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International Journal on Perceptive and Cognitive Computing

Simple quantum circuit for pattern recognition based on nearest mean classifier

Gharib Subhi Mahmoud Ahmed, Azeddine Messikh

Published Nov 12, 2016• 1 citation
Publisher

Abstract

Machine learning plays a key role in many applications such as data mining and image recognition.Classification is one subcategory under machine learning. In this paper we propose a simple quantum circuitbased on the nearest mean classifier to classified handwriting characters. Our circuit is a simplified circuit fromthe quantum support vector machine [Phys. Rev. Lett. 114, 140504 (2015)] which uses quantum matrix inversealgorithm to find optimal hyperplane that separated two different classes. In our case the hyperplane is foundusing projections and rotations on the Bloch sphere.

DOI
10.31436/ijpcc.v2i2.38

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Machine learning plays a key role in many applications such as data mining and image recognition.Classification is one subcategory under machine learning. In this paper we propose a simple quantum circuitbased on the nearest mean classifier to classified handwriting characters. Our circuit is a simplified circuit fromthe quantum support vector machine [Phys. Rev. Lett. 114, 140504 (2015)] which uses quantum matrix inversealgorithm to find optimal hyperplane that separated two different classes. In our case the hyperplane is foundusing projections and rotations on the Bloch sphere.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
The article contains a description of two quantum circuits for pattern recognition. The first approach is realized with use of k nearest neighbors algorithm and the second with support vector machine. The task is to distinguish between Hermitian and non-Hermitian matrices. The quantum circuits are constructed to accumulate elements of a learning set. After this process, circuits are able to produce a quantum state which contains the information if a tested element fits to the trained pattern. To improve the efficiency of presented solutions, the matrices were uniquely labeled with feature vectors. The role of the feature vectors is to highlight some features of the objects which are crucial in the process of classification. The circuits were implemented in Python programming language and some numeric experiments were conducted to examine the capacity of presented solutions in pattern recognition.
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.
The fundamental principle of artificial intelligence is the ability of machines to learn from previous experience and do future work accordingly. In the age of big data, classical learning machines often require huge computational resources in many practical cases. Quantum machine learning algorithms, on the other hand, could be exponentially faster than their classical counterparts by utilizing quantum parallelism. Here, we demonstrate a quantum machine learning algorithm to implement handwriting recognition on a four-qubit NMR test bench. The quantum machine learns standard character fonts and then recognizes handwritten characters from a set with two candidates. Because of the wide spread importance of artificial intelligence and its tremendous consumption of computational resources, quantum speedup would be extremely attractive against the challenges of big data.
Noisy data is ubiquitous in quantum computer, greatly affecting the performance of various algorithms. However, existing quantum support vector machine models are not equipped with anti-noise ability, and often deliver low performance when learning accurate hyperplane normal vectors from noisy data. To attack this issue, an anti-noise quantum support vector machine algorithm is developed in this paper. Specifically, a weight factor is first embedded into the hinge loss, so as to construct the objective function of anti-noise support vector machine. And then, an alternative iterative optimization strategy and a quantum circuit are designed for solving the objective function, aiming to obtain the normal vector and intercept of the hyperplane that finally divides the data. Finally, the classification and anti-noise effect of the algorithm are verified on artificial dataset and public dataset. Experimental results show that the proposed algorithm is efficient, yet maintains stable accuracy in noisy data.
Quantum Computing is a new way to create a different type of computer system from Quantum Mechanics. Quantum machine learning is one of the applications took the benefit from qauntum computers. In this experiment, we use the IBM Qiskit library to study how well a quantum machine learning classifier works. We made two different colored dots to represent the two-class dataset. The quantum circuit can be collected from the Qiskit library. The 1stand 2ndorder feature map schemes operated by oracle quantum oracle functions are applied before making a classification. Finally, we can call the quantum support vector machine or QSVM function to classify data. Kernel matrix from the studied qauntum model shows that quantum computing can be used to clearly classify classes of the dataset with 100 percent accuracy.