Scalable multi-objective genetic algorithm for quantum circuit optimization

Roumaissa Ghlib

doi:10.1038/s41598-026-47674-5

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Scalable multi-objective genetic algorithm for quantum circuit optimization

2026-04-18

Roumaissa Ghlib

Rania Bouhadouza

Faicel Hnaien *

DOI：10.1038/s41598-026-47674-5

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Abstract

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Designing compact and efficient quantum circuits that are compatible with Noisy Intermediate-Scale Quantum (NISQ) hardware remains a central challenge in quantum computing. Most existing optimization approaches rely on fidelity-based fitness functions that require computing the full unitary matrix of the circuit. However, this quickly becomes computationally intractable beyond 10–12 qubits due to the exponential memory and time complexity $$O(2^{2n})$$. In this work, we propose a scalable multi-objective genetic algorithm for quantum circuit optimization tailored to NISQ devices. Although evolutionary algorithms have demonstrated strong potential for circuit synthesis, current methods generally depend on full-unitary fidelity evaluation, which severely limits scalability. To address this bottleneck, we introduce two complementary strategies: (1) an independent block-based evaluation using graph partitioning, and (2) an overlapping sliding-window decomposition approach. Both strategies reduce computational complexity from $$O(2^{2n})$$ to $$O(2^{2k})$$, where $$k \ll n$$, making it possible to optimize circuits with more than 20 qubits in practice. Our methods are integrated into the NSGA-II multi-objective framework, enabling simultaneous optimization of fidelity, circuit depth, and gate cost, while maintaining structural compatibility with NISQ hardware–without requiring full-unitary simulation. Experimental results on benchmark circuits demonstrate high fidelity (above 0.94 for small circuits up to 8 qubits, above 0.85 for medium-scale circuits of 10–16 qubits, and above 0.80 for large-scale circuits up to 32 qubits), up to $$45\%$$ reduction in circuit depth, and a $$10\times$$ speedup compared to exact evaluation at 14 qubits.

Keywords:

Engineering

Mathematics and computing

Physics

Quantum computing

NSGA-II

Multi-objective optimization

Circuit synthesis

Fidelity

Circuit optimization

Science

Humanities and Social Sciences

multidisciplinary

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