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).

The 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.

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.