Quantum Complexity for Vector Domination Problem

K. A. Vidya, K. Venugopal

Lei Shi, Yonglong Luo, Caiyun Zhang

Secure two-party vector dominance means that the two sides of the computation want to judge whether their vectors have the dominance relation securely, a new problem which is called multi-dimensional vector comparison problem is proposed based on the vector dominance in this paper, it can be applied in many commercial areas, such as auction, bidding and so on. Two solutions are provided for this problem, using multiplication protocol and scalar products protocol respectively. Furthermore, we introduce the random algorithm to solve the problem, analyze the security, correctness and complexity, point out the differences between these two methods, and simulate by experiments.

P Jose, Shanmugasundaram Hariharan, M. Vimaladevi +3 more

Abstract Machine learning has emerged as a promising method for predicting breast cancer using quantum computation techniques. Quantum machine learning algorithms, such as quantum support vector machines (QSVMs), are demonstrating superior efficiency and economy in tackling complex problems compared to traditional machine learning methods. When compared with classical support vector machine, the quantum machine produces remarkably accurate results. The suggested quantum SVM model in this study effectively resolved the binary classification problem for diagnosing malignant breast cancer. This work introduces an enhanced approach to breast cancer diagnosis by integrating QSVM with elitist non‐dominated sorting genetic optimization (ENSGA), leveraging the strengths of both techniques to achieve more accurate and efficient classification results. ENSGA plays a crucial role in optimising QSVM parameters, ensuring that the model attains the best possible classification accuracy while considering multiple objectives simultaneously. Moreover, the quantum kernel estimation method demonstrated exceptional performance by achieving high accuracy within an impressive execution time of 0.14 in the IBM QSVM simulator. The seamless integration of quantum computation techniques with optimisation strategies such as ENSGA highlights the potential of quantum machine learning in revolutionising the field of healthcare, particularly in the domain of breast cancer diagnosis.

Satoshi Iriyama, Makoto Ohya

Haoqian Pan, Changhong Lü

In the wake of quantum computing advancements and quantum algorithmic progress, quantum algorithms are increasingly being employed to address a myriad of combinatorial optimization problems. Among these, the Independent Domination Problem (IDP), a derivative of the Domination Problem, has practical implications in various real-world scenarios. Despite this, existing classical algorithms for the IDP are plagued by high computational complexity, and quantum algorithms have yet to tackle this challenge. This paper introduces a Quantum Approximate Optimization Algorithm (QAOA)-based approach to address the IDP. Utilizing IBM's qasm_simulator, we have demonstrated the efficacy of the QAOA in solving the IDP under specific parameter settings, with a computational complexity that surpasses that of classical methods. Our findings offer a novel avenue for the resolution of the IDP.

R. Hayakawa, Tomoyuki Morimae