Adiabatic Quantum Optimization for Associative Memory Recall

Hopfield networks are a variant of associative memory that recall information stored in the couplings of an Ising model. Stored memories are fixed points for the network dynamics that correspond to energetic minima of the spin state. We formulate the recall of memories stored in a Hopfield network using energy minimization by adiabatic quantum optimization (AQO). Numerical simulations of the quantum dynamics allow us to quantify the AQO recall accuracy with respect to the number of stored memories and the noise in the input key. We also investigate AQO performance with respect to how memories are stored in the Ising model using different learning rules. Our results indicate that AQO performance varies strongly with learning rule due to the changes in the energy landscape. Consequently, learning rules offer indirect methods for investigating change to the computational complexity of the recall task and the computational efficiency of AQO.Comment: 22 pages, 11 figures. Updated for clarity and figures, to appear in Frontiers of Physic

Performance Models for Split-execution Computing Systems

Split-execution computing leverages the capabilities of multiple computational models to solve problems, but splitting program execution across different computational models incurs costs associated with the translation between domains. We analyze the performance of a split-execution computing system developed from conventional and quantum processing units (QPUs) by using behavioral models that track resource usage. We focus on asymmetric processing models built using conventional CPUs and a family of special-purpose QPUs that employ quantum computing principles. Our performance models account for the translation of a classical optimization problem into the physical representation required by the quantum processor while also accounting for hardware limitations and conventional processor speed and memory. We conclude that the bottleneck in this split-execution computing system lies at the quantum-classical interface and that the primary time cost is independent of quantum processor behavior.Comment: Presented at 18th Workshop on Advances in Parallel and Distributed Computational Models [APDCM2016] on 23 May 2016; 10 page

Approximate Mean-field Equations of Motion for Quasi-two-dimensional Bose-Einstein Condensates

We present a method for approximating the solution of the three-dimensional, time-dependent Gross-Pitaevskii equation (GPE) for Bose-Einstein-condensate systems where the confinement in one dimension is much tighter than in the other two. This method employs a hybrid Lagrangian variational technique whose trial wave function is the product of a completely unspecified function of the coordinates in the plane of weak confinement and a Gaussian in the strongly confined direction having a time-dependent width and quadratic phase. The hybrid Lagrangian variational method produces equations of motion that consist of (1) a two-dimensional (2D) effective GPE whose nonlinear coefficient contains the width of the Gaussian and (2) an equation of motion for the width that depends on the integral of the fourth power of the solution of the 2D effective GPE. We apply this method to the dynamics of Bose-Einstein condensates confined in ring-shaped potentials and compare the approximate solution to the numerical solution of the full 3D GPE