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IEEE International Conference on Nanotechnology (IEEE-NANO)

A High-Performance Cyclic-Mapping Encoding for Quantum Computing of Traveling Salesperson Problems on NISQ Devices

J. Wang, Takumi Kanezashi, Daisuke Tsukayama, Koki Awaya, R. Saito, Jun‐ichi Shirakashi

Published Jul 1, 2026• 0 citations
Publisher
DOI
10.1109/nano67986.2026.11667508

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Continued advancements in quantum computing have stimulated growing interest in translating quantum technologies into real-world applications. Consequently, the investigation of practically motivated NP-hard problems is of significant value. This study investigates the performance of a variational quantum eigensolver (VQE) in addressing the traveling salesperson problem (TSP) through noiseless simulations representative of noisy intermediate-scale quantum (NISQ) devices using higher-order binary optimization (HOBO) encodings. We construct a HOBO Hamiltonian with an efficient binary representation and propose an all-valid-state HOBO (AVS-HOBO) scheme based on cyclic mapping that eliminates one penalty term and reuses states that would otherwise be invalid. Using TSP instances of up to 20 cities, we compare the original HOBO and AVS-HOBO encodings from multiple perspectives, including the energy convergence behavior and the approximation, tour-length, and feasibility ratios. In addition to simulations, we perform computations on real quantum hardware with different device architectures, where we not only compare the performances of different chips but also investigate the effects of different error-mitigation methods on actual quantum machines. The results indicate that AVS-HOBO encoding enhances the practical reliability of VQE on NISQ devices and improves scalability for larger TSP instances, with broader applicability to constrained quantum optimization problems.
Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed or solution quality. Several suggestions have been made for encodings of routing problems to solve them with variational quantum algorithms. However, for an end user it is hard to decide a priori which encoding will give the best solutions according to their needs. In this work, we investigate different encodings for the Travelling Salesperson Problem. We compare their scaling and performance when using the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver and provide a clear guide for users when to choose which encoding. For small instances, we find evidence that the permutation encoding can yield good results since it does not suffer from feasibility issues.
We study a job-shop scheduling problem for an automatized robot in a high-throughput laboratory and a traveling-salesperson problem with recently proposed digitized counterdiabatic quantum optimization (DCQO) algorithms. In DCQO, we find the solution of an optimization problem via an adiabatic quantum dynamics, which is accelerated with counterdiabatic protocols. Thereafter, we digitize the global unitary to encode it in a digital quantum computer. For the job-shop scheduling problem, we aim at finding the optimal schedule for a robot executing a number of tasks under specific constraints, such that the total execution time of the process is minimized. For the traveling-salesperson problem, the goal is to find the path that covers all cities and is associated with the shortest traveling distance. We consider both hybrid and pure versions of DCQO algorithms and benchmark the performance against digitized quantum annealing and the quantum approximate optimization algorithm (QAOA). In comparison to QAOA, the DCQO solution is improved by several orders of magnitude in success probability using the same number of two-qubit gates. Moreover, we implement our algorithms on cloud-based superconducting and trapped-ion quantum processors. Our results demonstrate that circuit compression using counterdiabatic protocols is amenable to current noisy intermediate-scale quantum hardware and can solve logistics scheduling problems, where other digital quantum algorithms show insufficient performance.