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Communications in computer and information science

Quantum-Inspired Differential Evolution on Bloch Coordinates of Qubits

Ankit Pat, Ashish R. Hota, Avneet Singh

Published Jan 1, 2011• 4 citations
Publisher
DOI
10.1007/978-3-642-18440-6_3

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To enhance the optimization performance of differential evolution algorithm,by studying the implementation mechanism of differential evolution algorithm,a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper.In the proposed approach,the individuals are encoded by qubits described on Bloch sphere,and the rotation angles of qubits in current individual are obtained by differential strategy.The axis of rotation is designed by using vector product theory,and the rotation matrixes are constructed by using Pauli matrixes.Taking the corresponding qubits in current best individual as targets,the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere.The Hadamard gates are used to mutate individuals.The simulation results of optimizing the minimum value of functions indicate that,for an iterative step,the average time of the proposed approach is 13times as long as that of the classical differential evolution algorithm.When the same limited steps are applied in two approaches,the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm; when the same running time is applied in two approaches,the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm.These results suggest that the proposed approach is inefficient in computational ability; however,it is obviously efficient in optimization ability,and the overall optimization performance is better than the classical differential evolution algorithm.
Manta ray foraging optimisation (MRFO) algorithm, a recent bio-inspired technique, and quantum-motivated computing have proven effective in solving complex combinatorial optimisation problems. Leveraging their qualities, we propose a continuous space optimisation approach that offers a novel combination of encoding and evolution of the chromosomes. The qubits in the quantum individual are encoded with the phase parameters and are based on Bloch representation. The phase angle-encoded qubit simplifies the expression and evolution of an individual. The proposed algorithm can search the optimised solution simultaneously on three coordinate axes of the Bloch sphere, to possibly achieve better convergence. The performance of the proposed algorithm is examined vis-a-vis the standard MRFO algorithm for optimising the value of 20 benchmark functions. While both algorithms compete well in finding the best fitness values, the proposed approach shows better convergence for 16 out of 20 functions.