This work is a first study of search spaces and fitness landscapes in the context of quantum program evolution. Considering small instances of the Deutsch-Josza problem as a staring point for explorations of quantum program search spaces, we analyze the structure of mutation landscapes using autocorrelation characteristics and information measures. Our motivation is to obtain insights into the relationship between landscape characteristic and quantum circuit evolution with the aim to improve the efficiency of evolutionary search.
This work is a first study of search spaces and fitness landscapes in the context of quantum program evolution. Considering small instances of the Deutsch-Josza problem as a staring point for explorations of quantum program search spaces, we analyze the structure of mutation landscapes using autocorrelation characteristics and information measures. Our motivation is to obtain insights into the relationship between landscape characteristic and quantum circuit evolution with the aim to improve the efficiency of evolutionary search.
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.
Quantum Information represents a fundamentally different paradigm from classical information, offering the potential for exponential speedups in computation and communication. This paper explores the application of Landscape-Based Algorithms (LBAs) to optimization problems, specifically focusing on the challenge of efficiently navigating complex search spaces. We propose a novel algorithmic approach that models the problem space as a dynamic landscape, iteratively moving across this landscape to reward solutions that are closer to the optimal solution. This framework allows for exploration of vast possibilities, dramatically improving the search efficiency compared to traditional optimization methods. The core mechanism involves a dynamic reward function that adjusts based on the landscape's characteristics, encouraging the algorithm to escape local optima and converge to a global optimum. This paper provides a detailed explanation of the Landscape model, explores its implementation, and discusses its potential impact on optimization problems across diverse domains.
Recently, quantum computing has emerged as a new paradigm that promises to improve artificial intelligence techniques. One of the research fields that is certainly benefiting from this new computational paradigm is evolutionary optimization. In literature, efforts have been already made to run evolutionary algorithms on quantum computers using quantum effects such as superposition and entanglement to converge towards sub-optimal solutions of hard problems. However, the performance of these quantum evolutionary approaches is limited by the number of qubits available on current quantum devices. This limitation is more noticeable in the case of continuous optimization problems, where the search space is potentially infinite. This paper presents a recursive algorithmic structure that embodies a quantum evolutionary algorithm to overcome the limitations mentioned above. The result is an innovative and efficient approach in the context of quantum evolutionary optimization.
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.
Quantum-driven evolutionary computation offers a promising approach to solving complex constraint satisfaction problems (CSPs) by leveraging the unique capabilities of quantum annealing. This paper explores the integration of quantum annealing with evolutionary computation to achieve significantly faster and more efficient search for optimal solutions. We detail the design of a hybrid algorithm that combines the strengths of both paradigms, focusing on the generation of candidate solutions, refinement through evolutionary operators, and the efficient exploration of the solution space. The core mechanism centers around quantum annealing's ability to efficiently address high-dimensional search spaces, coupled with the evolutionary algorithm's capacity to explore diverse solutions and adapt to changing problem landscapes. This research investigates the effectiveness of this hybrid approach in tackling challenging CSPs, aiming to surpass the limitations of traditional classical methods.