The Admin Quantum Medic Conscious Optimizer (AQMCO) implements a qutrit-enhanced meta-conscious approach to the Traveling Salesman Problem. Each path permutation can occupy three possible “states” per iteration, inspired by quantum superposition, allowing richer exploration of solution space. The optimizer maintains a top-N memory of best paths while probabilistically selecting candidates for subsequent iterations, providing both exploitation of known good solutions and exploration of alternative routes. Benchmarked against classical TSP solvers, AQMCO demonstrates superior convergence efficiency on complex instances, highlighting the potential of quantum-inspired, meta-conscious optimization heuristics in combinatorial problem solving.
The Admin Quantum Medic Conscious Optimizer (AQMCO) implements a qutrit-enhanced meta-conscious approach to the Traveling Salesman Problem. Each path permutation can occupy three possible “states” per iteration, inspired by quantum superposition, allowing richer exploration of solution space. The optimizer maintains a top-N memory of best paths while probabilistically selecting candidates for subsequent iterations, providing both exploitation of known good solutions and exploration of alternative routes. Benchmarked against classical TSP solvers, AQMCO demonstrates superior convergence efficiency on complex instances, highlighting the potential of quantum-inspired, meta-conscious optimization heuristics in combinatorial problem solving.
The UHF Quantum-Classical Optimization Engine demonstrates robust performance across multiple optimization domains. In benchmarks including Traveling Salesperson Problem instances, lattice optimization, and extreme stress tests, UHF consistently outperforms classical, hybrid, and Google quantum-classical tools in computation speed, solution quality, and system stability. Leveraging meta-conscious heuristics and qutrit-inspired permutation strategies, the engine achieves high reproducibility and scalability across problem sizes. Detailed benchmark tables and CSV logs are provided to support reproducibility and comparison.
The Traveling Salesman Problem (TSP) is a widely studied NP-complete optimization challenge with significant theoretical and practical implications. This study proposes a hybrid quantum-classical framework using a Quantum-Inspired Evolutionary Algorithm (QEA) with Sort Gray Binary Encoding to solve the TSP. The proposed method guarantees the generation of valid TSP tours by eliminating invalid solutions. It employs quantum superposition with intrinsic randomness to enhance computational efficiency and scalability. The framework was implemented on cloud-based NISQ platforms, including IBM Quantum and AWS Braket, demonstrating its practicality and effectiveness. Experimental evaluations revealed that the proposed framework successfully solved TSP instances with up to 15 cities, achieving superior performance compared to classical methods and showcasing its ability to scale under NISQ constraints. The results also highlight the potential of hybrid quantum-classical approaches to overcome hardware limitations in current quantum systems. This study establishes a robust hybrid methodology for solving combinatorial optimization problems. It also sets a benchmark for leveraging the capabilities of NISQ-era quantum devices in real-world applications, thereby providing a foundation for future research in hybrid quantum-classical optimization techniques.
The Traveling Salesman Problem (TSP) is a canonical example of an NP-hard combinatorial optimization problem that has extensive applications in the context of logistics and routing and network design, where classical methods cannot be used in practice due to the large scale of the instances. The approach includes extensive research on a hybrid quantum and classical optimisation model, termed Grover-ACO, that combines the Grover quantum amplitude amplification with the elitist selection stage of the Ant Colony Optimization (ACO). This study can be described as an algorithm that includes candidate pool formation, quantum oracle design, amplitude amplification, and pheromone update algorithms, and give a mathematical model of the hybrid algorithm. The evaluation of standard TSPLIB benchmark instances is conducted experimentally on a quantum circuit simulator, and performance is measured in terms of the best and average tour costs, as well as computational overhead. Findings indicate that GroverACO is consistently able to achieve better quality solutions and discourage premature convergence than classical ACO, especially on medium and large-scale problems, albeit at a higher computational budget due to quantum simulation.
The Traveling Salesman Problem (TSP) is a canonical example of an NP-hard combinatorial optimization problem that has extensive applications in the context of logistics and routing and network design, where classical methods cannot be used in practice due to the large scale of the instances. The approach includes extensive research on a hybrid quantum and classical optimisation model, termed Grover-ACO, that combines the Grover quantum amplitude amplification with the elitist selection stage of the Ant Colony Optimization (ACO). This study can be described as an algorithm that includes candidate pool formation, quantum oracle design, amplitude amplification, and pheromone update algorithms, and give a mathematical model of the hybrid algorithm. The evaluation of standard TSPLIB benchmark instances is conducted experimentally on a quantum circuit simulator, and performance is measured in terms of the best and average tour costs, as well as computational overhead. Findings indicate that GroverACO is consistently able to achieve better quality solutions and discourage premature convergence than classical ACO, especially on medium and large-scale problems, albeit at a higher computational budget due to quantum simulation.
The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient variational quantum framework based on compact binary-register encoding, a permutation-preserving problem-inspired ansatz, and a complementary divide-and-conquer execution strategy. The compact encoding reduces the data-qubit requirement to O(n log n), while the divide-and-conquer formulation lowers the number of qubits required in each local hardware execution to the size of the largest subsystem. Numerical simulations on TSP instances with 4, 5, and 6 cities achieve best average success rates of 100%, 100%, and 95.5%, respectively. A local two-qubit implementation of the divide-and-conquer approximation is further evaluated for a 5-city TSP instance on SpinQ Gemini Pro and SpinQ Triangulum II NMR quantum computers. Taken together, the results indicate how compact encoding and divide-and-conquer execution with classical post-processing can be used to study small combinatorial optimization instances on resource-constrained quantum hardware.
Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone has still been unable to demonstrate this capability except for small-sized problems. Hybrid approaches, where QC and classical computing work together, have shown the most potential for solving real-world-scale problems. This work aims to show that we can enhance a classical optimization algorithm with QC so that it can overcome this limitation. We present a new Hybrid Quantum-classical Tabu Search (HQTS) algorithm to solve the Capacitated Vehicle Routing Problem (CVRP). Based on our prior work, HQTS leverages QC for routing within a classical tabu search framework. The quantum component formulates the Traveling Salesman Problem (TSP) for each route as a Quadratic Unconstrained Binary Optimization (QUBO) and solves it using D-Wave’s Advantage system. Experiments investigate the impact of quantum routing frequency and starting solution methods. Across different starting solution methods, including quantum-based and classical heuristics, it shows minimal overall impact. HQTS achieved optimal or near-optimal solutions for several CVRP problems, outperforming other hybrid CVRP algorithms and significantly reducing the optimality gap relative to preliminary research. The experimental results demonstrate that more frequent quantum routing improves solution quality and runtime. The findings highlight the potential of integrating QC within meta-heuristic frameworks for complex optimization in vehicle routing problems.