Make ions count - a quantum simulation approach to computational problems

Seminar

Trapped ions provide flexible emulators of spin Hamiltonians. In this talk, I will motivate to use ions for an implementation of a Mattis-type spin glass model, or of a Hopfield-like neural network model. Using the parity symmetry of the system, simple analytic solutions for the ground state can be obtained, but by destroying the symmetry the complexity can systematically be enhanced. In certain regimes, finding the ground state is equivalent to the optimization process in the number partitioning problem - a computational task known to be NP-hard. A transverse magnetic field introduces quantum effects and opens the door to quantum annealing.

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