Abstract This paper introduces a rotational quantum particle swarm optimizer (RQPSO) that updates particles via quantum rotation–gate dynamics on a compact phase representation. Real-valued amplitudes decoded from phases are mapped feasibly by construction into the decision space, removing the need for bound repair. Lightweight π -flip perturbations and brief stagnation-triggered reseeding sustain diversity, and a short local polish consolidates the incumbent near termination. RQPSO is benchmarked against Particle Swarm Optimization (PSO), Quantum Particle Swarm Optimization (QPSO), Grey Wolf Optimizer (GWO), Mayfly Algorithm (MA), self-adaptive Differential Evolution (jDE), and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) under a common protocol of 3000 function evaluations with 30 independent runs per problem. Reporting uses median [interquartile range (IQR)] as the primary statistic with Friedman/Nemenyi global tests and Holm-corrected Wilcoxon pairwise tests; effect sizes are summarized by Cliff’s δ . Experiments cover 23 classical functions and 10 CEC-2019 functions. On the classical suite, RQPSO attains the best or tied-best median on a majority of functions and achieves a leading global rank under the fixed budget. On CEC-2019, it records three best medians (including one tie) and a top mean rank; post-hoc tests show significant gains over MA and jDE and broadly comparable performance to PSO, QPSO, GWO, and CMA-ES. A combined economic–emission dispatch (CEED) study on a six-unit system with cubic cost and emission models further demonstrates budget-efficient performance. The RQPSO attains the lowest mean operating cost and the smallest dispersion at all loads versus PSO and QPSO. A percentage-recovery repair enforces generator limits and power balance without penalty functions by proportionally rescaling outputs. Together, the rotation-gate updates, feasibility-preserving decoding, and proportional repair provide a robust alternative to classical swarms for both benchmark and power-system optimization under tight evaluation budgets. The source code of RQPSO is publicly available at: (https://github.com/Naagdant/rotational-quantum-pso)
Abstract This paper introduces a rotational quantum particle swarm optimizer (RQPSO) that updates particles via quantum rotation–gate dynamics on a compact phase representation. Real-valued amplitudes decoded from phases are mapped feasibly by construction into the decision space, removing the need for bound repair. Lightweight π -flip perturbations and brief stagnation-triggered reseeding sustain diversity, and a short local polish consolidates the incumbent near termination. RQPSO is benchmarked against Particle Swarm Optimization (PSO), Quantum Particle Swarm Optimization (QPSO), Grey Wolf Optimizer (GWO), Mayfly Algorithm (MA), self-adaptive Differential Evolution (jDE), and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) under a common protocol of 3000 function evaluations with 30 independent runs per problem. Reporting uses median [interquartile range (IQR)] as the primary statistic with Friedman/Nemenyi global tests and Holm-corrected Wilcoxon pairwise tests; effect sizes are summarized by Cliff’s δ . Experiments cover 23 classical functions and 10 CEC-2019 functions. On the classical suite, RQPSO attains the best or tied-best median on a majority of functions and achieves a leading global rank under the fixed budget. On CEC-2019, it records three best medians (including one tie) and a top mean rank; post-hoc tests show significant gains over MA and jDE and broadly comparable performance to PSO, QPSO, GWO, and CMA-ES. A combined economic–emission dispatch (CEED) study on a six-unit system with cubic cost and emission models further demonstrates budget-efficient performance. The RQPSO attains the lowest mean operating cost and the smallest dispersion at all loads versus PSO and QPSO. A percentage-recovery repair enforces generator limits and power balance without penalty functions by proportionally rescaling outputs. Together, the rotation-gate updates, feasibility-preserving decoding, and proportional repair provide a robust alternative to classical swarms for both benchmark and power-system optimization under tight evaluation budgets. The source code of RQPSO is publicly available at: (https://github.com/Naagdant/rotational-quantum-pso)
Particle Swarm Optimization (PSO) is a popular algorithm used for optimization problems in various domains. However, the PSO algorithm suffers from some limitations, e.g., premature convergence and slow convergence rate. In this paper, we propose a new algorithm called Quantum Rotation Gate Particle Swarm Optimization (QPSO), which is based on the quantum rotation gate to address these shortcomings. The proposed QPSO algorithm aims to improve the optimization capability of the original PSO. We applied QPSO to optimize the neural network architecture for numerical anomaly detection on the self-noise aerodynamic wind tunnel test data set. Good results are achieved and the effectiveness of the proposed method is demonstrated. Compared to the original PSO algorithm, QPSO outperforms it in terms of convergence rate and accuracy.
This work proposes Rank-Refined Quantum-Behaved Particle Swarm Optimization (RR-QPSO) for high-dimensional parameter search in Quantum Molecular Generation (QMG). RR-QPSO targets the optimization bottleneck caused by expensive objective evaluations, where each candidate parameter vector requires stochastic circuit sampling, bitstring decoding, and molecular evaluation. The method provides a population-based alternative to Bayesian optimization (BO), combining Sobol-based initialization, a rank-refined mean-best update, and fitness-guided refinement based on validity and uniqueness. Experiments use the 9-heavy-atom QMG benchmark with a 134-parameter, 20-qubit CUDA-Q circuit and particle evaluations parallelized across 8 NVIDIA V100 GPUs. With M=64 particles and T=150 iterations, RR-QPSO reaches VxU = 0.930; increasing the swarm size to M=128 further improves the product to 0.942, compared with 0.902 for BO under the same protocol. A multi-objective extension targeting HBA=4 and HBD=3 further shows that RR-QPSO can guide molecular properties while preserving a higher validity--uniqueness product than BO. These results suggest that optimizer-level design can improve QMG without modifying the chemistry-inspired circuit or molecular decoding pipeline.
