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 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 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.
Abstract Quantum computing is conceived as a promising and powerful next-generation platform for information processing and it has been shown that it could bring significant accelerations to certain tasks, compared to its classical counterparts. With recent advances in noisy intermediate-scale quantum (NISQ) devices, we can process classical data from real-world problems using hybrid quantum systems. In this work, we investigate the critical problem of designing a gate-based hybrid quantum neuron under NISQ constraints to enable the construction of scalable hybrid quantum deep neural networks (HQDNNs). We explore and characterize diverse quantum circuits for hybrid quantum neurons and discuss related critical components of HQDNNs. We also utilize a new schema to infer multiple predictions from a single hybrid neuron. We further compose a highly customizable platform for simulating HQDNNs via Qiskit and test them on diverse classification problems including the iris and the wheat seed datasets. The results show that even HQDNNs with the simplest neurons could lead to superior performance on these tasks. Finally, we show that the HQDNNs are robust to certain levels of noise, making them preferred on NISQ devices. Our work provides a comprehensive investigation of building scalable near-term gate-based HQDNNs and paves the way for future studies of quantum deep learning via both simulations on classical computers and experiments on accessible NISQ devices.
Quantum Neural Networks (QNNs) have emerged as a promising avenue in the quest for next-generation machine learning capabilities.By harnessing the principles of quantum mechanics and quantum computing, QNNs offer the potential for exponential speedup and enhanced computational power compared to classical machine learning algorithms.This paper presents a comprehensive exploration of Quantum Neural Networks, covering their foundational concepts, various architectures, novel quantum-enhanced machine learning algorithms, practical implementations, advantages, and challenges.We begin with an overview of related work in Quantum Machine Learning, highlighting the achievements and progress in the field.Subsequently, we delve into the fundamental principles of Quantum Mechanics and Quantum Computing to provide a solid grounding for understanding QNNs.We then introduce the basics of Quantum Neural Networks, including quantum neurons, quantum gates, and quantum circuits for machine learning tasks.Various QNN architectures, such as Variational Quantum Circuits and Quantum Convolutional Neural Networks, are explored along with their potential applications.Additionally, quantum-enhanced machine learning algorithms, like Quantum Support Vector Machines and Quantum Generative Adversarial Networks, are discussed for a deeper understanding of QNN capabilities.Practical aspects, including hardware implementations, noise mitigation, and experimental results, are presented to shed light on the feasibility of QNNs in real-world scenarios.The paper concludes by discussing the advantages and challenges of Quantum Neural Networks and their potential implications for the future of machine learning and artificial intelligence.
The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are restricted by the scope of the hardware development. Nevertheless, many neural network algorithms had been proposed before GPUs become powerful enough for running very deep models. Similarly, quantum algorithms can also be proposed as knowledge reserves before real quantum computers are easily accessible. Specifically, taking advantage of both the neural networks and quantum computation and designing quantum deep neural networks (QDNNs) for acceleration on Noisy Intermediate-Scale Quantum (NISQ) processors is also an important research problem. As one of the most widely used neural network architectures, convolutional neural network (CNN) remains to be accelerated by quantum mechanisms, with only a few attempts have been demonstrated. In this paper, we propose a new hybrid quantum-classical circuit, namely Quantum Fourier Convolutional Network (QFCN). Our model achieves exponential speed-up compared with classical CNN theoretically and improves over the existing best result of quantum CNN. We demonstrate the potential of this architecture by applying it to different deep learning tasks, including traffic prediction and image classification.
A possible approach to tackling computationally demanding issues beyond the capabilities of conventional algorithms is the use of quantum circuits, which provide a fundamental foundation for utilizing the power of quantum computation. This abstract examines how quantum circuits are implemented, emphasizing important topics such as circuit optimization, gate operations, and qubit manipulation. We explore different methods of encoding quantum information into topological qubits, trapped ions, and superconducting circuits, among other physical qubit formats. Furthermore, we go over the function of gate operations in quantum circuits, emphasizing crucial gates like phase, Hadamard, and CNOT gates, which serve as the foundation for quantum algorithms. Additionally, we look at methods for maximizing the efficiency and dependability of quantum processing by designing quantum circuits to minimize gate counts, depth, and error rates. To enhance the capabilities of quantum computing, this abstract presents a novel synthesis of quantum neural networks (QNNs) and quantum parameterized circuits. Through the use of parameterized quantum circuits' inherent flexibility, our approach makes it easier to design and optimize quantum circuits with flexible parameters, providing a flexible foundation for a variety of quantum algorithms. Using this amalgamation, we unleash the capacity of quantum computers to address intricate optimization and machine learning assignments with unparalleled effectiveness and expandability. Our solution bridges the gap between traditional machine learning approaches and quantum computing paradigms by enabling the smooth integration of classical data processing techniques with quantum computation. We use quantum states as data representations in our implementation of quantum neural networks, and we optimize trainable parameters to meet predetermined goals. This new paradigm opens up the investigation of the inherent features of quantum states and provides new perspectives on their processing power compared to their classical counterparts. We show, by thorough testing and analysis, how effective quantum parameterized circuits and QNNs are at solving practical problems in a variety of fields. Our work sets the ground for revolutionary breakthroughs in quantum information processing by pushing the boundaries of quantum computation and machine learning integration, offering hitherto unseen insights and solutions to challenging challenges in science, engineering, and beyond.
