University timetabling is a classical NP-Hard combinatorial constraint problem that involves scheduling of courses, lecturers, students, classrooms, and timeslots while satisfying a set of constraints, with the main goal of minimizing conflicts. To solve this problem, we propose a novel Quantum Annealing and Topological Data Analysis (QA–TDA) algorithm that starts with an initial feasible solution, followed by iterative refinement using Quantum annealing configurations. TDA analyses the optimization landscape through persistent homology by detecting promising regions of interest in the solution space, which are clustered and subjected to quantum re-annealing using customized Hamiltonians-adaptive annealing schedules. QA-TDA model achieves a balance between global exploration and local exploitation, which improves convergence efficiency and solution robustness. Experimental results demonstrate that our hybrid model consistently outperforms baseline models across all evaluation metrics. In particularly on the most complex dataset, QA– TDA achieved a Conflict-Free Rate (CFR) of 94.3%. Additionally, an ablation study was conducted to validate the contribution of each component of the proposed model. Furthermore, clustering and K-Nearest Neighbour (K-NN) analyses confirm the robustness and consistency of the proposed approach across datasets of varying sizes and complexity. These findings highlight the great performance, scalability, and reliability of the integrated QA–TDA model for real-world academic scheduling applications.
University timetabling is a classical NP-Hard combinatorial constraint problem that involves scheduling of courses, lecturers, students, classrooms, and timeslots while satisfying a set of constraints, with the main goal of minimizing conflicts. To solve this problem, we propose a novel Quantum Annealing and Topological Data Analysis (QA–TDA) algorithm that starts with an initial feasible solution, followed by iterative refinement using Quantum annealing configurations. TDA analyses the optimization landscape through persistent homology by detecting promising regions of interest in the solution space, which are clustered and subjected to quantum re-annealing using customized Hamiltonians-adaptive annealing schedules. QA-TDA model achieves a balance between global exploration and local exploitation, which improves convergence efficiency and solution robustness. Experimental results demonstrate that our hybrid model consistently outperforms baseline models across all evaluation metrics. In particularly on the most complex dataset, QA– TDA achieved a Conflict-Free Rate (CFR) of 94.3%. Additionally, an ablation study was conducted to validate the contribution of each component of the proposed model. Furthermore, clustering and K-Nearest Neighbour (K-NN) analyses confirm the robustness and consistency of the proposed approach across datasets of varying sizes and complexity. These findings highlight the great performance, scalability, and reliability of the integrated QA–TDA model for real-world academic scheduling applications.
A new hybrid structure for solving academic scheduling issues is proposed in this paper that uses a combination of Topological Data Analysis (TDA) and Quantum Annealing (QA). The new framework allows for the modelling and solving of multi-constraint university scheduling problems by combining the characteristics of both QA and TDA. Using TDA, scheduling data is topologically analysed to provide structural and geometric information that can be used with the global optimization properties of QA to develop solutions to complex grement configurations.To test the proposed hybrid framework, the authors used real world data from the TUM for three datasets. The three datasets reflect different levels of complexity, with all datasets containing Certificate and Diploma Programs leading to the Undergraduate and Postgraduate timetable.Four model variants were considered: The configurations examined comprised QA-only, TDA-only, hybrid models without refinement, and hybrid models incorporating refinement. Each approach was assessed using four performance metrics: Conflict-Free Rate (CFR), Resource Utilization (RU), Computational Time (CT), and Energy Function Value (EFV). The experimental results demonstrate that hybrid approaches incorporating refinement consistently outperformed all baseline models across every evaluation metric. Notably, the top-performing hybrid configuration, evaluated on the most complex dataset, attained a CFR of 94.3%, a RU of 91.2%, and the lowest EFV among all the methods compared. Experimental results demonstrate that all hybrid-with-refinement configurations consistently outperformed the baseline models by a substantial margin. Notably, on the most challenging dataset, the refined hybrid approach attained a Conflict-Free Rate (CFR) of 94.3% and a Resource Utilization (RU) of 91.2%, while also yielding the minimum Energy Function Value (EFV). Additionally, clustering and K-NN analysis results confirmed that the proposed hybrid approach has consistent and robust behaviours across all datasets, demonstrating reliable behaviour regardless of the differing sizes or complexity of the problems.
