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Quantum Science and Technology

Quantum phase transition detection via quantum support vector machine

Youle Wang, Linyun Cao

Published Nov 28, 2024• 10 citations
Publisher

Abstract

Abstract Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.

DOI
10.1088/2058-9565/ad985f

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Abstract Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.
Quantum computing is a promising new approach to tackle the complex real-world computational problems by harnessing the power of quantum mechanics principles. The inherent parallelism and exponential computational power of quantum systems hold the potential to outpace classical counterparts in solving complex optimization problems, which are pervasive in machine learning. Quantum Support Vector Machine (QSVM) is a quantum machine learning algorithm inspired by classical Support Vector Machine (SVM) that exploits quantum parallelism to efficiently classify data points in high-dimensional feature spaces. We provide a comprehensive overview of the underlying principles of QSVM, elucidating how different quantum feature maps and quantum kernels enable the manipulation of quantum states to perform classification tasks. Through a comparative analysis, we reveal the quantum advantage achieved by these algorithms in terms of speedup and solution quality. As a case study, we explored the potential of quantum paradigms in the context of a real-world problem: classifying pancreatic cancer biomarker data. The Support Vector Classifier (SVC) algorithm was employed for the classical approach while the QSVM algorithm was executed on a quantum simulator provided by the Qiskit quantum computing framework. The classical approach as well as the quantum-based techniques reported similar accuracy. This uniformity suggests that these methods effectively captured similar underlying patterns in the dataset. Remarkably, quantum implementations exhibited substantially reduced execution times demonstrating the potential of quantum approaches in enhancing classification efficiency. This affirms the growing significance of quantum computing as a transformative tool for augmenting machine learning paradigms and also underscores the potency of quantum execution for computational acceleration.
Background Quantum support vector machines and quantum kernel methods have emerged as promising approaches within quantum machine learning, with the goal of leveraging quantum computing to enhance classification performance and computational efficiency. This review systematically surveys recent advances in QSVM and kernel‐based quantum classifiers, and analyzes their algorithmic frameworks, experimental implementations, and practical challenges. Methods We systematically examine QSVM approaches, including three schemes based on HHL algorithm, Hadamard test, and variational optimization, alongside multi‐class extension and quantum feature mapping. Result Findings indicate that QSVM can offer theoretical speed‐ups in specific settings, particularly when combined with quantum feature mappings that encode data into high‐dimensional Hilbert spaces. However, current implementations remain constrained by hardware limitations, and a lack of large‐scale general validation. Most studies focus on proof‐of‐principle experiments with limited real‐world applicability. Conclusion While promising, QSVM requires further work on scalability, noise resilience, and real‐world integration. Future research should focus on robust algorithms and empirical studies.
A basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely, to efficiently perform computations in an intractably large Hilbert space. In this Letter we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyze the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. The kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualize the working principle with two-dimensional minibenchmark datasets.
Quantum machine learning is at the crossroads of two of the most exciting current areas of research; quantum computing and classical machine learning. It explores the interaction between quantum computing and machine learning, investigating how results and techniques from one field can be used to solve the problems of the other. Here, we investigate quantum support vector machine (QSVM) algorithm and its circuit version on present quantum computers. We propose a general encoding procedure extending QSVM algorithm, which would allow one to feed vectors with higher dimension in the training-data oracle of QSVM. We compute the efficiency of the QSVM circuit implementation method by encoding training and testing data sample in quantum circuits and running them on quantum simulator and real chip for two datasets; 6/9 and banknote. We highlight the technical difficulties one would face while applying the QSVM algorithm on current NISQ era devices. Then we propose a new method to classify these datasets with enhanced efficiencies for the above datasets both on simulator and real chips.
Machine learning has emerged as a promising approach to unveil properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods---such as Monte Carlo---which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data-reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented quantum algorithm recovers. Finally, we propose a majority vote quantum classifier built from a nearest-neighbor (checkerboard) quantum neural network. This classifier is successfully trained to recognize phases of matter with 99% accuracy for the transverse field Ising model and 94% accuracy for the XXZXXZXXZ model. These findings suggest that a merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.
The integration of machine learning (ML) in materials science has accelerated the discovery and optimization of novel materials. However, classical ML approaches often face limitations in handling the increasing complexity and scale of modern datasets. Quantum machine learning (QML), leveraging quantum computing principles, offers a promising avenue to address these challenges. This study explores the application of the quantum support vector classifier (QSVC) to predict phase diagrams in the Al-Cu-Mg-Si-Zn quinary system. The prediction of the phase diagram of quinary systems contributes to the achievement of issues related to sustainable development goals by facilitating the creation of sophisticated materials that possess exceptional characteristics. This, in turn, promotes innovation and sustainable practices within the industrial sector. We used a comprehensive dataset from high-throughput CALPHAD calculations, and employed QSVC with advanced quantum feature transformations and kernel methods. Our results demonstrate significant improvements in predictive accuracy and efficiency compared to classical SVC, highlighting the potential of QML to advance material design.