The Quantum Approximate Optimization Algorithm with Quantum Walk Search (QAOA-QWS) is proposed as a hybrid quantum framework to address the ternary matching problem in rural cultural tourism resource allocation. The tripartite matching constraints and multi-objective optimization criteria are first encoded into an Ising-type cost Hamiltonian, where feasible allocations correspond to low-energy eigenstates. QAOA then executes parameterized quantum evolution to compress the exponential solution space into a high-quality approximate subspace dominated by low-energy matching states. Subsequently, QWS operates on the constraint-induced subgraph to directionally amplify the amplitudes of optimal ternary configurations through structured quantum walks, enabling efficient extraction of the global optimum via quantum measurement. Experimental validation across five progressively scaled instances ranging from 1,000 to 100,000 tourists demonstrates that QAOA-QWS achieves an expected objective value of 0.89, a tourist satisfaction rate of 0.87, an ICH coverage rate of 0.86, and an overall constraint satisfaction rate of 0.92 at the largest scale, significantly outperforming classical genetic and simulated annealing algorithms. Complexity analysis confirms that the proposed approach reduces the time complexity from exponential scaling with the problem size to a combination of polynomial and sub-linear square-root scaling relative to the feasible solution subspace, establishing a theoretical foundation for exponential acceleration in rural cultural tourism resource allocation. This framework establishes a theoretical foundation for exponentially accelerated quantum optimization in combinatorial resource allocation problems.
The Quantum Approximate Optimization Algorithm with Quantum Walk Search (QAOA-QWS) is proposed as a hybrid quantum framework to address the ternary matching problem in rural cultural tourism resource allocation. The tripartite matching constraints and multi-objective optimization criteria are first encoded into an Ising-type cost Hamiltonian, where feasible allocations correspond to low-energy eigenstates. QAOA then executes parameterized quantum evolution to compress the exponential solution space into a high-quality approximate subspace dominated by low-energy matching states. Subsequently, QWS operates on the constraint-induced subgraph to directionally amplify the amplitudes of optimal ternary configurations through structured quantum walks, enabling efficient extraction of the global optimum via quantum measurement. Experimental validation across five progressively scaled instances ranging from 1,000 to 100,000 tourists demonstrates that QAOA-QWS achieves an expected objective value of 0.89, a tourist satisfaction rate of 0.87, an ICH coverage rate of 0.86, and an overall constraint satisfaction rate of 0.92 at the largest scale, significantly outperforming classical genetic and simulated annealing algorithms. Complexity analysis confirms that the proposed approach reduces the time complexity from exponential scaling with the problem size to a combination of polynomial and sub-linear square-root scaling relative to the feasible solution subspace, establishing a theoretical foundation for exponential acceleration in rural cultural tourism resource allocation. This framework establishes a theoretical foundation for exponentially accelerated quantum optimization in combinatorial resource allocation problems.
Cloud computing resource management is a multi-dimensional optimization problem with numerous constraints that is very complex and difficult to solve by the traditional heuristic and hybrid algorithms due to constraints satisfaction and scalability. In this paper, we present a new approach that we call Quantum Constraint-Satisfying Allocation (QCSA), a completely quantum scheduling approach that incorporates the feasibility properties directly into the quantum state space. In contrast to penalty-based Quantum Approximate Optimization Algorithms (QAOA), QCSA only searches through feasible allocations, thereby avoiding post-repair overhead and decreasing sensitivity to the parameterization of the penalties. The proposed approach takes advantage of the constraint-satisfying quantum walks and multi-objective phase biasing to concentrate the computational probability mass on optimal solutions. We offer formal proof of feasibility invariance, bounds on success probability, and study convergence properties. Empirical tests on both synthetic and trace-based workloads on cloud configurations clearly show that QCSA outperforms classical and quantum baselines with respect to packing efficiency, SLA violations, and energy usage. In addition, QCSA is robust to workload variability, scalable across job sizes, and latency of quantum execution is low, which are valuable properties for future quantum-native cloud scheduling frameworks.
This paper presents a comprehensive theoretical framework that unifies various hybrid quantumclassical optimization approaches for combinatorial problems. Building upon recent advances in Quantum Approximate Optimization Algorithm (QAOA) and quantum-enhanced heuristics, we establish a mathematical foundation that connects amplitude amplification, counterdiabatic annealing, and classical relaxation techniques. We derive general convergence criteria and performance bounds for hybrid algorithms, demonstrating how quantum subroutines can be systematically integrated with classical optimization methods. The framework encompasses both unconstrained and constraint-preserving formulations, providing theoretical guarantees for problem classes including graph optimization, scheduling, and resource allocation. We analyze the trade-offs between quantum circuit depth, classical preprocessing overhead, and solution quality, establishing conditions under which exponential or polynomial speedups can be achieved. Our theoretical analysis reveals fundamental limitations and opportunities in hybrid algorithm design, offering guidelines for selecting appropriate quantum-classical decompositions based on problem structure. This work contributes to the growing understanding of quantum advantage in optimization and provides a roadmap for developing provably efficient hybrid algorithms across diverse application domains.
