promising for potential speedups and improvements in conventional machine learning (ML) tasks (e.g., classification/regression). The search for ideal QML models is an active research field. This includes identification of efficient classical-to-quantum data encoding scheme, construction of parametric quantum circuits (PQC) with optimal expressivity and entanglement capability, and efficient output decoding scheme to minimize the required number of measurements, to name a few. However, most of the empirical/numerical studies lack a clear path towards scalability. Any potential benefit observed in a simulated environment may diminish in practical applications due to the limitations of noisy quantum hardware (e.g., under decoherence, gate-errors, and crosstalk). We present a scalable quantum-classical hybrid deep neural network (DeepQMLP) architecture inspired by classical deep neural network architectures. In DeepQMLP, stacked shallow Quantum Neural Network (QNN) models mimic the hidden layers of a classical feed-forward multi-layer perceptron network. Each QNN layer produces a new and potentially rich representation of the input data for the next layer. This new representation can be tuned by the parameters of the circuit. Shallow QNN models experience less decoherence, gate errors, etc. which make them (and the network) more resilient to quantum noise. We present numerical studies on a variety of classification problems to show the trainability of DeepQMLP. We also show that DeepQMLP performs reasonably well on unseen data and exhibits greater resilience to noise over QNN models that use a deep quantum circuit. DeepQMLP provided up to 25.3% lower loss and 7.92% higher accuracy during inference under noise than QMLP.
Quantum neural networks (QNNs) based on parametrized quantum circuits are promising candidates for machine learning applications, yet many architectures lack clear connections to classical models, potentially limiting their ability to leverage established classical neural network techniques. We examine QNNs built from SWAP test circuits and discuss their equivalence to classical two-layer feedforward networks with quadratic activations under amplitude encoding. Evaluation on real-world and synthetic datasets shows that while this architecture learns many practical binary classification tasks, it has fundamental expressivity limitations: polynomial activation functions do not satisfy the universal approximation theorem, and we show analytically that the architecture cannot learn the parity check function beyond two dimensions, regardless of network size. To address this, we introduce generalized SWAP test circuits with multiple Fredkin gates sharing an ancilla, implementing product layers with polynomial activations of arbitrary even degree. This modification enables successful learning of parity check functions in arbitrary dimensions as well as binary n-spiral tasks, and we provide numerical evidence that the expressivity enhancement extends to alternative encoding schemes such as angle (Z) and ZZ feature maps. We validate the practical feasibility of our proposed architecture by implementing a classically pretrained instance on the IBM Torino quantum processor, achieving 84% classification accuracy on the three-dimensional parity check despite hardware noise. Our work establishes a framework for analyzing and enhancing QNN expressivity through correspondence with classical architectures, and demonstrates that SWAP test-based QNNs possess broad representational capacity relevant to both classical and potentially quantum learning tasks.
The increasing need for machine learning to run with less computer resources is causing quantum computing to be considered as a viable substitute for conventional computing. This paper presents a hybrid quantum-classical system that improves learning by means of a classical optimisation loop combined with parameterised quantum circuits. While conventional procedures handle parameter updates and convergence, the proposed approach stores and processes high-dimensional data using quantum variational circuits. Qiskit is used by us to construct this architecture and run it on conventional datasets like Iris, MNIST (binary), CIFAR-100 (subset), HIGGS, and GTEx (gene expression). Particularly for jobs with complex, nonlinear patterns, the findings indicate that the mixed approach is as accurate as or more accurate than classical baselines. Real quantum hardware also works well with the system; noise has no impact on its precision. This work demonstrates how combined quantum-classical learning models might circumvent hardware constraints and provide genuine quantum benefits for applications requiring large data processing.
Quantum machine learning (QML) offers a promising avenue for advancing representation learning in complex signal domains. In this study, we investigate the use of parameterised quantum circuits (PQCs) for speech emotion recognition (SER)-a challenging task due to the subtle temporal variations and overlapping affective states in vocal signals. We propose a hybrid quantum-classical architecture that integrates PQCs into a conventional convolutional neural network (CNN), leveraging quantum properties such as superposition and entanglement to enrich emotional feature representations. Experimental evaluations on three benchmark datasets IEMOCAP, RECOLA, and MSP-IMPROV-demonstrate that our hybrid model achieves improved classification performance relative to a purely classical CNN baseline, with over 50% reduction in trainable parameters. Furthermore, Adjusted Rand Index (ARI) analysis demonstrates that the quantum model yields feature representations with improved alignment to true emotion classes compared with the classical model, reinforcing the observed performance gains. This work provides early evidence of the potential for QML to enhance emotion recognition and lays the foundation for future quantum-enabled affective computing systems.
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.