Investigating the performance of an adiabatic quantum optimization processor

Abstract

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 123 78 K. Karimi et al. compare the median adiabatic times with the median running times of two classical solvers and find 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 significantly superior to those classical solvers for median spin glass problems of at least up to 128 qubits. We also discuss important additional constraints that affect the performance of a realistic system.

A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems

“…With our computational resources, we have been able to characterize the spectral gap for graphs of at most n = 7 vertices (i.e., for a system of 49 qubits, evolving in a Hilbert space isomorphic to C 823543 ). This does not allow for a study of the spectral behavior of the algorithm as a function of the input size [26,27]. By direct inspection of the spectral gap, however, it is easy to see that the "hardness" (i.e.…”

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“…Recent work to assess the scaling of the spectral gap that determines the minimum AQO annealing time has underscored that the relative height of energy barriers play a fundamental role in determining which Ising Hamiltonians are challenging [27,28,29,30]. Historically, learning rules that provide well separated but broad energy basins have been the goal of classical Hopfield networks, as these landscapes favor methods like gradient descent [1,6,7].…”

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