Large-scale portfolio optimization is hard because investors must balance risk, return, diversification, and liquidity across many assets with complex constraints. Classical methods, such as quadratic programming or metaheuristics, often become slow or less effective as the number of assets and factors grows. In this project, I explore the use of the Quantum Approximate Optimization Algorithm (QAOA) as a hybrid quantum–classical approach to portfolio selection. The framework encodes portfolio decisions as qubits and represents financial objectives—such as mean–variance trade-offs or risk-adjusted return—inside a parameterized quantum circuit. Classical optimization is then used to tune the circuit parameters so that the quantum system converges toward low-risk, high-return portfolios. Multi-factor constraints, including sector limits, liquidity rules, ESG scores, and macroeconomic risk factors, are integrated into the Hamiltonian as penalty terms. A qualitative comparison with classical solvers (e.g., mixed-integer programming and simulated annealing) suggests that QAOA can scale more gracefully in high-dimensional settings and handle complex constraint structures. Overall, the project shows how quantum hybrid optimization could support future portfolio management, linking theoretical quantum algorithms with practical, sustainability-aware investment strategies.
Path planning in complex and obstacle-constrained environments remains a challenging combinatorial optimization problem due to the exponential growth of the solution space and the limitations of classical algorithms in dynamic decision-making scenarios. Traditional approaches such as Dijkstra or A* may experience high computational costs and susceptibility to local optima when dealing with large-scale directed graphs containing obstacles. This study proposes a hybrid quantum computing approach that integrates the Grover Search Algorithm and the Quantum Approximate Optimization Algorithm (QAOA) to address optimal path planning on obstacle-oriented directed graphs. The Grover algorithm is first employed as an oracle-based filtering mechanism to detect and eliminate obstacle-containing edges, thereby generating a valid subgraph of feasible paths. Following this preprocessing step, QAOA is applied to the filtered graph within a nonlinear optimization framework to determine the minimum-cost path between source and destination nodes. The optimization model represents the graph as G=(V,E), where binary decision variables indicate whether an edge is included in the selected route while satisfying flow conservation constraints. By narrowing the solution space through Grover-based obstacle detection and performing optimization only on valid edges, the proposed method significantly reduces computational complexity compared to conventional approaches. Experimental analysis demonstrates that the hybrid quantum model effectively identifies optimal routes and adapts to different obstacle configurations while maintaining efficient convergence behavior. The results highlight the potential of integrating quantum search and quantum optimization techniques for solving combinatorial graph problems. This work contributes to the growing body of research on quantum-assisted optimization and demonstrates the feasibility of applying hybrid quantum algorithms to directed path planning problems relevant to autonomous navigation systems.
Abstract Airline itinerary and scheduling represent some of the most difficult computational problems that exist in transportation. The problems require choosing the best flight routes while determining schedules and allocating resources through various constraints which include regulatory requirements and maintenance schedules and dynamic demand patterns. The solution of small and medium-scale instances has been achieved through mixed-integer programming and heuristic methods including simulated annealing and genetic algorithms and branch-and-price but these methods become impractical for larger real-world instances due to exponential scaling issues. Quantum computing has introduced fresh solutions which enable the resolution of these problems. Quantum mechanical phenomena particularly superposition and entanglement enable optimization algorithms to examine an exponentially expanded solution space simultaneously. Our research applies a basic airline scheduling problem to the Traveling Salesman Problem (TSP) before converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The Quantum Approximate Optimization Algorithm (QAOA) serves as a hybrid quantum-classical method to solve this formulation. The experimental evaluation of a 4-city scenario shows that quantum-based optimization generates performance levels comparable to traditional methods and indicates that improved quantum hardware development will provide computational benefits for complex airline scheduling problems. This research holds dual importance because it can minimize operational expenses and improve scheduling performance and it establishes fundamental principles for complex combinatorial problem optimization across the transportation industry. The research establishes fundamental principles for quantum-enabled applications that will revolutionize airline operations and other transportation networks by solving critical scalability and solution quality problems.
We present QAMOO, a novel quantum computing framework for multi-objective portfolio optimization that simultaneously optimizes four distinct financial objectives—expected return, portfolio volatility, transaction costs, and entropy-based diversification—within a unified quantum Hamiltonian formulation. Unlike prior quantum finance approaches that treat diversification as a post-hoc penalty or encode transaction fees as scalarized weights, QAMOO embeds a Shannon entropy term directly into the quantum cost function through amplitude encoding of the portfolio weight vector. This formulation enables joint optimization over a non-convex objective landscape that cannot be faithfully reduced to a classical convex program without exponential complexity growth. The framework employs the Quantum Approximate Optimization Algorithm (QAOA) with pre-trained parameter transfer, executed on IBM Quantum hardware featuring heavy-hex topology processors with up to 156 qubits. A custom Pareto engine discovers the complete frontier of non-dominated portfolio solutions, enabling investors to select allocations matching their individual risk preferences. Empirical evaluation on a multi-asset portfolio demonstrates a 0.21% hypervolume improvement over the state-of-the-art classical multi-objective evolutionary algorithm (NSGA-III), while requiring approximately 30% fewer optimization cycles. The quantum-derived portfolios exhibit 23% lower turnover-adjusted volatility after accounting for realistic transaction fees. QAMOO establishes a new research direction at the intersection of quantum computing and quantitative finance, providing a hardware-aware optimization paradigm that integrates entropy-driven diversification directly into quantum annealing and gate-model formulations.