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Applied Soft Computing

Genetic algorithms as classical optimizer for the Quantum Approximate Optimization Algorithm

Giovanni Acampora, Angela Chiatto, Autilia Vitiello

Published Apr 25, 2023• 100 citations
Publisher
DOI
10.1016/j.asoc.2023.110296

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The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum optimization technique used for solving combinatorial optimization problems. However, in constrained binary optimization, QAOA’s reliance on equal initial probabilities for all solutions can lead to suboptimal outcomes. To enhance the performance of QAOA in this context, we propose a novel approach that combines QAOA with genetic algorithms. In this hybrid approach, the results obtained from QAOA serve as the initial population for a genetic algorithm. We apply this methodology to address the k-heaviest subgraph problem, a critical challenge in quantum computing research. Our experiments, conducted on benchmark datasets, demonstrate a significant improvement in solution quality.
This work investigates the performance of a Hybrid Quantum Genetic Algorithm (HQGA) compared to a classical Genetic Algorithm (GA) for solving the portfolio optimization problem. Our results indicate that the HQGA converges faster to the optimal solution than its classical counterpart, while also maintaining a higher level of population diversity throughout the optimization process. In addition, the HQGA requires significantly fewer evaluations-to-solution than a brute-force approach to reach the global optimum.
Quantum Genetic Algorithms (QGA) integrate genetic programming and quantum computing to address search and optimization problems. The standard strategy of the hybrid QGA approach is to add quantum resources to classical genetic algorithms (GA), thus improving their efficacy (i.e., quantum optimization of a classical algorithm). However, the extent of such improvements is still unclear. Conversely, Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that reduces the GA search for the best fitness in a population of potential solutions to running Grover's algorithm. Unfortunately, RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions of the problem) in exponential runtime, [[EQUATION]], where [[EQUATION]] is the number of qubits in the individuals' quantum register. This paper introduces a novel QGA optimization strategy, namely a classical optimization of a fully quantum algorithm, to address the Reduced Quantum Genetic Algorithm (RQGA) complexity problem. Accordingly, we control the complexity of theReduced Quantum Genetic Algorithm (RQGA) algorithm by selecting a limited number of qubits in the individuals' register and fixing the remaining ones as classical values of '0' and '1' with a genetic algorithm. We also improve the performance of RQGA by discarding unfit solutions and bounding the search only in the area of valid individuals. As a result, our Hybrid Quantum Algorithm with Genetic Optimization (HQAGO) solves search problems in [[EQUATION]] oracle queries, where [[EQUATION]] is the number of fixed classical bits in the individuals' register.