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Optimizing the optimization : Performance of evolutionary strategies for quantum control

Daan P. Sprünken, Janne Savolainen, Aliakbar Jafarpour, Jennifer L. Herek, Masha Kiseleva, Wim J. van der Zande

Published Oct 28, 2008• 0 citations
OpenAlex

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According to the characteristics of combinatorial optimization problems,a novel improved quantum evolutionary algorithm for combinatorial optimization problems(NIQEA) is proposed.The NIQEA initializes population based on the idea of niche cooperative evolutionary,increasing the diversity of individuals,and adopts the dynamic adjustment strategy to adjust the quantum rotation corner,speeding up convergence rate,and uses the cross strategy of excellent individuals to get crossover operation,enhancing local search ability.To validate its performance,the NIQEA is applied to solve the typical combinatorial optimization problems: two examples of multidimensional 0/1 knapsack problem,and the results show that the NIQEA is feasible and effective.

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Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy algorithms as well as the (nongreedy) genetic-algorithm method to realize two fast quantum computing gates: a qutrit phase gate and a controlled-not gate. We show that our evolutionary algorithm circumvents the trap to deliver effective quantum control in both instances. Even when greedy algorithms succeed, our evolutionary algorithm can deliver a superior control procedure, for example, reducing the need for high time resolution.
This paper investigates the potential of incorporating quantum mechanical concepts into evolutionary algorithms (EAs) to improve their optimization capabilities. Traditional EAs, while effective, often struggle with complex search spaces and can get trapped in local optima. We propose a framework for developing quantum-inspired EAs that leverages principles such as superposition and entanglement to enhance exploration and exploitation strategies. The core idea is to introduce probabilistic operators and adaptive parameter control mimicking quantum behaviors. We present a detailed description of the proposed algorithm, focusing on the mathematical formulation of the key components, including the representation of solutions, the selection process, and the mutation operator. The algorithm's performance is evaluated on several benchmark optimization problems, demonstrating its potential to outperform conventional EAs in scenarios demanding high accuracy and rapid convergence. Furthermore, we analyze the theoretical implications of this approach, highlighting the advantages derived from quantum-inspired mechanisms. This work contributes to the ongoing research at the intersection of evolutionary computation and quantum information theory, offering a novel approach to tackling complex optimization challenges.
According to the characteristics of combinatorial optimization problems,a novel improved quantum evolutionary algorithm for combinatorial optimization problems(NIQEA) is proposed.The NIQEA initializes population based on the idea of niche cooperative evolutionary,increasing the diversity of individuals,and adopts the dynamic adjustment strategy to adjust the quantum rotation corner,speeding up convergence rate,and uses the cross strategy of excellent individuals to get crossover operation,enhancing local search ability.To validate its performance,the NIQEA is applied to solve the typical combinatorial optimization problems: two examples of multidimensional 0/1 knapsack problem,and the results show that the NIQEA is feasible and effective.