Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem

Qian, Wenyang; Basili, Robert A. M.; Eshaghian-Wilner, Mary Mehrnoosh; Khokhar, Ashfaq; Luecke, Glenn; Vary, James P.

doi:10.3390/e25081238

Title: Comparative Study of Variations in Quantum Approximate Optimization Algorithms for the Traveling Salesman Problem

Journal Article · Mon Aug 21 00:00:00 EDT 2023 · Entropy

DOI:https://doi.org/10.3390/e25081238· OSTI ID:2278835

^[1]; Basili, Robert A. M. ^[2]; Eshaghian-Wilner, Mary Mehrnoosh ^[2]; Khokhar, Ashfaq ^[2]; Luecke, Glenn ^[2];

^[2]

Universidade de Santiago de Compostela (Spain); Iowa State University, Ames, IA (United States)
Iowa State University, Ames, IA (United States)

The traveling salesman problem (TSP) is one of the most often-used NP-hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layer-wise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find that a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show that the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.

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Research Organization:: Iowa State Univ., Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-87ER40371; SC0023692; SC0023707

OSTI ID:: 2278835

Journal Information:: Entropy, Vol. 25, Issue 8; ISSN 1099-4300

Publisher:: MDPICopyright Statement

Country of Publication:: United States

Language:: English

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