Mapping a logical representation of TSP to quantum annealing

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...

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Vydané v:Quantum information processing Ročník 20; číslo 12
Hlavní autori: Silva, Carla, Aguiar, Ana, Lima, Priscila M. V., Dutra, Inês
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.12.2021
Springer Nature B.V
Predmet:
Data Structures and Information Theory
Graphical representations
Mapping
Mathematical Physics
Nodes
Optimization
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Simulated annealing
Spintronics
Traveling salesman problem
Constraint and logic programming
Adiabatic quantum computation
Applications
Quadratic unconstrained binary optimization
Pseudo-Boolean optimization
ISSN:1570-0755, 1573-1332
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
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ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03321-8