Comparative Analysis of Quantum Support Vector Machines and Nonlinear Classical Support Vector Machines for Malignant Colorectal Cancer Diagnosis

Abstract

Colorectal cancer is the second most common cause of cancer death in the United States. Moreover, it is also the second most commonly misdiagnosed cancer. With a correct diagnosis at stage two of this cancer, the five-year survival rate is approximately 90% but drops drastically to 14% if diagnosed at stage four (Colon Cancer Coalition, n.d.). Previous work in the field has seen the use of various classical machine-learning models to identify patterns in digital images, gene expression, protein sequencing, etc. However, there are many technical challenges that exist from large feature sets to complex mathematical calculations. To address these challenges, quantum machine learning algorithms provide a potential solution. A “quantum advantage” may be obtained in terms of kernel calculations, higher dimensional mapping, and computational power. In order to assess the power of quantum-enhanced algorithms, this study proposes and compares two cancer classification systems based on a quantum support vector machine (qSVM) and a classical nonlinear support vector machine (SVM). We used over 10,000 histopathological images of colon tissue to extract 58 integrated features. The extracted features were used to train both the qSVM and SVM. Our results report an 89.7% and 94% accuracy rate, respectively for the qSVM and SVM in terms of classifying malignant and benign colorectal cancer tissue patches. The qSVM was trained with just one-third of the features compared to classical SVM, implying a quantum advantage. Additionally, with an increase in the number of features, the qSVM is guaranteed an exponential speed-up over a classical SVM, due to its better worst-time complexity of O(log(M x N)) compared to O(M^2(M + N)). We propose two successful cancer classification systems that demonstrate the great potential for the design and implementation of quantum machine learning algorithms in the future of healthcare technology advancement.