Automatic quantum circuit design is motivated by the difficulties in manual design, because quantum algorithms are highly non-intuitive and practical quantum computer hardware is not yet available. Thus, quantum computers have to be simulated on classical hardware which naturally entails an exponential growth of computational costs and allows only to simulate small quantum systems, i. e., with only few qubits. Huge search spaces render evolutionary approaches nearly unable to achieve breakthrough solutions in the development of new quantum algorithms. Consequently, at present we must be content to evolve essentially already existing (black-box) quantum algorithms. This thesis presents empirical results on the evolution of quantum circuits using genetic programming. For that purpose, a linear and a linear-tree GP system (allowing intermediate measurements) with integrated quantum computer simulator were implemented. Their practicality in evolving quantum circuits is shown in different experiments for 1-SAT (solutions act like Hogg's algorithm) and the Deutsch-Jozsa problem. These experiments confirm that the evolution of quantum circuits is practically feasible only for sufficiently small problem instances. In this context, scalability and the detection of scalability becomes very important. It is shown that scalable quantum circuits are evolvable to a certain degree: a general quantum circuit can be inferred manually from the evolved solutions for small instances of the given problem. Besides, further experiments indicate that 're-evolution' is effective for the evolution of scalable quantum circuits. With this method the start population of a problem instance is inoculated with evolved solutions for a smaller problem instance. Furthermore, investigations of fitness landscapes and selection strategies are made, with the aim of improving the efficiency of evolutionary search. A notable result is that using the crossover operator damages rather than benefits evolution of quantum circuits.
Automatic quantum circuit design is motivated by the difficulties in manual design, because quantum algorithms are highly non-intuitive and practical quantum computer hardware is not yet available. Thus, quantum computers have to be simulated on classical hardware which naturally entails an exponential growth of computational costs and allows only to simulate small quantum systems, i. e., with only few qubits. Huge search spaces render evolutionary approaches nearly unable to achieve breakthrough solutions in the development of new quantum algorithms. Consequently, at present we must be content to evolve essentially already existing (black-box) quantum algorithms. This thesis presents empirical results on the evolution of quantum circuits using genetic programming. For that purpose, a linear and a linear-tree GP system (allowing intermediate measurements) with integrated quantum computer simulator were implemented. Their practicality in evolving quantum circuits is shown in different experiments for 1-SAT (solutions act like Hogg's algorithm) and the Deutsch-Jozsa problem. These experiments confirm that the evolution of quantum circuits is practically feasible only for sufficiently small problem instances. In this context, scalability and the detection of scalability becomes very important. It is shown that scalable quantum circuits are evolvable to a certain degree: a general quantum circuit can be inferred manually from the evolved solutions for small instances of the given problem. Besides, further experiments indicate that 're-evolution' is effective for the evolution of scalable quantum circuits. With this method the start population of a problem instance is inoculated with evolved solutions for a smaller problem instance. Furthermore, investigations of fitness landscapes and selection strategies are made, with the aim of improving the efficiency of evolutionary search. A notable result is that using the crossover operator damages rather than benefits evolution of quantum circuits.
The goal of this work is to understand the application of the evolutionary programming approach to the problem of quantum circuit design. This problem is motivated by the following observations: In order to keep up with the seemingly insatiable demand for computing power our computing devices will continue to shrink, all the way down to the atomic scale, at which point they become quantum mechanical systems. In fact, this event, known as Moore?s Horizon, is likely to occur in less than 25 years. The recent discovery of several quantum algorithms which can solve some interesting problems more efficiently than any known classical algorithm. While we are not yet certain that quantum computers will ever be practical to build, there do now exist the first few astonishing experimental devices capable of briefly manipulating small quantities of quantum information. The programming of these devices is already a nontrivial problem, and as these devices and their algorithms become more complicated this problem will quickly become a significant challenge. The Evolutionary Programming (EP) approach to problem solving seeks to mimic the processes of evolutionary biology which have resulted in the awesome complexity of living systems, almost all of which are well beyond our current analysis and engineering capabilities. This approach is motivated by the highly successful application of Koza?s Genetic Programming (GP) approach to a variety of circuit design problems, and specifically the preliminary reports byWilliams and Gray and also Rubinstein who applied GP to quantum circuit design. Accompanying this work is software for evolutionary quantum circuit design which incorporates several advances over previous approaches, including: A formal language for describing parallel quantum circuits out of an arbitary elementary gate set, including gates with one or more parameters. A fitness assessment procedure that measures both average case fidelity with a respect for global phase equivalences, and implementation cost. A Memetic Programming (MP) based reproductive strategy that uses a combination of global genetic and local memetic searches to effectively search through diverse circuit topologies and optimize the parameterized gates they contain. Several benchmark experiments are performed on small problems which support the conclusion that Evolutionary Programming is a viable approach to quantum circuit design and that further experiments utilizing more computational resources and more problem insight can be expected to yield many new and interesting quantum circuits.
