Hybrid Quantum Algorithm Optimizes Resource Allocation in Rural Cultural Tourism Simulations

Computational researchers have demonstrated that coupling the Quantum Approximate Optimization Algorithm with a discrete-time coined quantum walk significantly improves the scheduling of rural cultural tourism resources in simulated environments. In a study published in the journal Discover Computing, investigators Jing Wang and Jing Ha formulated the complex coordination of tourist preferences, scenic spot carrying capacities, and intangible cultural heritage project services as a constrained ternary matching problem. Rather than relying entirely on conventional heuristic solvers or unassisted variational quantum circuits, the research team engineered a multi-stage hybrid framework termed QAOA-QWS. Across five synthetic problem instances of increasing scale, the hybrid approach achieved higher average per-tourist scheduling utility and superior constraint feasibility compared to standalone quantum approximation, simulated annealing, Tabu search, and genetic algorithms. The findings highlight how combining parameterized quantum energy minimization with graph-structured quantum walk refinement can navigate complex multi-stakeholder scheduling challenges within circuit simulation environments.

Rural cultural tourism systems involve intricate structural interactions among three distinct operational entities: visiting tourists, physical scenic spots, and living intangible cultural heritage projects. Conventional tourism management models often address binary pairings, such as recommending attractions to visitors or establishing travel routes across geographic sites. However, sustainable rural governance requires simultaneous tripartite coordination to avoid overcrowding fragile destinations while maintaining the living transmission of heritage activities. In this ternary ecosystem, heterogeneous tourist preferences must be reconciled with strict daily reception limits at rural scenic spots and service capacities of cultural heritage projects, which are tightly constrained by master artisan availability, physical venue space, and demonstration scheduling. When matching decisions involve thousands of tourists across numerous sites and craft projects, the combinatorial state space expands exponentially, generating a high-dimensional combinatorial optimization problem that challenges classical heuristics and exact solvers alike.

To establish a computationally tractable foundation, the authors introduced a domain-specific sparse candidate-triplet construction procedure before performing quantum mapping. Direct enumeration of every possible tourist, attraction, and heritage project combination would yield a full Cartesian product of decision variables that scales as the product of all three entity counts. To prevent this combinatorial explosion, the authors applied a multi-criteria screening filter based on tourist preference similarity, geographic accessibility, scenic spot carrying capacity, heritage thematic relevance, and cultural adaptation suitability. Retaining only viable candidate triplets reduced the decision space to a sparse subset while ensuring that every tourist retained at least one admissible option. Each viable triplet was assigned a normalized utility score combining tourist preference matching, spot-to-heritage adaptation, and tourist-to-spot suitability through non-negative weights that sum to one, establishing a baseline objective where maximizing total utility corresponds to maximizing average satisfaction per visitor.

The constrained utility maximization model was subsequently converted into a Quadratic Unconstrained Binary Optimization formulation and mapped onto an Ising-type cost Hamiltonian for quantum processing. Because standard quantum optimization algorithms minimize Hamiltonian expectation values, the utility maximization objective was inverted by assigning negative signs to the candidate utility weights. System constraints were incorporated through quadratic penalty functions. The exact tourist assignment constraint, which requires every individual tourist to receive exactly one service unit, was enforced quadratically without slack variables, penalizing both omitted assignments and duplicate selections. In contrast, inequality constraints governing scenic spot reception thresholds and heritage service capacities incorporated binary-expanded integer slack variables. This mathematical construction penalizes capacity overruns while leaving feasible under-capacity allocations unpenalized. Setting the penalty coefficients to unity aligned the penalty of a unit constraint residual with the maximum utility of a single triplet, creating an empirically balanced cost landscape.

Directly executing the complete quadratic unconstrained model on a single monolithic quantum circuit would have required up to 36,960 logical qubits for the largest tested instance, far exceeding the limits of classical simulation. To overcome this limitation, the authors designed a sequential block-decomposition heuristic that restricted every simulated QAOA circuit to an active budget of at most 20 qubits. Under this protocol, tourists were partitioned into sequential blocks of at most four individuals and optimized against an incumbent assignment obtained from a structural feasibility check. Unselected variables outside the active block were absorbed into reduced QUBO coefficients. Circuit simulations were conducted using Qiskit Aer’s matrix-product-state simulator on a multi-core central processing unit. The alternating circuit depth was scaled from four layers on smaller instances to eight layers on the largest problem, with circuit parameters optimized iteratively using the classical COBYLA algorithm over 1024 measurement shots per update.

A central architectural innovation of the framework is the cross-representation interface linking the blockwise QAOA sampling stage to the subsequent Quantum Walk Search refinement stage. Rather than attempting a coherent quantum state transfer between distinct circuits, the pipeline establishes an explicit classical measurement and re-encoding boundary. The binary solutions sampled across the QAOA blocks were assembled, decoded, and screened to construct a finite candidate set of at most 32 distinct feasible matching configurations stored in a classical lookup table. Each retained candidate scheme was mapped to a computational basis state in a five-qubit position register. Crucially, the empirical sampling frequencies recorded during QAOA measurement were transferred directly as the initial probability amplitudes of the position register. This cross-representation mapping allows the low-energy structural information discovered across the high-dimensional binary variable space to seed and guide quantum evolution within the low-dimensional candidate graph.

