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.
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.
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.
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.
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.
Recent development in quantum technology have shown that quantum computer can provide a dramatic advantage over classical computers for some algorithms. In particular, a polynomial-time algorithm for factoring, a problem which was previously thought to be hard for classical computers, has recently been developed [13]. Similarly, a quantum algorithm searching for unsorted database in square root of time it would take on a classical computer has also been described by Grover [4] - [3]. Both algorithms rely upon the inherent parallelism, superposition and entanglement property of quantum computing to achieve their improvements. Since most problems of real interest for genetic algorithms have a vast search space, it seems appropriate how quantum parallelism can be applied to Genetic Algorithms. In this paper we provide a brief background of quantum computers. We explain why and how quantum algorithms provides a fundamental improvements over classical ones for some problems. Further, we present here the Conventional Genetic Algorithm and the quantum approach of Genetical Algorithms(QGA) as well. The benefits and drawbacks of QGA are also analyzed. Moreover, this paper provides an improved version over the conventional QGA. This improvement originates from the best partial immigration technique applied to the quantum chromosomes. The main objective of the best partial immigration is to consider the string of qubits from the quantum chromosomes having best fitness and transfer the same randomly to the chromosomes of next generation for better mixing. The process is reiterated. To observe the performance the best partial immigration technique we have considered some popular optimization problems and performed the experiment on it. These problems are namely Travelling Salesman Problem(TSP), Binpacking Problem and Vertex Cover Problem. It has been observed that the obtained results outperforms the conventional QGA.
The developments in the area of Evolvable Quantum Hardware (QEHW) are based on successful quantum genetic algorithms (QGAs) that take advantage of both the Genetic Algorithms (GAs) and Quantum Computation (QC) parallelism. This paper presents a new Quantum Inspired Genetic Algorithm (QIGA) based on the evolution of a single chromosome. A simple combinational circuit has been implemented using a conventional GA (CGA), a single chromosome QGA (SCQGA), and the new QIGA. In the last case, the total evolution time has been considerably reduced, by changing the population size used in the evolution.
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.