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International Computer Science and Engineering Conference

Experiments on Quantum Circuits for Compact Genetic Algorithm

Kamonluk Suksen, Naphan Benchasattabuse, Prabhas Chongstitvatana

Published Nov 18, 2021• 0 citations
Publisher

Abstract

Programming a quantum computer is still a challenge for researchers. Quantum computers operate based on a fundamentally different paradigm from classical computers. Programming a quantum computer today is somewhat like programming a classical computer in the 1950s, in a manner close to assembly language. This paper presents a Grover-assisted compact genetic algorithm to solve some real-world problems on a quantum computer. This method is a combination of Grover's search algorithm initializing with the probability distribution, and a compact genetic algorithm with elite (cGA*), which keeps the current best individual. The compact genetic algorithm (cGA) is a powerful and popular method in evolutionary computation. The results of the proposed algorithm are compared with the cGA running on classical computers in terms of the solution quality and the number of function evaluations. The compared results illustrate that the proposed methodology can successfully reach 100% accuracy of the solution with a higher number of function evaluations than the cGA.

DOI
10.1109/icsec53205.2021.9684643

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Programming a quantum computer is still a challenge for researchers. Quantum computers operate based on a fundamentally different paradigm from classical computers. Programming a quantum computer today is somewhat like programming a classical computer in the 1950s, in a manner close to assembly language. This paper presents a Grover-assisted compact genetic algorithm to solve some real-world problems on a quantum computer. This method is a combination of Grover's search algorithm initializing with the probability distribution, and a compact genetic algorithm with elite (cGA*), which keeps the current best individual. The compact genetic algorithm (cGA) is a powerful and popular method in evolutionary computation. The results of the proposed algorithm are compared with the cGA running on classical computers in terms of the solution quality and the number of function evaluations. The compared results illustrate that the proposed methodology can successfully reach 100% accuracy of the solution with a higher number of function evaluations than the cGA.
Programming a quantum computer posts a challenge. It is not straight forward to transfer the current programming skill on a classical computer to a quantum computer. This work presents an example of programming a quantum computer. The compact genetic algorithm is used as a target as it is powerful and popular method in evolutionary computation. A quantum bit (qubit) concept was introduced as a basis for storing information. The representation of quantum register has benefits over classical computing, i.e. the quantum operation allows manipulating qubits in the way that it is impossible in a classical computer. This paper demonstrates the enhancement in terms of solution quality and speed introduced by quantum computation. The simulation of quantum computing is carried out for solving a problem using the compact genetic algorithm.
Quantum Genetic Algorithms (QGA) integrate genetic programming and quantum computing to address search and optimization problems. The standard strategy of the hybrid QGA approach is to add quantum resources to classical genetic algorithms (GA), thus improving their efficacy (i.e., quantum optimization of a classical algorithm). However, the extent of such improvements is still unclear. Conversely, Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that reduces the GA search for the best fitness in a population of potential solutions to running Grover's algorithm. Unfortunately, RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions of the problem) in exponential runtime, [[EQUATION]], where [[EQUATION]] is the number of qubits in the individuals' quantum register. This paper introduces a novel QGA optimization strategy, namely a classical optimization of a fully quantum algorithm, to address the Reduced Quantum Genetic Algorithm (RQGA) complexity problem. Accordingly, we control the complexity of theReduced Quantum Genetic Algorithm (RQGA) algorithm 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 RQGA by discarding unfit solutions and bounding the search only in the area of valid individuals. As a result, our Hybrid Quantum Algorithm with Genetic Optimization (HQAGO) solves search problems in [[EQUATION]] oracle queries, where [[EQUATION]] is the number of fixed classical bits in the individuals' register.
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.
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: Evolving solutions rather than computing them certainly represents a promising programming approach. Evolutionary computation has already been known in computer science since more than 4 decades. More recently, another alternative of evolutionary algorithms was invented: Quantum Genetic Algorithms (QGA). In this paper, we outline the approach of QGA by giving a comparison with Conventional Genetic Algorithm (CGA). Our results have shown that QGA can be a very promising tool for exploring search spaces.
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.