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Journal of Applied Physics

Variational algorithm of quantum neural network based on quantum particle swarm

Yumin Dong, Jianshe Xie, Wanbin Hu, Cheng Liu, Yi Luo

Published Sep 12, 2022• 3 citations
Publisher

Abstract

Most models of quantum neural networks are optimized based on gradient descent, and like classical neural networks, gradient descent suffers from the barren plateau phenomenon, which reduces the effectiveness of optimization. Therefore, this paper establishes a new QNN model, the optimization process adopts efficient quantum particle swarm optimization, and tentatively adds a quantum activation circuit to our QNN model. Our model will inherit the superposition property of quantum and the random search property of quantum particle swarm. Simulation experiments on some classification data show that the model proposed in this paper has higher classification performance than the gradient descent-based QNN.

DOI
10.1063/5.0098702

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Most models of quantum neural networks are optimized based on gradient descent, and like classical neural networks, gradient descent suffers from the barren plateau phenomenon, which reduces the effectiveness of optimization. Therefore, this paper establishes a new QNN model, the optimization process adopts efficient quantum particle swarm optimization, and tentatively adds a quantum activation circuit to our QNN model. Our model will inherit the superposition property of quantum and the random search property of quantum particle swarm. Simulation experiments on some classification data show that the model proposed in this paper has higher classification performance than the gradient descent-based QNN.
Quantum machine learning stands out as one of the most promising applications of quantum computing, widely believed to possess potential quantum advantages. In the era of noisy intermediate-scale quantum, the scale and quality of quantum computers are limited, and quantum algorithms based on fault-tolerant quantum computing paradigms cannot be experimentally verified in the short term. The variational quantum algorithm design paradigm can better adapt to the practical characteristics of noisy quantum hardware and is currently one of the most promising solutions. However, variational quantum algorithms, due to their highly entangled nature, encounter the phenomenon known as the “barren plateau” during the optimization and training processes, making effective optimization challenging. This paper addresses this challenging issue by researching a variational quantum neural network optimization method based on collective intelligence algorithms. The aim is to overcome optimization difficulties encountered by traditional methods such as gradient descent. We study two typical applications of using quantum neural networks: random 2D Hamiltonian ground state solving and quantum phase recognition. We find that the collective intelligence algorithm shows a better optimization compared to gradient descent. The solution accuracy of ground energy and phase classification is enhanced, and the optimization iterations are also reduced. We highlight that the collective intelligence algorithm has great potential in tackling the optimization of variational quantum algorithms.
In this work, the Particle Swarm Optimization (PSO) algorithm has been used to train various Variational Quantum Circuits (VQCs). This approach is motivated by the fact that commonly used gradient-based optimization methods can suffer from the barren plateaus problem. PSO is a stochastic optimization technique inspired by the collective behavior of a swarm of birds. The dimension of the swarm, the number of iterations of the algorithm, and the number of trainable parameters can be set. In this study, PSO has been used to train the entire structure of VQCs, allowing it to select which quantum gates to apply, the target qubits, and the rotation angle, in case a rotation is chosen. The algorithm is restricted to choosing from four types of gates: Rx, Ry, Rz, and cNOT. The proposed optimization approach has been tested on various datasets of the MedMNIST, which is a collection of biomedical image datasets designed for image classification tasks. Performance has been compared with the results achieved by classical stochastic gradient descent applied to a predefined VQC. The results show that the PSO can achieve comparable or even better classification accuracy across multiple datasets, despite the PSO using a lower number of quantum gates than the VQC used with gradient descent optimization.
Abstract The artificial neural network (ANN), as a powerful data analytical tool, has played a major role in facial recognition, nature language processing (NLP), etc. However, the efficiency of classical networks is seriously challenged by big data, however, the development of quantum theory can be combined with ANN to help overcome this problem. In this paper, we propose a quantum neural network, in which the quantum particle swarm optimization (QPSO) is used to optimize parameters. To analysze the system performance, it has been applied to function fitting and data classification and it is shown by classical simulation and experimentation that the proposed model is more efficient and powerful than ANN for a lot of experimental tasks. We hope that this scheme can be implemented on a quantum computer in the future.
Quantum Machine Learning refers to the interdisciplinary area of research, blending principles from quantum physics and machine learning that can process information on quantum computers. Quantum machine learning (QML) intentions to exploit the superposition (qubit can exist in multiple states) property and other effects of quantum mechanics for enhanced efficiency and speed in specific machine learning computations, promising exponential-power superiority in particular computations. This paper focusses on Quantum Machine Learning Models to develop the framework to learn complicated associations within the data through the adjustment of the variational parameters during training. This framework serves as a foundational structure for implementing quantum neural networks, allowing for further experimentation and growth in quantum machine learning applications. It highlights the quantum circuits to process and learn from data in a mode distinct from classical neural networks. As the retrieve of quantum computing grows, such frameworks can be adapted and expanded to explore more sophisticated quantum algorithms and architectures. In the circumstances of Quantum Neural Networks, gradient descents is used in minimizing cost or loss function by iteratively adjusting the variational parameters based onto the gradient of the loss with admire to those parameters. The output that indicates the process of installing the Quantum information science Kit (Qiskit) library in Python specifically version 3.7 along with its dependencies.
Processing data through a quantum classifier is a powerful alternative to traditional machine learning. A quantum classifier consists of a series of parameterized quantum circuits that train known quantum data to approximate classification functions and accurately classify unknown data. Considering the development limitations of quantum computers, this paper proposes a kind of lightweight quantum classifier which contains fewer circuit parameters and integrated with the classical optimization algorithm in order to achieve high-precision classification. The architecture design of quantum classifier is inspired on tensor network states such as matrix product state, tree network (TTN) and multi-scale entangled renormalization (MERA), the classical optimization algorithm adopts gradient descent (GD), particle swarm optimization (PSO) and quantum behavior improved particle swarm optimization (QPSO). The whole classical-quantum hybrid model could theoretically be implemented on near-term devices, and its performance is proved on Anderson Iris data set.
Quantum many-body computation is a central challenge across multiple domains of scientific research, and Monte Carlo method has emerged as one of the most effective numerical techniques for investigating large-scale many-body systems. In recent years, the integration of Monte Carlo methods with machine learning has led to the development of neural quantum state approach. Quantum neural networks (QNNs) offer superior expressiveness compared to classical neural networks. In this paper, we propose a novel Quantum Neural Network Quantum State (QNNQS) method, based on the variational Monte Carlo framework. This approach leverages a quantum neural network to represent the many-body quantum state, and optimizes it iteratively through gradient descent to determine the ground-state energy. To assess the performance of this method, we conduct simulations of the one-dimensional transverse-field Ising model, investigating the influence of quantum circuit architecture on circuit expressibility, entangling capability, and computational accuracy. The results demonstrate that the QNNQS method achieves comparable simulation accuracy while utilizing significantly fewer parameters and requiring less training resources than classical network quantum state methods.