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IEEE Latin American Conference on Computational Intelligence (LA-CCI)

A Propose of Genetic Operators for Quantum Algorithms with Real Representation

Eduardo Dessupoio Moreira Dias, Marley M. B. R. Vellasco

Published Nov 2, 2021• 1 citation
Publisher

Abstract

In the literature, there are many Quantum Inspired Evolutionary Algorithms (QIEA) that proved good performance and results when applied to solving a myriad of problems. However, the real quantum representation increases precision for numerical optimisation problems and reduces the memory storage need, alternatively to the binary representation. On the other hand, evolutionary algorithms' performance mainly depends on the crossover and mutation operators, reaching equilibrium between the explorative and exploitative features of evolutionary algorithms. This paper proposes new quantum genetic operators for real quantum representation, instead of the 1/5 rule present in AEIQ-R, to improve the performance of the quantum genetic algorithm with real representation. Three crossover and two mutation operators are proposed and tested to optimise four functions with different dimensions. Friedman's test indicated a significant difference between the combinations, and that combination composed of quantum arithmetic crossover and quantum creep mutation have the best performance.

DOI
10.1109/la-cci48322.2021.9769847

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In the literature, there are many Quantum Inspired Evolutionary Algorithms (QIEA) that proved good performance and results when applied to solving a myriad of problems. However, the real quantum representation increases precision for numerical optimisation problems and reduces the memory storage need, alternatively to the binary representation. On the other hand, evolutionary algorithms' performance mainly depends on the crossover and mutation operators, reaching equilibrium between the explorative and exploitative features of evolutionary algorithms. This paper proposes new quantum genetic operators for real quantum representation, instead of the 1/5 rule present in AEIQ-R, to improve the performance of the quantum genetic algorithm with real representation. Three crossover and two mutation operators are proposed and tested to optimise four functions with different dimensions. Friedman's test indicated a significant difference between the combinations, and that combination composed of quantum arithmetic crossover and quantum creep mutation have the best performance.
This paper presents a comparative study regarding the evolutionary design of quantum operators in the form of unitary matrices. Three different techniques allowing the generation of unitary matrices are investigated whose parameters are tuned by means of evolutionary algorithms. Such problem may be considered as a numerical optimisation task because the unitary matrices are represented by complex numbers with real-valued coefficients. Specifically, Genetic Algorithm and Evolution Strategy are applied, each in four different setups, and evaluated on three case studies: the 2-qubit Controlled-NOT gate, 3-qubit entanglement operator and 4-qubit detector of an element with the maximum amplitude. The evolutionary algorithms in combination with the given representation techniques are evaluated in order to determine the abilities of various experimental setups to solve the given tasks. The main contribution is the utilisation of QR decomposition, a technique for generating unitary matrices from theoretically any sequence of complex numbers, that has been applied for the first time in this paper for the evolution of quantum operators. It will be demonstrated that the QR decomposition exhibits a good performance especially in solving more complex quantum operators in comparison with other representations.
Genetic Quantum Algorithm (GQA) is an evolutionary algorithm in the class of quantum inspired evolutionary algorithms inspired by the principles of quantum computing such as Q-bits, super position, quantum gates, interference and coherence. GQA adopts Q-bit representation and applies quantum rotation gate (QR gate) as genetic operator. The performance of the quantum inspired evolutionary algorithms largely depends upon the effectiveness of quantum gates applied as the genetic operator. Researchers have attempted to improve the performance of quantum inspired evolutionary algorithms by designing various quantum evolutionary operators using different strategies. In this paper, an effort is made to study the impact of Random search based QR gate strategy in GQA, and subsequently a Random search and greedy selection based Genetic Quantum Algorithm (RSGS-GQA) is proposed. The performance of RSGS-GQA algorithm is compared with the standard quantum inspired evolutionary algorithms (QIEA) on knapsack problem. The results indicate that, the RSGS-GQA algorithm performs better than the standard QIEA variants in terms of the quality of the solution and convergence.
Genetic Algorithms (GAs) are optimization methods that search near-optimal solutions by applying well-known operations such as selection, crossover and mutation. In particular, crossover and mutation are aimed at creating new solutions from selected parents with the goal of discovering better and better solutions in the search space. In literature, several approaches have been defined to create new solutions from the mating pool to try to improve the performance of genetic optimization. In this paper, the literature is enriched by introducing a new mating operator that harnesses the stochastic nature of quantum computation to evolve individuals in a classical genetic workflow. This new approach, named Quantum Mating Operator, acts as a multi-parent operator that identifies alleles' frequency patterns from a collection of individuals selected by means of conventional selection operators, and encodes them through a quantum state. This state is successively mutated and measured to generate a new classical chromosome. As shown by experimental results, GAs equipped with the proposed operator outperform those equipped with traditional crossover and mutation operators when used to solve well-known benchmark functions.
Genetic algorithms are widely used for solving optimization problems. As the search space of the problem is augmented, the probability of falling into local minima will be augmented as well. Previous works showed that the adjusted phase (i.e. required modification per generation), may enhance badly the optimality reaching. Moreover, the search for suitable probabilities on crossover and mutation results in huge computational complexity. Recent developments in quantum technology have shown that quantum computers can provide a dramatic advantage over classical computers. This paper will be oriented toward computer scientists interested in the quantum genetic algorithm (QGA). Therefore, we will present a discussion, of the pros, and cons of classical GA. We survey the “state of the art” of the most known techniques for evolving evolutionary algorithms and quantum computing. We intend in this work to help researchers and application developers in gaining insights into the power of quantum computing mechanisms. This science can inherently treat the balance between exploration and exploitation of the search space. This property is due to the use of Q-bits. The orientation toward the best solution is due to the use of Q-gates.
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.
We investigate two modified Quantum Evolutionary methods for solving real value problems. The Quantum Inspired Evolutionary Algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to real value problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding respectively, while keeping close to the original quantum computing metaphor. We evaluate our approaches against sets of multimodal mathematical test functions and real world problems, using five performance metrics and include comparisons to published results. We report the issues encountered while implementing some of the published real QIEA techniques. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (especially for the more complex and challenging ones), demonstrating faster convergence and accuracy.