The Quantum Walk Search stage executes a discrete-time coined quantum walk across a regularized transition graph constructed over the retained matching schemes. Graph edges represent admissible local transitions between matching configurations, such as reassignment of a single tourist, attraction substitutions, or utility-preserving swaps, regularized with self-loops to maintain a uniform maximum degree of eight. The complete quantum walk circuit comprised ten qubits, incorporating the five-qubit position register, a three-qubit coin register, a phase kickback ancilla, and a validity ancilla. The lowest-energy 20% of candidate solutions were marked by an oracle that applied a phase inversion to corresponding basis states. Over up to 120 iterative walk steps combining a Grover coin operator and a flip-flop graph shift, quantum interference systematically amplified the probability amplitudes of the marked low-energy candidates, concentrating measurement outcomes on superior matching schemes without requiring exhaustive state exploration.

Following final quantum measurement, candidate binary strings were processed through a deterministic classical decoding and feasibility-repair procedure. If residual constraint violations persisted, such as overlapping assignments for a single tourist or capacity overruns at popular heritage workshops, the repair routine preserved highest-marginal-utility assignments while reassigning conflicting tourists to secondary feasible alternatives. In extensive convergence-based evaluations across five synthetic benchmarks, ranging from 100 tourists in instance S1 to 2,000 tourists in instance S5, QAOA-QWS consistently attained the highest normalized objective values. On the largest S5 instance, the hybrid framework achieved a normalized objective score of 0.869, outperforming standalone QAOA at 0.845, simulated annealing at 0.808, Tabu search at 0.792, and a genetic algorithm at 0.775. Paired pre- and post-repair diagnostic evaluations revealed that the quantum walk refinement produced an 83.6% pre-repair feasibility rate, significantly reducing the post-processing objective loss compared to the baseline algorithms.

To verify that the performance advantage was not an artifact of unequal runtime budgets, the researchers conducted an independent evaluation under a strict fixed-wall-clock protocol across all stochastic methods. Under this protocol, every algorithm was terminated at an identical hard time limit, ranging from 240 seconds for S1 to 5,000 seconds for S5, while continuously updating its best feasible incumbent solution. QAOA-QWS maintained its superior ranking across all scales, delivering a normalized objective score of 0.866 on S5 compared to 0.843 for unrefined QAOA and 0.802 for simulated annealing. Furthermore, extended benchmarking on the tractable S1 and S2 instances against exact Mixed-Integer Linear Programming demonstrated that QAOA-QWS achieved objective values within 1.71% and 2.16% of the true mathematical optima, outperforming Adaptive Large Neighborhood Search. Component-wise ablation confirmed that while classical repair resolves boundary infeasibilities, quantum walk search drives substantive improvements in candidate quality and low-energy sampling concentration.

Despite these promising computational results, the authors emphasized critical limitations regarding current physical hardware readiness and modeling scope. The entire investigation was conducted within a classical circuit simulation environment rather than on physical quantum processors, and the results do not demonstrate hardware-level quantum supremacy or asymptotic complexity speedups. The sequential block-decomposition strategy exhibits an operational dependence on tourist processing order, meaning that different visiting sequences could alter the final allocation plan. Additionally, the computational burden scales primarily through the thousands of simulated QAOA circuit batches and tens of millions of measurement shots required to process successive tourist blocks. The research team noted that future work must focus on testing the algorithm against real-world tourism flow datasets, implementing order-invariant block decompositions, and exploring problem-specific mixer Hamiltonians that preserve feasibility directly during quantum execution.

Subject of Research: Simulation of a hybrid QAOA–QWS quantum heuristic for rural cultural tourism resource allocation

Article Title: Simulation-based hybrid quantum–classical QAOA–QWS heuristic for tourist–scenic spot–ICH ternary matching in rural cultural tourism

Article References: Wang, J., & Ha, J. (2026). Simulation-based hybrid quantum–classical QAOA–QWS heuristic for tourist–scenic spot–ICH ternary matching in rural cultural tourism. Discover Computing, 29(1), Article 837. https://doi.org/10.1007/s10791-026-10791-w

Image Credits: AI Generated

DOI: 10.1007/s10791-026-10791-w

Keywords: quantum approximate optimization algorithm, quantum walk search, coined quantum walk, quadratic unconstrained binary optimization, ising Hamiltonian, ternary matching, rural cultural tourism, intangible cultural heritage, resource allocation, combinatorial optimization, block decomposition, qiskit aer, matrix product state, mixed-integer linear programming, circuit simulation, feasibility repair, tourist scheduling