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Mathematical Problems in Engineering

Quantum Genetic Algorithm Based on Qutrits and Its Application

Valerii M. Tkachuk

Published Jan 1, 2018• 23 citations
Publisher

Abstract

Typical approaches to designing quantum genetic algorithms are based on a concept of a qubit, a two-level quantum system. But many-valued quantum logic is more perspective from the point of view of the computational power. This paper proposes a quantum genetic algorithm based on a three-level quantum system in order to accelerate evolutionary process. Simulation using a set of standard test functions proves that the given algorithm is more effective and precise than the conventional quantum genetic algorithm.

DOI
10.1155/2018/8614073

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Typical approaches to designing quantum genetic algorithms are based on a concept of a qubit, a two-level quantum system. But many-valued quantum logic is more perspective from the point of view of the computational power. This paper proposes a quantum genetic algorithm based on a three-level quantum system in order to accelerate evolutionary process. Simulation using a set of standard test functions proves that the given algorithm is more effective and precise than the conventional quantum genetic algorithm.
We present a new evolutionary algorithm on the basis of quantum computations technology for solving optimization problems. The algorithm is built using many-valued quantum logic concept, which is more prospective from the computing power’s point of view. We compare the suggested algorithm to the traditional quantum genetic algorithm to demonstrate its high effectiveness on the example of test function global optimization problems. The advantages can be observed in the running time, the convergence speed, and the solution precision. The proposed implementation for the algorithm of quantum gate operator has an adaptive nature and does not require a lookup table. The role and the influence mechanism of the quantum disaster operator on the proposed algorithm effectiveness are also analyzed.
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so called Quantum Evolutionary Programming has two major sub-areas: Quantum Inspired Genetic Algorithms (QIGAs) and Quantum Genetic Algorithms (QGAs). The former adopts qubit chromosomes as representations and employs quantum gates for the search of the best solution. The later tries to solve a key question in this field: what GAs will look like as an implementation on quantum hardware? As we shall see, there is not a complete answer for this question. An important point for QGAs is to build a quantum algorithm that takes advantage of both the GA and quantum computing parallelism as well as true randomness provided by quantum computers. In the first part of this paper we present a survey of the main works in GAs plus quantum computing including also our works in this area. Henceforth, we review some basic concepts in quantum computation and GAs and emphasize their inherent parallelism. Next, we review the application of GAs for learning quantum operators and circuit design. Then, quantum evolutionary programming is considered. Finally, we present our current research in this field and some perspectives.
This paper proposes a novel evolutionary computing method called a genetic quantum algorithm (GQA). GQA is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting qubit chromosome as a representation GQA can represent a linear superposition of solutions due to its probabilistic representation. As genetic operators, quantum gates are employed for the search of the best solution. Rapid convergence and good global search capability characterize the performance of GQA. The effectiveness and the applicability of GQA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that GQA is superior to other genetic algorithms using penalty functions, repair methods and decoders.
Quantum genetic algorithms(QGA) typically construct traditional quantum chromosomes as independent quantum bit systems, which has facilitated the enhancement of search speed and precision in genetic algorithms, demonstrating powerful problem-solving capabilities in optimization issues. Although traditional QGA have enriched population diversity, they still tend to fall into local optima, and the evolutionary update operations require rotation directions to be determined by lookup tables, a process involving multiple conditional judgments that affect algorithm efficiency. To address these issues, an improved method has been proposed to further enhance the performance of QGA. In the initial population selection, a population grouping evolution method based on microhabitat coevolution strategy is used to prevent the algorithm from getting trapped in local optima when solving complex function problems. Additionally, quantum entanglement is introduced on top of quantum super-position by implementing quantum entanglement using quantum registers, and higher-order quantum rotation gates are employed that do not involve multiple conditional judgments of lookup tables, thus improving the efficiency of quantum chromosome measurement and evolutionary updates. Finally, traditional QGA and higher-order quantum genetic algorithms were applied to test functions in multiple experiments. The results indicate that, compared to traditional QGA, the higher-order quantum genetic algorithms have achieved an increase in convergence speed, an approximate 14.3% improvement in convergence precision, and possess enhanced global search capabilities.
Genetic quantum algorithms (GQA) are population based evolutionary algorithms that imitate quantum physics by introducing quantum bits for a basic probabilistic genotypic representation and hence better population diversity, and quantum gates for evolving the population of solutions. While quantum inspired gates play an important role in the evolutionary process, there is no specific method for their design, i.e. they are mostly developed through ad hoc procedures. Here, we propose a multi-objective meta-level GQA in order to determine parameters of QG which is applicable for a wide variety of optimization problems. Specifically, a two-layer GQA is constructed, in which the lower layer's objective is to optimize the four junction types: Dejong, Peak, Easoms, and Griewank. And the higher layer's objective is to determine optimal parameters for QG that helps the proposed algorithm find best solutions. GQA optimization performance, with optimized parameter of QG is compared with GA on several benchmark problems and the superiority of the proposed method is statistically shown.