Quantum Evolution: A New Approach to Optimization

Author: Denis Avetisyan

Harnessing the power of quantum mechanics, researchers have developed a genetic algorithm that explores solution spaces with unprecedented efficiency.

Across varying computational depths and generational limits—spanning 10, 30, and 50 generations—a quantum gate set leveraging superposition consistently outperformed a classical gate set in optimizing the Rastrigin function, as demonstrated through an average of 5000 independent trials, suggesting an inherent advantage in quantum computation for complex function optimization.

This paper presents a gate-based Quantum Genetic Algorithm utilizing superposition and entanglement to improve performance on real-valued global optimization problems.

Classical optimization algorithms often struggle with complex, high-dimensional search spaces, demanding innovative approaches to enhance exploration and convergence. This is addressed in ‘A Gate-Based Quantum Genetic Algorithm for Real-Valued Global Optimization’, which introduces a novel evolutionary framework leveraging gate-based quantum circuits to represent and manipulate candidate solutions. The authors demonstrate that encoding individuals as quantum circuits—and utilizing both superposition and inter-individual entanglement—significantly improves performance on benchmark optimization problems compared to classical genetic algorithms. Could this gate-based approach pave the way for robust and scalable quantum-enhanced solutions to real-world optimization challenges?

Breaking the Optimization Barrier

Classical optimization algorithms often falter on complex, high-dimensional problems, becoming trapped in local optima. Quantum computing offers a potential escape through superposition and entanglement, enabling more efficient exploration of the solution space. However, the limitations of current quantum hardware necessitate algorithms inspired by quantum principles, executable on classical systems. Quantum Genetic Algorithms (QGAs) have emerged as a powerful alternative, demonstrably achieving lower fitness values across benchmark problems – a sign of enhanced optimization capabilities. Ultimately, the pursuit of optimal solutions isn’t merely about finding the lowest point, but about understanding the contours of the entire landscape—and sometimes, dismantling the map itself.

For the Rastrigin function with a population size of 50, the fitness of the best individuals correlates with Shannon entropy, as the classical configuration (red) maintains zero entropy while the quantum configuration (blue) explores a broad spectrum, indicating a potential benefit of increased complexity.

Encoding Possibility: Quantum Circuits as Solutions

Quantum Generative Algorithms (QGAs) represent candidate solutions as ‘Gate-Based Quantum Circuits,’ leveraging quantum mechanics to explore complex landscapes. These circuits utilize superposition and entanglement to represent and manipulate multiple possibilities concurrently, allowing QGAs to explore exponentially larger solution spaces. Variable-Depth Circuits manage computational complexity, adapting to the problem’s difficulty. The ‘Circuit Space’ defines the range of possible circuits the algorithm explores, navigated by evolutionary strategies that select and modify circuits based on their performance.

After 140 generations for the Rastrigin function with a population size of 50, both the classical (red) and quantum (blue) configurations demonstrate a preference for deeper circuits, suggesting an evolutionary drive towards greater expressive power.

The Algorithm Evolves: Operators and Evaluation

The Quantum Genetic Algorithm (QGA) employs evolutionary operators—crossover and mutation—to generate and refine quantum circuits. Crossover exchanges genetic material, while mutation introduces random alterations, fostering exploration and preventing premature convergence. Fitness Evaluation, using benchmark functions like the Rastrigin and Ackley functions, quantifies circuit effectiveness, consistently demonstrating superior performance for quantum configurations. The algorithm iteratively applies these operators and evaluates fitness, driving the population towards optimal solutions. This cycle of selection, crossover, and mutation continues until a termination criterion is met, yielding a highly optimized circuit.

For the Rastrigin function with a population size of 50, the fitness of the best individuals improves with the number of generations for both the classical (red) and quantum (blue) configurations, as demonstrated by averaging over 5000 independent runs.

Beyond Individual Search: Collective Quantum Intelligence

Recent advancements introduce Inter-Individual Entanglement, a mechanism for enhanced population-wide search capabilities. This entanglement establishes correlations between circuits, enabling information sharing and accelerating optimization. Consequently, QGAs demonstrate faster convergence rates. Quantifying superposition and entanglement through Shannon Entropy reveals a correlation: higher entropy circuits exhibit lower fitness, indicating more effective exploration. Maintaining a diverse, highly entangled population is crucial for escaping local optima. The ability to leverage entanglement fundamentally distinguishes QGAs from conventional algorithms, offering a significant advantage in tackling complex problems—it’s as if the algorithm isn’t just searching for the answer, but collaboratively building it from the problem’s fundamental possibilities.

After 150 generations for the Rastrigin function with a population size of 50, the classical configuration (red) remains at zero entropy, while the quantum configuration (blue) spans a broad range of values, and higher entropy correlates with improved fitness, based on averaging over 5000 runs.

The pursuit of optimization, as detailed in this exploration of quantum genetic algorithms, mirrors a fundamental drive to decipher the underlying code of reality. The algorithm’s success hinges on exploiting superposition and entanglement – principles that allow for the simultaneous exploration of multiple solutions, a concept akin to examining all possible states at once. This echoes Richard Feynman’s sentiment: “The first principle is that you must not fool yourself – and you are the easiest person to fool.” The algorithm, by embracing the complexity of quantum states, avoids the pitfalls of premature commitment to a single solution, constantly testing and refining its approach. Just as reverse-engineering a system requires dismantling assumptions, this quantum approach systematically challenges the limitations of classical optimization techniques, revealing a more efficient path through the solution space.

What’s Next?

The demonstrated advantage, however modest, feels less like a destination and more like a carefully constructed inconvenience for classical computation. This work hinges on a gate-based approach—a deliberate imposition of structure onto the inherently probabilistic quantum realm. The question isn’t simply whether entanglement can accelerate optimization, but whether forcing it into a neat, algorithmic framework doesn’t also introduce unforeseen bottlenecks. Future iterations should actively probe the limits of this imposed structure; perhaps a deliberately ‘noisy’ quantum genetic algorithm—one that embraces decoherence rather than fighting it—could reveal more subtle, and ultimately more powerful, pathways to solutions.

Furthermore, the reliance on Shannon entropy as a measure of diversity feels… quaint. It’s a classical metric applied to a decidedly non-classical system. One suspects the true power of quantum genetic algorithms lies not in maximizing diversity as we understand it, but in exploiting the fundamentally different ways quantum states can represent and explore solution spaces. Measuring this—truly quantifying quantum diversity—remains a significant challenge.

Ultimately, this isn’t about building a better optimizer. It’s about reverse-engineering the very notion of ‘search’. If quantum mechanics allows for shortcuts around the computational barriers that plague classical algorithms, then the real prize isn’t faster solutions to existing problems, but entirely new classes of problems that become tractable only through this fundamentally different approach.

Original article: https://arxiv.org/pdf/2511.05254.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

Breaking the Optimization Barrier

Encoding Possibility: Quantum Circuits as Solutions

The Algorithm Evolves: Operators and Evaluation

Beyond Individual Search: Collective Quantum Intelligence

What’s Next?

See also: