Evolutionary systems (ES) include software applications that solve problems using heuristic methods instead of the deterministic ones. The classical computing used for ES development involves random methods to improve different kinds of genomes. The mappings of these genomes lead to individuals that correspond to the searched solutions. The individual evaluations by simulations serve for the improvement of their genotypes. Quantum computations, unlike the classical computations, can describe and simulate a large set of individuals simultaneously. This feature is used to diminish the time for finding the solutions. Quantum Petri Nets (QPNs) can model dynamical systems with probabilistic features that make them appropriate for the development of ES. Some examples of ES applications using the QPNs are given to show the benefits of the current approach. The current research solves quantum evolutionary problems using quantum genetic algorithms conceived and improved based on QPN. They were tested on a dynamic system using a Quantum Discrete Controlled Walker (QDCW).
Evolutionary systems (ES) include software applications that solve problems using heuristic methods instead of the deterministic ones. The classical computing used for ES development involves random methods to improve different kinds of genomes. The mappings of these genomes lead to individuals that correspond to the searched solutions. The individual evaluations by simulations serve for the improvement of their genotypes. Quantum computations, unlike the classical computations, can describe and simulate a large set of individuals simultaneously. This feature is used to diminish the time for finding the solutions. Quantum Petri Nets (QPNs) can model dynamical systems with probabilistic features that make them appropriate for the development of ES. Some examples of ES applications using the QPNs are given to show the benefits of the current approach. The current research solves quantum evolutionary problems using quantum genetic algorithms conceived and improved based on QPN. They were tested on a dynamic system using a Quantum Discrete Controlled Walker (QDCW).
Many applications of quantum computers require the classical and quantum implementation of dynamic systems (DSs). These applications comprise interacting quantum and classical tasks. While quantum tasks evolve in the quantum domain, classical tasks behave in the classical domain. Besides tackling these kinds of tasks, the computational gap between these domains is covered by the current study. The quantum computing feature All at Once (A@O) executions is appropriate for static systems but less for DSs. The novelty of the proposed approach consists of using Distributed Quantum-Centric Petri Net (DQCPN) models composed of quantum and high-level Petri Nets for specification, design, verification, and implementation of classical–quantum applications. Quantum Processing Units (QPUs) are linked to classical components implementing the control and optimization operations in the proposed application. Many practical applications combine quantum and classical computing to address optimization problems. Quantum computers can be built with a combination of qubits and bosonic qumodes, leading to a new paradigm toward quantum computing. The optimizations are performed by some Evolutionary Algorithms (EAs), including Particle Swarm Optimization (PSO) methods and Genetic Algorithms (GAs). For experiments, an Urban Vehicle Traffic System (UVTS) is used as an open distributed system. The vehicle flows are implemented by discrete qubits, discrete vectors of qubits, or qumodes.
The development of quantum software applications requires models capable to describe quantum features (superposition, entanglement, reversibility etc.) as well as the software algorithm requirements. The newly proposed Quantum Petri Nets (QPNs) have the structure of the classical Petri Nets (PNs), but their tokens represent superposed quantum states fulfilling the Hilbert space features. Instead of the integer numerical values of the PN marking, QPNs use quantum marking describing an extreme huge space. New conditions for the transition enabling and new mappings for the transition executions are conceived. A PN based language is used for the structure analysis. Replacing the classical tokens with the probability distribution of the quantum vectors, the QPN simulation is possible as well as the construction of a reachability graph.
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.
By violating the extended Church-Turing thesis, the quantum computing (QC) paradigm has emerged as a serious contender to classical computing. We now know that certain classical exponential problems (NP (nondeterministic polynomial time)-complete) can be solved in polynomial time by QC. Shor’s integer factorization and Grover’s method for unstructured search are perhaps the most well-known quantum algorithms. QC has been successfully applied to a variety of domains including optimization problems. Optimization can be solved by using deterministic/numerical as well as stochastic methods. Genetic algorithms (GA) belong to the latter category. Incorporating quantum mechanical properties such as superposition, entanglement, interference into the structure of GA has resulted in a more efficient evolutionary computing method called the quantum-inspired genetic algorithm. This method has been successfully applied to image processing, signal processing, economic load dispatch, coalition formation, task scheduling, etc. This chapter presents an overview of the current trends and developments in the domain of quantum-inspired genetic algorithms with the aim of investigating areas of further research in this sphere.
This paper proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, evaluation function, and population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, experiments were carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional genetic algorithm.
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.