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IEEE International Conference on Consumer Electronics - Berlin (ICCE-Berlin)

Course Selection Optimization using pVSQA on Quantum Computers

Takeru Ota, Tatsuhiko Shirai, Nozomu Togawa

Published Sep 6, 2025• 0 citations
Publisher

Abstract

Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm capable of solving combinatorial optimization problems on gate-based quantum computers. Postprocessing Variationally Scheduled Quantum Algorithm (pVSQA) is an enhanced approach that combines a quantum variational algorithm like QAOA with a postprocessing step that transforms infeasible solutions into feasible ones. Compared to QAOA, pVSQA can more efficiently solve constrained combinatorial optimization problems. In this paper, we define the personalized course selection problem (PCSP), which involves finding the optimal combination of courses for a student, and then propose a method that integrates a postprocessing algorithm into pVSQA to effectively solve PCSP. Experimental results show that, compared to conventional QAOA, pVSQA significantly improves both the probability to obtain feasible solutions and the energy expectation among feasible solutions.

DOI
10.1109/icce-berlin67488.2025.11277633

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Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm capable of solving combinatorial optimization problems on gate-based quantum computers. Postprocessing Variationally Scheduled Quantum Algorithm (pVSQA) is an enhanced approach that combines a quantum variational algorithm like QAOA with a postprocessing step that transforms infeasible solutions into feasible ones. Compared to QAOA, pVSQA can more efficiently solve constrained combinatorial optimization problems. In this paper, we define the personalized course selection problem (PCSP), which involves finding the optimal combination of courses for a student, and then propose a method that integrates a postprocessing algorithm into pVSQA to effectively solve PCSP. Experimental results show that, compared to conventional QAOA, pVSQA significantly improves both the probability to obtain feasible solutions and the energy expectation among feasible solutions.
Quantum approximate optimization algorithm (QAOA) is an algorithm for solving combinatorial optimization problems (COP), which can be implemented on gate based quantum computers. However, many practical COPs such as a personalized course selection problem (PCSP) have not been solved by QAOA yet. In this paper, we solve a PCSP using QAOA by transforming the problem into a quadratic unconstrained binary optimization (QUBO), and investigate the solution properties when the weight of the problem's constraint is changed. Experimental evaluations demonstrate that tuning the weight value improves the probability of obtaining optimal solutions and reduces the energy expectation value averaged over the obtained feasible solutions.
We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a quantum annealer or gate-based quantum device. Variational methods are used to find an optimal schedule function that leads to high-quality solutions in a short amount of time. Post-processing techniques convert the output solutions of the quantum devices to satisfy the constraints of the COPs. pVSQA combines the variational methods and the post-processing technique. We obtain a sufficient condition for constrained COPs to apply pVSQA based on a greedy post-processing algorithm. We apply the proposed method to two constrained NP-hard COPs: the graph partitioning problem and the quadratic knapsack problem. pVSQA on a simulator shows that a small number of variational parameters is sufficient to achieve a (near-)optimal performance within a predetermined operation time. Then building upon the simulator results, we implement pVSQA on a quantum annealer and a gate-based quantum device. The experimental results demonstrate the effectiveness of our proposed method.
This study investigates the graph partitioning problem as a constrained combinatorial optimization problem and evaluates the effectiveness of the Postprocessing Variationally Scheduled Quantum Algorithm(pVSQA)(\mathbf{p V S Q A})(pVSQA)on the instances of up to 30 qubits. We executed pVSQA using Fujitsu's highperformance quantum simulator in a single-node configuration and compared its performance with the conventional Quantum Approximate Optimization Algorithm (QAOA). Experimental results on various instances show that pVSQA consistently outperforms QAOA in terms of feasibility and optimality, successfully obtaining optimal solutions even for30\mathbf{3 0}30-qubit instances. The study also demonstrates that Fujitsu's quantum simulator is effective for the stable execution of large-scale quantum circuits.
A combinatorial optimization problem is a problem finding an optimal combination of variables that maximizes or minimizes an objective function while satisfying given constraints. Such problems arise in various fields, including transportation and communication. Many combinatorial optimization problems are NP-hard, meaning that the number of possible combinations grows exponentially as the number of variables increases. As a result, it is often difficult to solve large-scale combinatorial optimization problems for conventional classical computers. Recently, Ising machines, including quantum annealers, have gained attention as a promising architecture for efficiently solving combinatorial optimization problems. One real-world example of a combinatorial optimization problem isuniversity course selection. Many students manually choose their courses, but this process is time consuming and labor intensive due to the large number of available options. To address this, in this paper, we formulate course selection as a combinatorial optimization problem, which we define as a Personalized Course Selection Problem (PCSP). To solve it efficiently, we use an Ising machine, a specialized computer designed for combinatorial optimization. We propose a Quadratic Unconstrained Binary Optimization (QUBO) formulation for solving PCSP and solve the problem with an Ising machine. Experimental evaluations demonstrate that, for the largest instance tested, the proposed method solves the problem 20X times faster than the conventional simulated annealing while achieving the same total course cost.
Hybrid Quantum–Classical Optimization combines the advantages of quantum computing and classical optimization to address complex combinatorial optimization problems. The Quantum Approximate Optimization Algorithm (QAOA), as an outstanding Variational Quantum Algorithm (VQA), shows great potential in solving combinatorial optimization problems. Classical optimization methods play a crucial role in tuning the parameters of quantum circuits, affecting the algorithm’s convergence speed and solution quality. This paper designs and simulates QAOA circuits based on the Qiskit framework, focusing on comparing the performance of three classical optimizers— Adaptive Moment Estimation (Adam), Constrained Optimization BY Linear Approximations (COBYLA), and Simultaneous Perturbation Stochastic Approximation (SPSA)—in parameter optimization. Adam and SPSA perform more stably in deeper circuits, making them suitable for high-dimensional parameter spaces, whereas COBYLA tends to get trapped in local optima and exhibits greater fluctuations under limited iterations. The results further highlight the importance of classical optimizer selection and hyperparameter tuning in enhancing the performance of hybrid quantum–classical optimization algorithms.
The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum optimization technique used for solving combinatorial optimization problems. However, in constrained binary optimization, QAOA’s reliance on equal initial probabilities for all solutions can lead to suboptimal outcomes. To enhance the performance of QAOA in this context, we propose a novel approach that combines QAOA with genetic algorithms. In this hybrid approach, the results obtained from QAOA serve as the initial population for a genetic algorithm. We apply this methodology to address the k-heaviest subgraph problem, a critical challenge in quantum computing research. Our experiments, conducted on benchmark datasets, demonstrate a significant improvement in solution quality.