Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard Ising spin glass instance class with up to 128 binary variables. Using parameters obtained from a realistic superconducting adiabatic quantum processor, we extract the minimum gap and matrix elements using high performance Quantum Monte Carlo simulations on a large-scale Internet based computing platform. We compare the median adiabatic times with the median running times of two classical solvers and fi nd that, for the considered problem sizes, the adiabatic times for the simulated processor architecture are about 4 and 6 orders of magnitude shorter than the two classical solvers' times. This shows that if the adiabatic time scale were to determine the computation time, adiabatic quantum optimization would be signi ficantly superior to those classical solvers for median spin glass problems of at least up to 128 qubits. We also discuss important additional constraints that a ffect the performance of a realistic system.
First, the above consideration ignores the e ffect of the environment, especially the fact that the lowest feasible temperature at which such a processor can be operated is larger than the median minimum energy gaps of problems with 48 or more variables. Although recent calculations suggest that a weak coupling to the environment does not signi ficantly aff ect the time required to reach the final ground state with a measurable probability, even if the minimum gap is below the temperature, a fair comparison should consider the performance of an open and not closed system. Unfortunately, such open system simulations are not feasible beyond 20 qubits.
The second point is that for the small problems we investigate here, the adiabatic time does not dominate the running time of the real hardware. A fair comparison between the classical solvers and the AQO processor should include the time needed for operations such as programming the chip, readout, and thermalization (to ensure that the chip returns to its operational temperature before the next problem is solved). In the real processor, readout and thermalization times completely dominate the problem solving time for these small-scale problems. At the time of writing this paper, serial readout takes roughly 36 microseconds per qubit, and thermalization time is experimentally chosen to be 1000 s, as compared with median adiabatic time of 10 s for 128 variable problems. These numbers depend on the processors' design and fabrication details, as well as the e fficiency of cryogenic components used to cool the processor to 21 mK, and are expected to change over time.
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