Probing topological defect formation in a quantum annealer

When a quantum phase transition is crossed in finite time, the breakdown of adiabatic dynamics leads to the formation of topological defects. The average density of defects scales with the quench rate following a universal power-law predicted by the Kibble- Zurek mechanism. The later provides useful heuristics for adiabatic quantum computation. Physics beyond the Kibble-Zurek mechanism can be probed by characterizing the full counting statistics of topological defects. We argue that the distribution of the number of defects generally follows a Poisson binomial distribution with all cumulants exhibiting a universal power-law scaling with the quench rate. As an example, we report the exact kink number distribution in the transverse-field quantum Ising model. For this system, we test kink statistics in a D-Wave machine and show that the study of the kink number distribution can be used to benchmark the performance of a quantum processor.

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