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Laser Physics Letters

Quantum state classification via complex-valued neural networks

Yu-Chao Dong, Xikun Li, Ming Yang, Lu Yan, Yan-Lin Liao, Arif Ullah, Zhi Lin

Published Sep 6, 2024• 1 citation
Publisher

Abstract

Abstract To efficiently complete quantum information processing tasks, quantum neural networks (QNNs) should be introduced rather than the common classical neural networks, but the QNNs in the current noisy intermediate-scale quantum era cannot perform better than classical neural networks because of scale and the efficiency limits. So if the quantum properties can be introduced into classical neural networks, more efficient classical neural networks may be constructed for tasks in the field of quantum information. Complex numbers play an indispensable role in the standard quantum theory, and constitute an important feature in quantum theory. So if complex numbers are introduced in classical neural networks, they may outperform the common classical neural networks in dealing with the tasks in the quantum information field. In this paper, we verify this conjecture by studying quantum state classification via complex-valued neural networks (CVNNs). The numerical results show that the performance of CVNNs is much better than the real-valued neural network in classifying the entangled states. Our results not only provide a new way to improve the performance of artificial neural networks in quantum state classifiers, but also might shed light on the study of CVNNs in the field of other quantum information processing tasks before the appearance of the universal quantum computer.

DOI
10.1088/1612-202x/ad7246

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Abstract To efficiently complete quantum information processing tasks, quantum neural networks (QNNs) should be introduced rather than the common classical neural networks, but the QNNs in the current noisy intermediate-scale quantum era cannot perform better than classical neural networks because of scale and the efficiency limits. So if the quantum properties can be introduced into classical neural networks, more efficient classical neural networks may be constructed for tasks in the field of quantum information. Complex numbers play an indispensable role in the standard quantum theory, and constitute an important feature in quantum theory. So if complex numbers are introduced in classical neural networks, they may outperform the common classical neural networks in dealing with the tasks in the quantum information field. In this paper, we verify this conjecture by studying quantum state classification via complex-valued neural networks (CVNNs). The numerical results show that the performance of CVNNs is much better than the real-valued neural network in classifying the entangled states. Our results not only provide a new way to improve the performance of artificial neural networks in quantum state classifiers, but also might shed light on the study of CVNNs in the field of other quantum information processing tasks before the appearance of the universal quantum computer.
Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most existing models employ real-valued neural networks (RVNNs) that inherently mismatch the complex-valued nature of quantum mechanics. By decoupling the real and imaginary parts of the density matrix, RVNNs can obscure essential amplitude-phase correlations, compromising physical consistency. Here, we introduce complex-valued neural networks (CVNNs) as a physics-consistent framework for learning quantum dissipative dynamics. CVNNs operate directly on complex-valued inputs, preserve the algebraic structure of quantum states, and naturally encode quantum coherences. Through numerical benchmarks on the spin-boson model and few variants of the Fenna-Matthews-Olson complex, we demonstrate that CVNNs outperform RVNNs in convergence speed, training stability, and physical fidelity-including significantly improved trace conservation and Hermiticity. These advantages increase with system size and coherence complexity, establishing CVNNs as a robust, scalable, quantum-aware classical approach for simulating open quantum systems in the pre-fault-tolerant quantum era.
This research explores the development of Quantum Neural Networks (QNNs) as a transformative approach for complex data classification. Utilizing a numerical example, we illustrate the foundational quantum principles of superposition and entanglement within QNNs. The hybrid quantum-classical processing paradigm is introduced, emphasizing the seamless integration of quantum and classical components, acknowledging the challenges of quantum error correction and noise in Noisy Intermediate-Scale Quantum (NISQ) devices. While the example is deliberately simple, it serves as a starting point for understanding the unique advantages and challenges associated with QNNs. Our findings highlight the potential of quantum computation for parallel processing but also underscore the need to address current limitations for practical applications. Future research directions include investigating sophisticated quantum circuits, exploring error mitigation strategies, and assessing QNN performance across diverse datasets. Collaboration between quantum computing and machine learning communities is essential for the advancement of QNNs, and developments in quantum hardware will play a pivotal role in realizing their full potential. This study contributes to the evolving discourse at the intersection of quantum computing and machine learning, providing foundational insights and laying the groundwork for further exploration in this rapidly advancing field.
This paper explores the potential of Quantum Neural Networks (QNNs) for advanced feature extraction and classification tasks. Classical neural networks often struggle with complex datasets and computational bottlenecks. QNNs, leveraging principles of quantum mechanics like entanglement and superposition, offer a fundamentally different approach. This research investigates the construction and application of a QNN architecture designed to exploit these quantum properties. We present a model utilizing quantum gates and qubits to perform parallel computations and generate more effective feature representations compared to traditional neural networks. The core claim of this work is the demonstration of QNNs surpassing the performance of classical networks in complex classification problems. We detail the theoretical framework, model design, and discuss the potential impact of QNNs on various applications, highlighting their ability to unlock new levels of accuracy and efficiency in data analysis. The key mechanisms driving this potential are the inherent parallelism and superior feature representation capabilities of QNNs.
The field of quantum neural networks, an emerging interdisciplinary frontier bridging quantum computing and machine learning, has recently garnered substantial attention in the scientific community. In this work, we propose a complex-valued quantum neural network in the quantum circuit framework through expanding the number domains of conventional quantum machine learning architecture from the real-valued domain to the complex-valued plane. Such an expansion can alleviate the unitary constraints in quantum feature maps and optimization blocks, and introduce enhanced nonlinear characteristics. It is proven theoretically that the expressivity can be significantly enhanced through the frequency-dependent adaptability and the exponential or hyperbolic functional distribution extension for the Fourier coefficients of quantum models' outputs. Moreover, analysis based on covering numbers indicates that our algorithm can achieve an adaptive balance between expressivity and generalization via the trainable scaling factor, while exhibiting superior parameter efficiency relative to unitary quantum learning models. The performance of the proposed algorithms is demonstrated through extensive numerical simulations in regression and classification tasks, including an experimental realization on the superconducting quantum processor. Our work advances the harnessing of imaginarity resources of quantum theory for learning tasks, achieving a theoretically grounded performance enhancement, and underscores the potential of improving quantum neural networks through structured design for future applications.
This study explores the performance of Quantum Support Vector Classifiers (QSVCs) and Quantum Neural Networks (QNNs) in comparison to classical models for machine learning tasks. By evaluating these models on the Iris and MNIST-PCA datasets, we find that quantum models tend to outperform classical approaches as the problem complexity increases. While QSVCs generally provide more consistent results, QNNs exhibit superior performance in higher-complexity tasks due to their increased quantum load. Additionally, we analyze the impact of hyperparameter tuning, showing that feature maps and ansatz configurations significantly influence model accuracy. We also compare the PennyLane and Qiskit frameworks, concluding that Qiskit provides better optimization and efficiency for our implementation. These findings highlight the potential of Quantum Machine Learning (QML) for complex classification problems and provide insights into model selection and optimization strategies
The power of quantum computers is still somewhat speculative. Although they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical complexity theory. This means that we do not know for which calculations there will be a "quantum advantage," once an algorithm is found. One way to answer the question is to find those algorithms, but finding truly quantum algorithms turns out to be very difficult. In previous work, over the past three decades, we have pursued the idea of using techniques of machine learning to develop algorithms for quantum computing. Here, we compare the performance of standard real- and complex-valued classical neural networks with that of one of our models for a quantum neural network, on both classical problems and on an archetypal quantum problem: the computation of an entanglement witness. The quantum network is shown to need far fewer epochs and a much smaller network to achieve comparable or better results.