Due to the non- intuitive nature of Quantum algorithms, it becomes difficult for a classically trained person to efficiently construct new ones. So rather than designing new algorithms manually, lately, Genetic algorithms (GA) are being implemented for this purpose. GA is a technique to automatically solve a problem using principles of Darwinian evolution. This has been implemented to explore the possibility of evolving an n-qubit circuit when the circuit matrix has been provided using a set of single, two and three qubit gates. Using a variable length population and universal stochastic selection procedure, a number of possible solution circuits, with different number of gates can be obtained for the same input matrix during different runs of GA. The given algorithm has also been successfully implemented to obtain two and three qubit Boolean circuits using Quantum gates. The results demonstrate the effectiveness of the GA procedure even when the search spaces are large.
This paper demonstrates an application of an evolutionary approach for solving a class of non-trivial, hardware-design problems. Array processing features of the computer language APL simplify the implementation of an evolutionary solution in which simulation is performed by a genetic algorithm on a population of candidate solutions until one or more are satisfactory quantum algorithms. The objective of the simulation model is the automatic discovery of quantum computer algorithms. The algorithms are expressed in a circuit model that specifies the sequences in which quantum operators are to be applied. The automatically configured circuits operate as quantum computers that for the present have their domains of application limited to evaluation of only a few specific functions. The simulations use a small collection of basic and relatively low-level operators to obtain perfect results for five different target functions. These functions were chosen to demonstrate how, on a personal computer, an evolutionary method is able to discover novel designs of computing hardware. The results establish that it is feasible to use genetic algorithms in an evolutionary method to invent correct hardware designs. The progress of simulated evolution is directed by input/output constraints and a fitness function. Alternative configurations of circuit models can obtain algorithms with promise for future quantum computers. Current simulations yield primitive quantum algorithms with a total of twelve or fewer inputs and outputs. The discovered algorithms produce the correct results for evaluating the five selected logical and arithmetic functions.
This paper demonstrates an application of an evolutionary approach for solving a class of non-trivial, hardware-design problems. Array processing features of the computer language APL simplify the implementation of an evolutionary solution in which simulation is performed by a genetic algorithm on a population of candidate solutions until one or more are satisfactory quantum algorithms. The objective of the simulation model is the automatic discovery of quantum computer algorithms. The algorithms are expressed in a circuit model that specifies the sequences in which quantum operators are to be applied. The automatically configured circuits operate as quantum computers that for the present have their domains of application limited to evaluation of only a few specific functions. The simulations use a small collection of basic and relatively low-level operators to obtain perfect results for five different target functions. These functions were chosen to demonstrate how, on a personal computer, an evolutionary method is able to discover novel designs of computing hardware. The results establish that it is feasible to use genetic algorithms in an evolutionary method to invent correct hardware designs. The progress of simulated evolution is directed by input/output constraints and a fitness function. Alternative configurations of circuit models can obtain algorithms with promise for future quantum computers. Current simulations yield primitive quantum algorithms with a total of twelve or fewer inputs and outputs. The discovered algorithms produce the correct results for evaluating the five selected logical and arithmetic functions.
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.
Designing effective quantum circuits remains a central challenge in quantum computing, as circuit structure strongly influences expressivity, trainability, and hardware feasibility. Current approaches, whether using manually designed circuit templates, fixed heuristics, or automated rules, face limitations in scalability, flexibility, and adaptability, often producing circuits that are poorly matched to the specific problem or quantum hardware. In this work, we propose the Evolutionary eXploration of Augmenting Quantum Circuits (EXAQC), an evolutionary approach to the automated design and training of parameterized quantum circuits (PQCs) which leverages and extends on strategies from neuroevolution and genetic programming. The proposed method jointly searches over gate types, qubit connectivity, parameterization, and circuit depth while respecting hardware and noise constraints. The method supports both Qiskit and Pennylane libraries, allowing the user to configure every aspect. This work highlights evolutionary search as a critical tool for advancing quantum machine learning and variational quantum algorithms, providing a principled pathway toward scalable, problem-aware, and hardware-efficient quantum circuit design. Preliminary results demonstrate that circuits evolved on classification tasks are able to achieve over 90% accuracy on most of the benchmark datasets with a limited computational budget, and are able to emulate target circuit quantum states with high fidelity scores.