Publications

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Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque and unwieldy. We show how to transform the process matrix of a gate into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent the error generator of any gate as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just 9N2 parameters that describes almost all commonly predicted errors on an N-qubit processor.

We present a combination of machine-learned models that predicts the surface elastic properties of general free surfaces in face-centered cubic (FCC) metals. These models are built by combining a semi-analytical method based on atomistic simulations to calculate surface properties with the artificial neural network (ANN) method or the boosted regression tree (BRT) method. The latter is also used to link bulk properties and surface orientation to surface properties. The surface elastic properties are represented by their invariants considering plane elasticity within a polar method. The resulting models are shown to accurately predict the surface elastic properties of seven pure FCC metals (Cu, Ni, Ag, Au, Al, Pd, Pt). The BRT model reveals the correlations between bulk and corresponding surface properties in terms of invariants, which can be used to guide the design of complex nano-sized particles, wires and films. Finally, by expressing the surface excess energy density as a function of surface elastic invariants, fast predictions of surface energy as a function of in-plane deformations can be made from these model constructs.

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For decades, it has been observed that the commonly used Borgnakke-Larsen method for energy redistribution in Direct Simulation Monte Carlo codes fails to satisfy the principle of detailed balance when coupled to a wide variety of temperature dependent relaxation models, while seemingly satisfying detailed balance when coupled to others. Many attempts have been made to remedy the issue, yet much ambiguity remains, and no consensus appears in the literature regarding the root cause of the intermittent compatibility of the Borgnakke-Larsen method with temperature dependent relaxation models. This paper alleviates that ambiguity by presenting a rigorous theoretical derivation of the Borgnakke-Larsen method's requirement for satisfying detailed balance. Specifically, it is shown that the Borgnakke-Larsen method maintains detailed balance if and only if the probability of internal-energy exchange during a collision depends only on collision invariants (e.g., total energy). The consequences of this result are explored in the context of several published definitions of relaxation temperature, including translational, total, and cell-averaged temperatures. Of particular note, it is shown that cell-averaged temperatures, which have been widely discussed in the literature as a way to ensure equilibrium is reached, also fail in a similar, although less dramatic, fashion when the aforementioned relationship is not enforced. The developed theory can be used when implementing existing or new relaxation models and will ensure that detailed balance is satisfied.

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