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 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.
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)
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.
We propose Scalable Quantum Molecular Generation (SQMG), a variational quantum-circuit for sampling molecular graphs using chemical priors on atoms and bonds. SQMG assigns a fixed 3-qubit register to each heavy atom and reuses a single 2-qubit bond register to generate bonds sequentially, yielding an ''atom no-reuse, bond reuse'' architecture with linear qubit scaling. Measurement results are mapped to molecular graphs via lightweight classical decoding with structural constraints. In CUDA-Q, we benchmark the state-vector simulation (CPU/GPU) and the tensor-network simulation (GPU). At N=8 heavy atoms, the state-vector simulator (GPU) and the tensor-network simulator (GPU) achieve speeds of up to 4.5×104 and 2.2×103 over the state-vector (CPU) baseline, respectively. Crucially, tensor-network simulation extends exact simulation to N=40 heavy atoms, where state-vector methods become memory-limited. For training, Bayesian optimization outperforms COBYLA on a Validity×Uniqueness objective, and the same architecture supports \textit{de novo} generation, scaffold decoration, and linker design. Overall, SQMG provides a scalable, reproducible testbed for evaluating accelerated tensor-network simulation and future quantum molecular generation algorithms.
In this paper a new optimization algorithm named Adaptive Hybrid Quantum-Inspired Optimization Algorithm (AHQSOA) is presented for solving the complex optimization problems effectively. Stochastic traditional algorithms typically fail to come to be stuck in local optimum solutions and they need quite few iterations for converging. Our method integrates two quantum-inspired methodology: Quantum Particle Swarm Optimization (QPSO) for searching a large set solutions based on properties of quantum mechanics - superposition, point are located as randomly as possible, and Quantum Evolutionary Algorithms (QEA) for refining potential solutions by mutation and crossover operation. An adaptive tuning component based on the reinforcement learning dynamically adjusts the algorithm’s parameters, thus balancing the exploration in the wide interval and exploitation in the precise interval. Assessed on the commonly used benchmark functions like Sphere, Rosenbrock, Rastrigin, AHQSOA exhibits faster convergence (only 400 iterations in comparison to 1200 in standard methods), global search superiority (94% whereas 75–87% the traditional methods), and low computational simplicity. These results show all of our algorithm are nicer and faster and more efficient and robust makes for it a good candidate as for high dimensional and complex optimization problems.
Quantum-inspired algorithms (QIAs) are computationally efficient algorithms that generate a quantum model in classical hardware as an alternative to the use of quantum models. In this research paper, the researchers carried out an experimental appraisal of four quantum-inspired algorithms in quantum-inspired Evolutionary Algorithm (QEA), quantum-behaved Particle Swarm Optimization (QPSO), quantum-inspired Genetic Algorithm (QIGA) and quantum Simulated Annealing (QSA) on benchmark optimization functions. The introduction of a simulation-based methodology was done in Python to test the convergence speed, global search capability, accuracy and robustness. According to the experimental findings, QPSO always performs well compared with other methods in the achievement of faster convergence and enhanced global optimality, but QEA is highly successful in cases of discrete combinatorial problems. The paper concludes that quantum-inspired models are effective in modeling the key quantum concepts like probabilistic superposition and tunneling to attain high quality optimization results with conventional computing platforms. Such results demonstrate the opportunities of QIAs as scalable pre-quantum tools of designing, AI, and industrial optimization.
The generation of chemical molecular structures is crucial for advancements in drug design, materials science, and related fields. With the rise of artificial intelligence, numerous generative models have been developed to propose promising molecular structures to specific challenges. However, exploring the vast chemical space using classical generative models demands extensive chemical structure data, considerable computational resources, and a large number of model parameters, which hinders their efficiency. Quantum computing presents a promising alternative by exploiting quantum parallelism and entanglement, potentially reducing the computational overhead required for such tasks. In this study, we designed a quantum-based molecular generator (QMG) specifically tailored to generate small molecules containing carbon, nitrogen, and oxygen atoms. This model imposes strict constraints on the quantum circuit's output quantum states, significantly eliminating mathematically invalid connection graphs and enabling more efficient sampling of valid molecular structures. Remarkably, our quantum circuit, utilizing only 134 parameters, is capable of enumerating all molecular structures comprising up to nine heavy atoms, showcasing the parameter efficiency achievable through quantum superposition and entanglement. Our experimental results show that the output generated by this circuit exhibits a high degree of validity and uniqueness after Bayesian optimization, showing comparable performance to classical deep generative models. Furthermore, by fixing specific parameters in the quantum circuits, the quantum generator can constrain the chemical space and exclusively generate chemical molecules containing specified functional groups. This feature underscores its potential value for targeted applications in specific domains, especially in drug discovery. Overall, this compact design not only reduces parameter demands but also enables efficient exploration of a nontrivial portion of chemical space, demonstrating a key advantage of quantum-based generative models over larger classical counterparts.