This paper proposes a new binary particle swarm optimization (BPSO) approach inspired by quantum computing, namely quantum-inspired BPSO (QBPSO). Although BPSO-based approaches have been successfully applied to the combinatorial optimization problems in various fields, the BPSO algorithm has some drawbacks such as premature convergence when handling heavily constrained problems. The proposed QBPSO combines the conventional BPSO with the concept and principles of quantum computing such as a quantum bit and superposition of states. The QBPSO adopts a Q-bit individual for the probabilistic representation, which replaces the velocity update procedure in the particle swarm optimization. To improve the search capability of the quantum computing, this paper also proposes a new rotation gate, that is, a coordinate rotation gate for updating Q-bit individuals combined with a dynamic rotation angle for determining the magnitude of rotation angle. The proposed QBPSO is applied to unit commitment (UC) problems for power systems which are composed of up to 100-units with 24-h demand horizon.
Adaptive quantum machine learning (QML) represents an exciting frontier at the intersection of quantum computing and classical bio-inspired optimization. The constraints of noisy intermediate-scale quantum (NISQ) devices—limited qubit counts, significant decoherence, and measurement uncertainties—pose formidable challenges to training parameterized quantum circuits (PQCs) using traditional gradient-based methods. To overcome these hurdles, we propose a novel Adaptive PSO–QML framework that integrates a particle swarm optimization (PSO)–inspired algorithm with dynamic hyperparameter adjustment, enabling real-time tuning of PQC parameters based on performance feedback. Unlike static optimizers, our approach continuously adapts its inertia weight and cognitive/social coefficients to balance exploration and exploitation, responding to stagnation or rapid improvement in measured fitness. We evaluate this hybrid algorithm on two benchmark classification tasks: the classical Iris dataset encoded into a 2-qubit circuit and a quantum-encoded subset of the MNIST dataset on 4 qubits. Our experiments, conducted on the Qiskit Aer simulator under realistic noise models (depolarizing, amplitude damping, and mixed), demonstrate that Adaptive PSO–QML achieves an average accuracy improvement of 12% over fixed-parameter PSO and 15% over Adam-based gradient descent, with p-values below 0.01 across paired t-tests. Statistical analysis summarized in Table 1 confirms the significance of these gains. Detailed simulation research further reveals that the adaptive mechanism not only accelerates convergence by approximately 30%—reducing total circuit evaluations—but also exhibits robust performance across varying circuit depths (1–3 entangling layers) and noise intensities. Our findings suggest that bio-inspired adaptation is a powerful tool for mitigating barren plateaus and noise effects in NISQ-era QML, paving the way for scalable quantum advantage in near-term hardware.
In the field of finding ground and excited states, where quantum computation holds significant promise, using a variational quantum eigensolver (VQE) is a typical approach. However, the success of this approach is vulnerable to two factors: classical optimization for the ansätz parameters and noise from quantum devices. To address these challenges, we adopted particle swarm optimization (PSO) based on swarm intelligence for VQE and presented its performance. Furthermore, a modified PSO, gradient-based adaptive quantum-behaved particle swarm optimization (GAQPSO), is proposed. This algorithm adaptively upgrades parameters based on gradients or shared information within the swarm, enhancing optimization capability and noise resistance. We tested this algorithm using VQE simulations on several molecular systems with different geometries and found that, when using random initial values, GAQPSO achieves accurate results even in the presence of noise, whereas traditional PSO, QPSO, COBYLA, and gradient-based algorithms (GD and L-BFGS-B) fail. The GAQPSO algorithm presents a novel approach to optimizing VQE, demonstrating superior performance in parameter optimization and noise resilience compared to traditional optimization algorithms. This effectively advances the process of achieving a quantum advantage for quantum computing in quantum chemistry problems.
As modern data environments continue to scale in volume and dimensionality, classical metaheuristics like Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) struggle to balance convergence efficiency with solution quality. The challenge is further amplified in big data optimization, where stagnation in local minima and prohibitive computation time impede real-time applicability. Existing methods fail to simultaneously address the need for global search intelligence and computational scalability, especially under high-dimensional constraints and distributed workloads. To bridge this gap, we propose QIESO—a Quantum-Inspired Evolutionary Swarm Optimizer that integrates quantum amplitude encoding, probabilistic gate rotation, swarm coordination, and tunnelingbased mutation to escape local traps and accelerate convergence. Unlike traditional optimizers, QIESO leverages quantum principles simulated classically to maintain coherence across the search space while reducing evaluation overhead. Empirical validation across datasets up to 100 million records shows QIESO achieves a 51.7% reduction in runtime over GA and 42.7% faster convergence than PSO, with a relative error margin consistently under 2.1%. The method exhibits sublinear scalability in time complexity due to dimensionality-agnostic encoding. This work significantly advances scalable optimization for high-throughput environments, making it ideal for applications in autonomous systems, real-time analytics, and next-gen intelligent infrastructures.