Crossover interaction between individuals in structured Quantum Evolutionary Algorithms

Zhihui Xing, Haibin Duan, Chunfang Xu

Shengchao Ding

Coding the individual with amplitude,and applying the crossover operator of classical genetic algorithm to the evolutionary goals of quantum-inspired evolutionary algorithm,a hybrid quantum-inspired evolutionary algorithm is proposed.Combining the self-adaptive rotation,defining a self-adaptive mutation operator with respect to mutation degree,and exchanging the information of the evolutionary goals by crossover operator regularly,the novel algorithm avoids converging prematurely and yields high efficiency.Also the algorithm exceeds QEA and CGA when they solve the numerical optimization problems.The Need-in-a-Haystack problem can be figured out perfectly.Additionally,the algorithm’s computing speed is similar to the classical one.

Xin Wei, Shigeru Fujimura

Abstract Based on the concept and principles of quantum computing, this paper proposes a new evolutionary algorithm called multiupdate mode quantum evolutionary algorithm (MMQEA). MMQEA, like the other classic evolutionary algorithms, is also characterized by the representation of the individual evaluation function and the population dynamics; however, instead of binary, numeric, or symbolic representation, MMQEA uses two interactional q‐bit strings as an individual. Update modes are introduced as a variational operation that evolves the individuals to make a better solution. The proposed individual structure and update modes are inspired by quantum entanglement. Update modes perform as reproducing the states of a pair of q‐bit strings of individual simultaneously. For guiding the individual evolution to maintain the population diversity and avoid prematurity, each q‐bit string of individual provides its evolutionary history information to another. To demonstrate its effectiveness and applicability, the proposed algorithm was tested on two famous combinatorial optimization problems, namely, the knapsack problem and flow shop problem. The results show that MMQEA performs very well compared to quantum evolutionary algorithm (QEA) and the conventional genetic algorithm. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Daniel Johannsen, Piyush P. Kurur, Johannes Lengler

Yi Jiang, Li Yan -

Leandro C. Souza, Laurent E. Dardenne, Renato Portugal

We propose a gate-based Quantum Genetic Algorithm (QGA) for real-valued global optimization. In this model, individuals are represented by quantum circuits whose measurement outcomes are decoded into real-valued vectors through binary discretization. Evolutionary operators act directly on circuit structures, allowing mutation and crossover to explore the space of gate-based encodings. Both fixed-depth and variable-depth variants are introduced, enabling either uniform circuit complexity or adaptive structural evolution. Fitness is evaluated through quantum sampling, using the mean decoded output of measurement outcomes as the argument of the objective function. To isolate the impact of quantum resources, we compare gate sets with and without the Hadamard gate, showing that superposition consistently improves convergence and robustness across benchmark functions such as the Rastrigin function. Furthermore, we demonstrate that introducing pairwise inter-individual entanglement in the population accelerates early convergence, revealing that quantum correlations among individuals provide an additional optimization advantage. Together, these results show that both superposition and entanglement enhance the search dynamics of evolutionary quantum algorithms, establishing gate-based QGAs as a promising framework for quantum-enhanced global optimization.