Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum algorithms. In this article, we propose a framework that builds quantum neurons based on kernel machines, where the quantum neurons differ from each other by their feature space mappings. Besides contemplating previous quantum neurons, our generalized framework has the capacity to instantiate other feature mappings that allow us to solve real problems better. Under that framework, we present a neuron that applies a tensor-product feature mapping to an exponentially larger space. The proposed neuron is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. The previous quantum neuron applies a phase-based feature mapping with an exponentially expensive circuit implementation, even using multiqubit gates. Additionally, the proposed neuron has parameters that can change its activation function shape. Here, we show the activation function shape of each quantum neuron. It turns out that parametrization allows the proposed neuron to optimally fit underlying patterns that the existing neuron cannot fit, as demonstrated in the nonlinear toy classification problems addressed here. The feasibility of those quantum neuron solutions is also contemplated in the demonstration through executions on a quantum simulator. Finally, we compare those kernel-based quantum neurons in the problem of handwritten digit recognition, where the performances of quantum neurons that implement classical activation functions are also contrasted here. The repeated evidence of the parametrization potential achieved in real-life problems allows concluding that this work provides a quantum neuron with improved discriminative abilities. As a consequence, the generalized framework of quantum neurons can contribute toward practical quantum advantage.
Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum algorithms. In this article, we propose a framework that builds quantum neurons based on kernel machines, where the quantum neurons differ from each other by their feature space mappings. Besides contemplating previous quantum neurons, our generalized framework has the capacity to instantiate other feature mappings that allow us to solve real problems better. Under that framework, we present a neuron that applies a tensor-product feature mapping to an exponentially larger space. The proposed neuron is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. The previous quantum neuron applies a phase-based feature mapping with an exponentially expensive circuit implementation, even using multiqubit gates. Additionally, the proposed neuron has parameters that can change its activation function shape. Here, we show the activation function shape of each quantum neuron. It turns out that parametrization allows the proposed neuron to optimally fit underlying patterns that the existing neuron cannot fit, as demonstrated in the nonlinear toy classification problems addressed here. The feasibility of those quantum neuron solutions is also contemplated in the demonstration through executions on a quantum simulator. Finally, we compare those kernel-based quantum neurons in the problem of handwritten digit recognition, where the performances of quantum neurons that implement classical activation functions are also contrasted here. The repeated evidence of the parametrization potential achieved in real-life problems allows concluding that this work provides a quantum neuron with improved discriminative abilities. As a consequence, the generalized framework of quantum neurons can contribute toward practical quantum advantage.
Quantum computing has been revolutionizing the development of algorithms, which in- cludes remarkable advances in artificial neural networks. The exploration of inherently quantum phenomena holds the promise of transcending classical computing. However, only noisy intermediate-scale quantum devices are available currently. To demonstrate advantages in this quantum era, the development of quantum algorithms needs to satisfy several software requirements due to the insufficiency of quantum computing resources. In this research, we propose a kernel-based framework of quantum neurons that not only contemplates existing quantum neurons but also makes room to define countless others, including quantum neurons that comply with the present hardware restrictions. For exam- ple, we propose here a quantum neuron that is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. Existing quantum neurons are im- plemented by exponentially expensive circuits, even using complex multi-qubit gates. We improve the proposed quantum neuron through a parametrization that can change its ac- tivation function shape in order to fit underlying patterns that existing quantum neurons cannot fit. As an initial demonstration, we show the proposed quantum neuron producing optimal solutions for six classification problems that an existing quantum neuron can solve only two of them. After, we benchmark classical and quantum neurons in several classifi- cation problems. As a result, in the majority of the cases, the proposed quantum neuron is the best over all neurons, which solidly confirms its superiority. The parametrization offers flexibility to not only fit a wide range of problems but also to optimize the margin between classes, at least better than the classical neurons and existing quantum ones. In light of those advantages, this research paves the way to develop quantum neural networks that can demonstrate a practical quantum advantage in the current quantum era already.
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.
The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate theoretical research into practical solutions. Previous studies have shown the advantages of quantum algorithms on artificially generated datasets, and initial experiments with small binary classification problems have yielded comparable outcomes to classical algorithms. However, it is essential to investigate the potential quantum advantage using real-world data. To the best of our knowledge, this study is the first to propose the utilization of quantum systems to classify neuron morphologies, thereby enhancing our understanding of the performance of automatic multiclass neuron classification using quantum kernel methods. We examined the influence of feature engineering on classification accuracy and found that quantum kernel methods achieved similar performance to classical methods, with certain advantages observed in various configurations.
Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model for quantum neural computing using (classically controlled) single-qubit operations and measurements on real-world quantum systems with naturally occurring environment-induced decoherence, which greatly reduces the difficulties of physical implementations. Our model circumvents the problem that the state-space size grows exponentially with the number of neurons, thereby greatly reducing memory requirements and allowing for fast optimization with traditional optimization algorithms. We benchmark our model for handwritten digit recognition and other nonlinear classification tasks. The results show that our model has an amazing nonlinear classification ability and robustness to noise. Furthermore, our model allows quantum computing to be applied in a wider context and inspires the earlier development of a quantum neural computer than standard quantum computers.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.
Abstract Quantum kernel methods have emerged as a powerful paradigm for extending classical machine learning into high-dimensional quantum Hilbert spaces, offering potential advantages in complex, nonlinear pattern recognition. However, their performance on near-term quantum devices remains constrained by circuit depth, noise sensitivity, and suboptimal parameterization of quantum feature maps. This paper introduces an Adaptive Quantum Kernel Optimization (AQKO) framework that integrates circuit-level adaptability, hybrid optimization, and regularization to enhance both expressivity and robustness in quantum kernel learning. The proposed method employs Adaptive Quantum Feature Maps (AQFM) that dynamically adjust rotation and phase parameters through a hybrid gradient-based optimization routine, reducing overfitting and improving generalization. Furthermore, a regularized quantum kernel objective is formulated to stabilize eigenvalue spectra under Noisy Intermediate-Scale Quantum (NISQ) conditions. Extensive experiments on nonlinear benchmark datasets — including Moons , Circles , and Iris — demonstrate that AQKO achieves up to 8.5% higher classification accuracy and 32% lower circuit depth compared to static quantum kernels. Hardware validation using IBM’s ibmq_quito device confirms AQKO’s resilience under depolarizing noise (p = 0.02) with a 41% error mitigation efficiency gain. These findings highlight AQKO’s potential as a scalable and noise-tolerant foundation for real-world quantum-enhanced learning, bridging the gap between theoretical quantum kernel models and practical NISQ implementations.