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Mapping a logical representation of TSP to quantum annealing

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Abstract

This work presents the mapping of the traveling salesperson problem (TSP) based in pseudo-Boolean constraints to a graph of the D-Wave Systems Inc. We first formulate the problem as a set of constraints represented in propositional logic and then resort to the SATyrus approach to convert the set of constraints to an energy minimization problem. Next, we transform the formulation to a quadratic unconstrained binary optimization problem (QUBO) and solve the problem using different approaches: (a) classical QUBO using simulated annealing in a von Neumann machine, (b) QUBO in a simulated quantum environment, (c) QUBO using the D-Wave quantum machine. Moreover, we study the amount of time and execution time reduction we can achieve by exploring approximate solutions using the three approaches. Results show that for every graph size tested with the number of nodes less than or equal to 7, we can always obtain at least one optimal solution. In addition, the D-Wave machine can find optimal solutions more often than its classical counterpart for the same number of iterations and number of repetitions. Execution times, however, can be some orders of magnitude higher than the classical or simulated approaches for small graphs. For a higher number of nodes, the average execution time to find the first optimal solution in the quantum machine is 26% (\(n = 6\)) and 47% (\(n = 7\)) better than the classical.

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Notes

  1. More on QPU times can be found at:https://docs.dwavesys.com/docs/latest/timing_qa_cycle_time.htmlhttps://docs.dwavesys.com/docs/latest/timing_overview.html.

  2. https://docs.dwavesys.com/docs/latest/doc_leap_hybrid.html.

  3. https://docs.ocean.dwavesys.com/projects/qbsolv/en/latest/.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Sciences, University of Porto, Porto, Portugal

    Carla Silva

  2. Instituto de Telecomunicações and Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Porto, Portugal

    Ana Aguiar

  3. PESC/COPPE/CT and Tercio Pacitti Institute/CCMN, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Priscila M. V. Lima

  4. CINTESIS and Department of Computer Science, Faculty of Sciences, University of Porto, Porto, Portugal

    Inês Dutra

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  1. Carla Silva
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  2. Ana Aguiar
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  3. Priscila M. V. Lima
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  4. Inês Dutra
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Correspondence to Inês Dutra.

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Silva, C., Aguiar, A., Lima, P.M.V. et al. Mapping a logical representation of TSP to quantum annealing. Quantum Inf Process 20, 386 (2021). https://doi.org/10.1007/s11128-021-03321-8

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