This paper investigates the application of quantum annealing algorithms to the field of topological optimization, specifically focusing on a probabilistic approach. Traditional topological optimization relies on iterative refinement of a mesh, often computationally expensive. We propose a novel method leveraging the quantum annealing algorithm's inherent probabilistic search capabilities, combined with topological structural information, to achieve more efficient solutions for complex optimization problems. The core concept involves translating the optimization problem into a search problem within the space of possible topological structures. The quantum annealing algorithm then explores this space probabilistically, guided by the topological constraints, with the goal of identifying the optimal topology. This approach aims to reduce the computational burden associated with conventional iterative methods and potentially unlock solutions that are inaccessible through classical optimization techniques. The presented framework is theoretically grounded and offers a promising avenue for future research in hybrid quantum-classical optimization. The key performance indicator for this approach is the convergence rate and the quality of the solutions obtained compared to traditional methods. The algorithm's success depends heavily on the effective encoding of the problem's constraints into the topology search space.
Constraint Satisfaction Problems (CSPs) represent a significant class of computationally challenging problems across diverse fields, including scheduling, routing, and artificial intelligence. Traditional quantum annealing (QA) approaches often face difficulties in effectively tackling complex CSPs, primarily due to challenges in accurately embedding the problem's structure onto the quantum hardware and efficiently exploring the solution space. This research proposes an adaptive quantum annealing (AQA) algorithm designed to mitigate these limitations. The AQA algorithm employs reinforcement learning (RL) to dynamically adjust the embedding strategy and refine the annealing schedule during the QA process. Specifically, the RL agent learns to optimize the problem's representation on the quantum hardware and adapt the annealing parameters based on real-time feedback from the observed solution landscape. The core innovation lies in the integration of adaptive control within the QA framework, potentially unlocking significant improvements in performance for complex CSPs. We present a theoretical framework and outline the key components of the AQA algorithm, demonstrating its potential to overcome the limitations associated with conventional QA methods. The algorithm's ability to dynamically respond to the problem's characteristics offers a promising avenue for enhancing the effectiveness of QA in solving challenging CSP instances.
Timetabling is an NP-Hard problem that searches for periodic scheduling of events that must meet a set of hard and soft constraints. Because of the difficulty in finding an exact solution, the use of heuristics to address the problem is a common practice. When only the hard constraints are considered, the timetabling problem can be reduced to graph vertex coloring. This similarity between both problems has motivated the use of graph coloring heuristics as a means to solve the timetabling problem. We propose the use of the Quantum Approximate Optimization Algorithm as a heuristic to solve the school timetabling problem. The QAOA is a hybrid quantum-classical algorithm that can be used to address combinatorial optimization problems. We simulated QAOA in a minimal example with 42 qubits using the Ket Quantum Programming Language and our results showed that it is possible to apply QAOA to the school timetabling problem.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
The optimization of multidrug cancer treatment schedules is a high-dimensional combinatorial optimization problem involving nonlinear tumor dynamics, pharmacokinetic interactions, and stringent toxicity constraints. When exploring large therapeutic search spaces, conventional optimization algorithms often exhibit limited scalability and become trapped in local optima. This simulation study proposes a hybrid quantum-classical optimization framework that employs QA to generate adaptive treatment schedules for precision oncology. The treatment scheduling problem is formulated as a quadratic unconstrained binary optimization (QUBO) model, which encodes drug combinations, dosing intervals, toxicity constraints, and synergistic interactions within an Ising Hamiltonian compatible with D-Wave quantum annealing hardware. Global combinatorial optimization is performed using a D-Wave Advantage quantum annealer, while sequential least squares programming refines continuous dosage parameters under pharmacokinetic and toxicity constraints. Tumor progression is represented using a modified Gompertz growth model coupled with first-order pharmacokinetic dynamics. The proposed framework was evaluated using synthetic Digital Twin datasets generated from clinically realistic pharmacokinetic and tumor growth parameters. Simulation results demonstrated a maximum tumor regression ratio of 0.98 ± 0.02, compared with 0.82 ± 0.05 for standard-of-care protocols, while maintaining a lower cumulative toxicity index (40 ± 5 versus 75 ± 8) and reducing optimization time to less than 2 s for 120-variable scheduling problems. The hybrid framework exhibited near-linear computational scalability and maintained robustness under stochastic dosage perturbations (TRR > 0.95 at σ = 0.25). However, predictive classification performance remained limited (AUC = 0.49), highlighting the need for validation using longitudinal clinical datasets and multimodal patient-specific data. These findings demonstrate the potential of hybrid quantum-classical optimization as a scalable computational framework for adaptive treatment scheduling and personalized precision oncology.