A STUDY OF QUANTUM ANNEALING DEVICES FROM A CLASSICAL PERSPECTIVE
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Spin glasses are experiencing a revival due to applications in quantum information theory. In particular, they are the archetypal native benchmark problem for quantum annealing machines. Furthermore, they find applications in fields as diverse as satisfiability, neural networks, and general combinatorial optimization problems. As such, developing and improving algorithms and methods to study these computationally complex systems is of paramount importance to many disciplines. This body of work attempts to attack the problem of solving combinatorial optimization problems by simulating spin glasses from three sides: classical algorithm development, suggestions for quantum annealing device design, and improving measurements in realistic physical systems with inherent noise. I begin with the introduction of a cluster algorithm based on Houdayer’s cluster algorithm for two-dimensional Ising spin-glasses that is applicable to any space dimension and speeds up thermalization by several orders of magnitude at low temperatures where previous algorithms have difficulty. I show improvement for the D-Wave chimera topology and the three-dimensional cubic lattice that increases with the size of the problem. One consequence of adding cluster moves is that for problems with degenerate solutions, ground-state sampling is improved. I demonstrate an ergodic algorithm to sample ground states through the use of simple Monte Carlo with parallel tempering and cluster moves. In addition, I present a non-ergodic algorithm to generate new solutions from a bank of known solutions. I compare these results against results from quantum annealing utilizing the D-Wave Inc. quantum annealing device. Finally, I present an algorithm for improving the recovery of ground-state solutions from problems with noise by using thermal fluctuations to infer the correct solution at the Nishimori temperature. While this method has been demonstrated analytically and numerically for trivial ferromagnetic and Gaussian distributions, a useful metric for more complex Gaussian distributions with added Gaussian noise is unavailable. We show improved recovery of numerical solutions on the chimera graph with a ferromagnetic distribution and added Gaussian noise. Next, I direct my focus to the design of future generations of quantum annealers. The first design is the two-dimensional square-lattice bimodal spin glass with next-nearest ferrromagnetic interactions proposed by Lemke and Campbell claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest neighbor interactions. Our results from finite-temperature simulations show the system is in a paramagnetic state in the thermodynamic limit, thus not useful for quantum annealing device designs that would benefit from a spin-glass phase transition. The second design is the diluted next-nearest neighbor Ising spin-glass with Gaussian interactions in an attempt to improve the estimation of critical parameter with smaller system sizes by implementing averaging of observables over different graph dilutions. To date, this model has shown no improvement. Finally, I make suggestions for the choice of distributions of interactions that are robust to noise and present a method for using previously unaccessible continuous distributions. I begin with showing the best-case performance of quantum annealing devices. I show results for the resilience, the probability that the ground-state solution has changed due to inherent analog noise in the device, and present strategies for developing robust instance classes. The analog noise is also detrimental to interactions chosen from continuous distributions. Using Gaussian quadratures, I present a method for discretizing continuous distributions to reduce noise effects. Simulations on the D-Wave show that the average residual of the ground-state energy with the true ground-state energy is calculated and shown to be smaller in the case of the discrete distribution.
Ochoa, Andrew J. (2017). A STUDY OF QUANTUM ANNEALING DEVICES FROM A CLASSICAL PERSPECTIVE. Doctoral dissertation, Texas A & M University. Available electronically from