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Communications in Theoretical Physics

Variational quantum support vector machine based on Hadamard test

Xu Li, Xiaoyu Zhang, Jin‐Min Liang, Jing Wang, Ming Li, Ling Jian, Shu‐Qian Shen

Published Apr 2, 2022• 9 citations
Publisher

Abstract

Abstract Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data, while quantum machine learning algorithms could deal with big data with ease and provide exponential acceleration over classical counterparts. Meanwhile, variational quantum algorithms are widely proposed to solve relevant computational problems on noisy, intermediate-scale quantum devices. In this paper, we apply variational quantum algorithms to quantum support vector machines and demonstrate a proof-of-principle numerical experiment of this algorithm. In addition, in the classification stage, fewer qubits, shorter circuit depth, and simpler measurement requirements show its superiority over the former algorithms.

DOI
10.1088/1572-9494/ac6358

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Abstract Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data, while quantum machine learning algorithms could deal with big data with ease and provide exponential acceleration over classical counterparts. Meanwhile, variational quantum algorithms are widely proposed to solve relevant computational problems on noisy, intermediate-scale quantum devices. In this paper, we apply variational quantum algorithms to quantum support vector machines and demonstrate a proof-of-principle numerical experiment of this algorithm. In addition, in the classification stage, fewer qubits, shorter circuit depth, and simpler measurement requirements show its superiority over the former algorithms.
Abstract Classical machine learning algorithms seem to be totally incapable of processing tremendous data, while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts. In this paper, we propose two quantum support vector machine algorithms for multi classification. One is the quantum version of the directed acyclic graph support vector machine. The other one is to use the Grover search algorithm before measurement, which amplifies the amplitude of the phase storing of the classification result. For k classification, the former provides quadratic reduction in computational complexity when classifying. The latter accelerates the training speed significantly and more importantly, the classification result can be read out with a probability of at least 50% using only one measurement. We conduct numerical simulations on two algorithms, and their classification success rates are 96% and 88.7%, respectively.
Quantum Machine Learning is an active research field where the power of quantum mechanics is integrated into machine learning algorithms to solve problems that are intractable for classical computers. Quantum support vector machine (QSVM) was one of the first quantum algorithms that got implemented on real quantum hardware. It demonstrated promising outcomes as compared to classical Support vector machine (SVM) through many implementations. However, it encounters challenges in scaling with large datasets and in resource effectiveness when compare to the usage of innovative classical algorithms in the Noisy Intermediate Scale Quantum era. Here is a review of some latest developments of QSVM and discussion on prospects of QSVM application in the future.
In this paper, we present a performance comparison of machine learning algorithms executed on traditional and quantum computers. Quantum computing has potential of achieving incredible results for certain types of problems, and we explore if it can be applied to machine learning. First, we identified quantum machine learning algorithms with reproducible code and had classical machine learning counterparts. Then, we found relevant data sets with which we tested the comparable quantum and classical machine learning algorithm's performance. We evaluated performance with algorithm execution time and accuracy. We found that quantum variational support vector machines in some cases had higher accuracy than classical support vector machines on multi-class classification problems. The main conclusion was that quantum multi-class SVM classifiers have the potential to be useful in the future as quantum computer’s available number of qubits increases.
Abstract A kernel-based quantum classifier is the most interesting and powerful quantum machine learning technique for hyperlinear classification of complex data, which can be easily realized in shallow-depth quantum circuits such as a SWAP test classifier. A variational quantum approximate support vector machine (VQASVM) can be realized inherently and explicitly on these circuits by introduction of a variational scheme to map the quadratic optimization problem of the support vector machine theory to a quantum-classical variational optimization problem. Probability weight modulation in index qubits of a classifier can designate support vectors among training vectors, which can be achieved with a parameterized quantum circuit (PQC). The classical parameters of PQC is then transferred to many copies of other decision inference circuits. Our VQASVM algorithm is experimented with toy example data sets on cloud-based quantum machines for feasibility evaluation, and numerically investigated to evaluate its performance on a standard iris flower and MNIST data set. The empirical run-time complexity of VQASVM is estimated to be sub-quadratic on the training data set size, while that of the classical solver is quadratic.
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.
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.