Optimizing quantum cloning circuit parameters based on adaptive guided differential evolution algorithm

Essam H Houssein; Mohamed A Mahdy; Manal G Eldin; Doaa Shebl; Waleed M Mohamed; Mahmoud Abdel-Aty

doi:10.1016/j.jare.2020.10.001

Optimizing quantum cloning circuit parameters based on adaptive guided differential evolution algorithm

J Adv Res. 2020 Oct 17:29:147-157. doi: 10.1016/j.jare.2020.10.001. eCollection 2021 Mar.

Authors

Essam H Houssein¹, Mohamed A Mahdy², Manal G Eldin³, Doaa Shebl², Waleed M Mohamed¹, Mahmoud Abdel-Aty⁴

Affiliations

¹ Faculty of Computers and Information, Minia University, Minia, Egypt.
² Faculty of Computers and Artificial Intelligence, Beni-Suef University, Beni-Suef, Egypt.
³ Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt.
⁴ Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.

Abstract

Introduction: Quantum cloning operation, started with no-go theorem which proved that there is no capability to perform a cloning operation on an unknown quantum state, however, a number of trials proved that we can make approximate quantum state cloning that is still with some errors.

Objectives: To the best of our knowledge, this paper is the first of its kind to attempt using meta-heuristic algorithm such as Adaptive Guided Differential Evolution (AGDE), to tackle the problem of quantum cloning circuit parameters to enhance the cloning fidelity.

Methods: To investigate the effectiveness of the AGDE, the extensive experiments have demonstrated that the AGDE can achieve outstanding performance compared to other well-known meta-heuristics including; Enhanced LSHADE-SPACMA Algorithm (ELSHADE-SPACMA), Enhanced Differential Evolution algorithm with novel control parameter adaptation (PaDE), Improved Multi-operator Differential Evolution Algorithm (IMODE), Parameters with adaptive learning mechanism (PALM), QUasi-Affine TRansformation Evolutionary algorithm (QUATRE), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Cuckoo Search (CS), Bat-inspired Algorithm (BA), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA).

Results: In the present study, AGDE is applied to improve the fidelity of quantum cloning problem and the obtained parameter values minimize the cloning difference error value down to $10^{- 8}$ .

Conclusion: Accordingly, the qualitative and quantitative measurements including average, standard deviation, convergence curves of the competitive algorithms over 30 independent runs, proved the superiority of AGDE to enhance the cloning fidelity.

Keywords: AGDE; Adaptive guided differential evolution; Cloned qubits; Cloning fidelity; Meta-heuristics; Quantum cloning.