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An implementation of compact genetic algorithm on a quantum computer

Sorrachai Yingchareonthawornchai, Chatchawit Aporntewan, Prabhas Chongstitvatana

Published May 1, 2012• 10 citations
Publisher

Abstract

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.

DOI
10.1109/jcsse.2012.6261939

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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.
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.
Quantum computers are computational devices that use the dynamics of atomic-scale objects to store and manipulate information.Only a few, small-scale quantum computers have been built to date, but quantum computers can in principle outperform all possible classical computers in significant ways.Quantum computation is therefore a subject of considerable theoretical interest that may also have practical applications in the future.Genetic programming can automatically discover new algorithms for quantum computers [Spector et al., 1998].We describe how to simulate a quantum computer so that the fitness of a quantum algorithm can be determined on classical hardware.We then describe ways in which three different genetic programming approaches can drive the simulator to evolve new quantum algorithms.The approaches are standard tree-based genetic programming, stack-based linear genome genetic programming, and stackless linear genome genetic programming.We demonstrate the techniques on four different problems: the two-bit early promise problem, the scaling majority-on problem, the four-item database search problem, and the two-bit and-or problem.For three of these problems (all but majority-on) the automatically discovered algorithms are more efficient than any possible classical algorithms for the same problems.One of the better-than-classical algorithms (for the two-bit and-or problem) is in fact more efficient than any previously known quantum algorithm for the same problem, suggesting that genetic programming may be a valuable tool in the future study of quantum programming.
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.
Using quantum computing for drug design is among the most promising applications in quantum technologies. Genetic algorithms with their evolutionary iterations make it a propitious approach in various tasks, including drug discovery, gene prediction, docking of ligands to receptors, and the design to combinatorial libraries. As its computational power and methods limits classical computing, quantum computing intends to break these limits with exponential computing capabilities. This application complements both quantum theory and genetic programming as we use true randomness with mutation and fitness function based on information encoded onto qubits storing quantum data. In this article, we present the results of encoding quantum data to our quantum genetic algorithm, which predicts the best possible drug structure to bind onto the target protein. The qubits hold the genome structure to perform bit string mutation over quantum gates. These results are later than compared to classical computing with various approaches in the evolutionary algorithm's parameters.
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.
Genetic programming can be used to automatically discover algorithms for quantum computers that are more efficient than any classical computer algorithms for the same problems. In this paper we exhibit the first evolved betterthan-classical quantum algorithm, for Deutsch’s “early promise ” problem. We also demonstrate a technique for evolving scalable quantum gate arrays and discuss other issues in the application of genetic programming to quantum computation and vice versa. 1. Quantum Computing Quantum computers are computational devices that use atomic-scale objects, for example 2-state particles, to store and manipulate information (Steane, 1997; for an elementary on-line tutorial see Braunstein, 1995; for an introduction for the general reader see Milburn, 1997). The physics of these devices allows them to do things that common digital (henceforth “classical”) computers cannot. Although quantum computers and classical computers appear to be bound by the same limits of Turing computability, physicists argue that quantum computers can solve certain problems using less resources (time and space) than classical computers are thought to require (Jozsa, 1997). For example, Shor’s quantum algorithm finds the prime factors of an n-digit number in time O(n 3), while the best known classical factoring algorithms