Quantum computing has emerged as a transformative approach for tackling complex problems in quantum chemistry, particularly in simulating multielectron systems and electron-phonon interactions. However, the current noisy intermediate-scale quantum (NISQ) devices face significant challenges in implementing practical quantum algorithms due to error accumulation caused by increased circuit depth, qubit counts, and gate operations. To address these challenges, we present TenCirChem, an open-source Python package specifically designed for implementing variational quantum algorithms in quantum computational chemistry. TenCirChem demonstrates exceptional performance in simulating unitary coupled-cluster circuits through its innovative use of compact representations for quantum states and excitation operators. This package supports noisy circuit simulation and provides advanced algorithms for variational quantum dynamics, enabling researchers to explore complex chemical phenomena. Its capabilities are exemplified in various applications, including the calculation of potential energy curves and the investigation of quantum gate error impacts on molecular systems. Moreover, TenCirChem’s seamless integration with real quantum hardware makes it a versatile tool for both simulation and experimentation. A key innovation developed within the TenCirChem framework is the Clifford-based Hamiltonian engineering approach for molecules (CHEM). This algorithm addresses the critical challenge of achieving chemical accuracy with shallow quantum circuits, a fundamental requirement for practical applications on NISQ devices. CHEM employs a sophisticated Clifford-based Hamiltonian transformation that operates within the variational quantum eigensolver (VQE) framework using hardware-efficient ansatz. The method ensures four crucial advantages: (1) generation of initial circuit parameters corresponding to Hartree-Fock energy, (2) maximization of initial energy gradients with respect to circuit parameters, (3) minimal classical processing overhead without additional quantum resource requirements, and (4) compatibility with any circuit topology. Through quantum hardware emulator demonstrations, CHEM has achieved chemical accuracy for systems up to 12 qubits with fewer than 30 two-qubit gates, representing a significant advancement in practical quantum computational chemistry. To enhance the efficiency of variational quantum algorithms, we developed the sequential optimization with approximate parabola (SOAP) method, specifically designed for parameter optimization in unitary coupled-cluster ansatz. SOAP addresses the critical bottleneck of measurement requirements in VQE by implementing an innovative optimization strategy that approximates the energy landscape as quadratic functions. This approach minimizes the number of energy evaluations while incorporating parameter correlations through the integration of average directions from previous iterations. Benchmark studies demonstrate SOAP’s superior performance, showing faster convergence and enhanced noise robustness compared to traditional optimization methods. The method’s scalability has been validated through numerical simulations of up to 20 qubits, and its practical efficacy has been confirmed through experiments on superconducting quantum computers. For simulating electron-phonon systems, we introduce a variational basis state encoding algorithm that significantly reduces resource requirements compared to conventional unary and binary encoding schemes. Our approach achieves smaller scaling than traditional methods for qubits and gates for systems obeying the area law of entanglement entropy, this remarkable reduction in resource requirements comes at the cost of a constant amount of additional measurements. The algorithm’s effectiveness has been validated through both numerical simulations and quantum hardware experiments, demonstrating that using just one or two qubits per phonon mode can produce quantitatively accurate results across various coupling regimes. The integration of these innovations within the TenCirChem library represents a significant advancement in quantum computational chemistry. The software package provides researchers with a comprehensive toolkit for developing, testing, and implementing quantum algorithms, while the novel methods address fundamental challenges in circuit depth, parameter optimization, and resource efficiency. These developments collectively enhance the practicality of quantum computing for addressing real-world chemical problems in the NISQ era, offering improved accuracy, efficiency, and noise robustness.