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| Home > Publications database > Simulating on the D-Wave Two and emulating its behavior on an ordinary computer |
| Master Thesis | FZJ-2015-06771 |
2015
Please use a persistent id in citations: http://hdl.handle.net/2128/9586
Abstract: This work presents the results of random spanning tree and 2-SAT problems, which weresolved using a D-Wave Two processor.Firstly, the results for random spanning tree problems, translated to Ising spin problemsare discussed. The results suggest that the Z2-symmetry of the Ising spin systemimplemented on the D-Wave Two processor is severely broken. It is furthermore shown,that isolated regions of qubits on the D-Wave Two processor behave statistically independent.A date and time dependency of the solution frequency is observed as the solutionfrequency of the same problem on different days differs significantly with respect to thestatistical errors.When starting to operate on a new D-Wave processor, the random spanning tree problemspresented in this work can be used as good test cases that allow obtaining basicinformation on the processor’s characteristics. The results of the random spanning treeproblem also suggest that, in order to get statistically reproducible results, computationson the D-Wave Two processor need to be performed over long time periods and in differentregions of the processor.Secondly, the solving frequencies for 2-SAT problems with very small minimum gapssolved on the D-Wave Two processor are compared to those obtained via emulation i.e.simulation of the actual physical behavior of the D-Wave Two quantum processor on aclassical computer. A comparison of the solving frequencies shows, that 2-SAT problemswith minimum gaps larger than the operating temperature of the D-Wave Two processorare solved by quantum annealing. For problems with minimum gaps significantly smallerthan the operating temperature of the D-Wave Two processor, the results suggest thatfinding a solution is assisted by thermal effects. For problems with minimum gaps close tothe operating temperature of the D-Wave Two processor, a transition between the quantumannealing process and the thermally assisted process can be assumed.In order to gain a more detailed insight into the behavior of the D-Wave Two processor,further studies of the 2-SAT problems are planned. An investigation of additionalproblems in the area of transition is expected to deliver a better understanding of the prevailingprocesses. It should also be of interest to investigate at what point a problem with asmaller minimum gap than the processor’s operating temperature would lead to a decreaserather than an increase of the solution frequency. A decrease of the solution frequency isexpected since the energy barriers between states are so small that the likelihood of thermaloccupation of exited states increases and also that calibration errors of the D-WaveTwo processor become more dominant.
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