Brittle and Non-Brittle Events in a Continuum-Granular Earthquake Experiment

We report moment distribution results from a laboratory earthquake fault experiment consisting of sheared elastic plates separated by a narrow gap filled with a two dimensional granular medium. Local measurement of strain displacements of the plates at over 800 spatial points located adjacent to the gap allows direct determination of the moments and their spatial and temporal distributions. We show that events consist of localized, larger brittle motions and spatially-extended, smaller non-brittle events. The non-brittle events have a probability distribution of event moment consistent with an $M^{-3/2}$ power law scaling. Brittle events have a broad, peaked moment distribution and a mean repetition time. As the applied normal force increases, there are more brittle events, and the brittle moment distribution broadens. Our results are consistent with mean field descriptions of statistical models of earthquakes and avalanches.

Reduced Space-Time and Time Costs Using Dislocation Codes and Arbitrary Ancillas

We propose two distinct methods of improving quantum computing protocols based on surface codes. First, we analyze the use of dislocations instead of holes to produce logical qubits, potentially reducing spacetime volume required. Dislocations induce defects which, in many respects, behave like Majorana quasi-particles. We construct circuits to implement these codes and present fault-tolerant measurement methods for these and other defects which may reduce spatial overhead. One advantage of these codes is that Hadamard gates take exactly $0$ time to implement. We numerically study the performance of these codes using a minimum weight and a greedy decoder using finite-size scaling. Second, we consider state injection of arbitrary ancillas to produce arbitrary rotations. This avoids the logarithmic (in precision) overhead in online cost required if $T$ gates are used to synthesize arbitrary rotations. While this has been considered before, we consider also the parallel performance of this protocol. Arbitrary ancilla injection leads to a probabilistic protocol in which there is a constant chance of success on each round; we use an amortized analysis to show that even in a parallel setting this leads to only a constant factor slowdown as opposed to the logarithmic slowdown that might be expected naively.