Application of quantum approximate optimization algorithm to job shop scheduling problem - Kurowski, Krzysztof; Pecyna, Tomasz; Slysz, Mateusz; Różycki, Rafał; Waligóra, Grzegorz; Wȩglarz, Jan (European journal of operational research, 2023)
•Demonstrate how to efficiently apply Quantum Approximate Optimization Algorithm (QAOA) to Job Shop Scheduling Problem (JSSP).•Investigation of the behaviour of the QAOA-based quantum algorithm in a series of experiments using quantum noiseless simulations.•Evaluation of the quantum algorithm’s efficiency and accuracy, particularly the relation between makespan and energy in achieving feasible and infeasible solutions.•Applicability of quantum optimization algorithms and appropriate technical steps for application developers interested in applying gate-based quantum approaches for solving other scheduling problems. The Job Shop Scheduling Problem (JSSP) has always been considered as one of the most complex and industry essential scheduling problems. Optimizing the makespan of a given schedule generally involves using dedicated algorithms, local search strategies, or metaheuristics. These approaches, however, heavily rely on classical computational power, which is bounded by the physical limits of microcontrollers and power issues. Inspired by the promising results achieved for Quantum Annealing (QA) based approaches to solve JSSP instances, we propose a new approach that uses gate-model quantum architecture as an alternative to QA. We find that we can make use of the time-indexed JSSP instance representation to build a cost Hamiltonian, which can be embedded into Quantum Approximate Optimization Algorithm (QAOA) to find an optimal solution to a basic JSSP instance. We demonstrate the use of QAOA to solve the JSSP, and we evaluate its efficiency and accuracy for this problem from experimental results, as there is an increased urgency to demonstrate the applicability of quantum optimization algorithms. We also find that optimal variational parameters form patterns that can facilitate computation in bigger quantum circuits. Additionally, we compare the obtained noiseless simulation results of gate-model quantum circuits demonstrating the relationship between two evaluation criteria - makespan and energy. Finally, we analyze and present the overall performance of our approach with the increasing deadline and simulated depth of QAOA circuits.