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International Journal of Bio-Inspired Computation

Expediting population diversification in evolutionary computation with quantum algorithm

Jun Suk Kim, Chang Wook Ahn

Published Jan 1, 2021• 1 citation
Publisher

Abstract

Quantum computing's uniqueness in commencing parallel computation renders unprecedented efficient optimisation as possible. This paper introduces the adaptation of quantum processing to crowding, one of the genetic algorithmic procedures to secure undeveloped individual chromosomes in pursuit of diversifying the target population. We argue that the nature of genetic algorithm to find the best solution in the process of optimisation can be greatly enhanced by the capability of quantum computing to perform multiple computations in parallel. By introducing the relevant quantum mathematics based on Grover's selection algorithm and constructing its mechanism in a quantum simulator, we come to conclusion that our proposed approach is valid in such a way that it can precisely reduce the amount of computation query to finish the crowding process without any impairment in the middle of genetic operations.

DOI
10.1504/ijbic.2021.113356

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Quantum computing's uniqueness in commencing parallel computation renders unprecedented efficient optimisation as possible. This paper introduces the adaptation of quantum processing to crowding, one of the genetic algorithmic procedures to secure undeveloped individual chromosomes in pursuit of diversifying the target population. We argue that the nature of genetic algorithm to find the best solution in the process of optimisation can be greatly enhanced by the capability of quantum computing to perform multiple computations in parallel. By introducing the relevant quantum mathematics based on Grover's selection algorithm and constructing its mechanism in a quantum simulator, we come to conclusion that our proposed approach is valid in such a way that it can precisely reduce the amount of computation query to finish the crowding process without any impairment in the middle of genetic operations.
Abstract Quantum computers promise to revolutionize the world of computing thanks to some features of quantum mechanics that can enable massive parallelism in computation. This benefit may be particularly relevant in the design of evolutionary algorithms, where the quantum paradigm could support the exploration of multiple regions of the search space in a concurrent way. Although some efforts in this research field are ongoing, the potential of quantum computing is not yet fully expressed due to the limited number of qubits of current quantum processors. This limitation is even more acute when one wants to deal with continuous optimization problems, where the search space is potentially infinite. The goal of this paper is to address this limitation by introducing a hybrid and granular approach to quantum algorithm design, specifically designed for genetic optimization. This approach is defined as hybrid, because it uses a digital computer to evaluate fitness functions, and a quantum processor to evolve the genetic population; moreover, it uses granular computing to hierarchically reduce the size of the search space of a problem, so that good near-optimal solutions can be identified even on small quantum computers. As shown in the experiments, where IBM Q family processors are used, the usage of a granular computation scheme statistically enhances the performance of the state-of-the-art evolutionary algorithm implemented on quantum computers, when it is run to optimize well-known benchmark continuous functions.
This paper proposes a novel approach to optimization problems by integrating quantum entanglement with the Genetic Algorithm (GA). The core idea is to leverage the inherent parallelism and enhanced information transfer capabilities of quantum entanglement to significantly improve the search performance of the GA. We represent genetic algorithm chromosomes as quantum states and employ quantum entanglement to facilitate rapid information exchange and crossover operations across multiple qubits. This mechanism allows for parallel exploration of the search space, mitigating the limitations of traditional GA's tendency towards local optima. The theoretical framework and the underlying principles are presented, demonstrating the potential for the Quantum Entanglement Genetic Algorithm (QGA) to accelerate the solution of complex optimization problems. The algorithm's effectiveness is discussed through a mathematical formulation, focusing on the key components of the QGA and its advantages over conventional GA. The ultimate goal is to demonstrate a robust and efficient method for tackling challenging optimization tasks.
This paper presents a new methodology for running Genetic Algorithms on a Quantum Computer. To the best of our knowledge and according to reference [6]there are no feasible solutions for the implementation of the Quantum Genetic Algorithms (QGAs). We present a new perspective on how to build the corresponding QGA architecture. It turns out that the genetic strategy is not particularly helpful in our quantum computation approach; therefore our solution consists of designing a special-purpose oracle that will work with a modified version of an already known algorithm (maximum finding [1]), in order to reduce the QGAs to a Grover search. Quantum computation offers incentives for this approach, due to the fact that the qubit representation of the chromosome can encode the entire population as a superposition of basis-state values.
Abstract Quantum-assisted algorithms are expected to improve the computing performance of classical computers. A quantum genetic algorithm utilizes the advantages of quantum computation by combining the truncation selection in a classical genetic algorithm with the quantum Grover’s algorithm. The parallelism of evaluation can create global search and reduce the need of crossover and mutation in a conventional genetic algorithm. In this work, we aim to demonstrate and simulate the performance of an implementable quantum-assisted genetic algorithm. The algorithm was tested by using quadratic unconstrained binary optimization (QUBO) for 100 iterations; and the results were compared with those from a classical counterpart for 2000 iterations, where both simulations were performed over 100 repetitions. The results showed that the quantum algorithm converges to the optimal solution faster. While the variance is higher at early stage, it quickly and greatly reduces as the algorithm converges. The histograms of possible solutions consistently exhibits this behavior.
Abstract Quantum Genetic Algorithms (QGAs) integrate genetic programming and quantum computing to address search and optimization problems. Most QGA approaches add quantum features to genetic algorithm operators, such as selection, crossover, or mutation. Oppositely, the Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that encodes the entire search space (i.e., population) as a superposition of all possible solutions (chromosomes) using the individuals’ quantum register; the fitness function takes the individuals’ quantum register as input to generate corresponding fitness values within the chromosomes’ superposition. RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions) using Grover’s algorithm. The complexity of Grover’s algorithm is O(2N⁄2), where N is the number of superposed individual chromosomes. However, RQGA operates on an exponentially-big search space (N = 2n, where n is the number of qubits in the individuals’ quantum register), which entails an exponential runtime of O(2n⁄2). This paper introduces an optimization solution for RQGA that controls the algorithm complexity by selecting a limited number of qubits in the individuals’ register and fixing the remaining ones as classical values of ’0’ and ’1’ with a genetic algorithm. We also improve the performance of the RQGA by discarding unfit solutions and bounding the search only in the valid individuals’ area. Putting it all together, we introduce a novel quantum genetic algorithm—Hybrid Quantum Algorithm with Genetic Optimization (HQAGO)—that solves search problems in O(2(n-k)⁄2) oracle queries, where k is the number of fixed classical bits in the individuals’ register. We illustrate instantiations of HQAGO that solve the NP-hard knapsack and graph coloring problems, analyze the complexity of the new algorithm, and study the convergence of its heuristic part.
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.