The D-Wave 2000 qubit computer is highly analogue and nondeterministic. The difficulties seem to include noise that hinders the hardware from distinguishing small numeric differences, sensitive parameters that need adjusting for the distances of TSPs, and imprecise qubit biases and coupling strengths that represent the TSP formulation. These obstructions are hardware snags that impede the best software for solving the TSP.
Therefore, a new demonstration that we are recommending will help to determine the extent to which the D-Wave hardware can find optimal tours for a variety of TSPs.
We recommend that software be designed, implemented and made available to solve ATSPs on the next generation D-Wave processor (21, 22). The software shall be designed to find an optimal tour for ATSPs with random distances. The software shall have the following capabilities.
Design features: N is a fixed, positive integer. It is an upper bound for the number of cities.
n is an integer such that 4 ≤ n ≤ N. It is the number of cities to be processed.
B is a fixed, positive integer. It is an upper bound for the distances.
N and B can be used for sizing the software or replaced with a library.
User inputs: Integer n.
An n × n matrix whose ij entry is the integer distance from city i to city j.
Parameters for the D-Wave processor.
Outputs from a classical processor: When feasible, all optimal tours (12) for the n-city ATSP and length of an optimal tour for the n-city ATSP.
Outputs from a D-Wave processor: Tours and their length for the lowest energy solution, the number of samples that have the lowest energy, and the lowest energy.
Statistics: (shortest tour length for the lowest energy solution) minus (length of an optimal tour). Percent of variance of (the length of a lowest energy solution) from (the length of an optimal tour). Percent of 100 different TSPs, all with the same number of cities and random distances, that are solved optimally (12).
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