Non-Pauli errors in the three-dimensional surface code

A powerful feature of stabilizer error correcting codes is the fact that stabilizer measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code performance. However, logical non-Clifford operations can map Pauli errors to non-Pauli (Clifford) errors, and while subsequent stabilizer measurements will project the Clifford errors back to Pauli errors the resulting distributions will possess additional correlations that depend on both the nature of the logical operation and the structure of the code. Previous work has studied these effects when applying a transversal T gate to the three-dimensional color code and shown the existence of a nonlocal "linking charge"phenomenon between membranes of intersecting errors. In this paper we generalise these results to the case of a CCZ gate in the three-dimensional surface code and find that many aspects of the problem are much more easily understood in this setting. In particular, the emergence of linking charge is a local effect rather than a nonlocal one. We use the relative simplicity of Clifford errors in this setting to simulate their effect on the performance of a single-shot magic state preparation process and find that their effect on the threshold is largely determined by probability of X errors occurring immediately prior to the application of the gate, after the most recent stabilizer measurement

A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes

Braiding defects in topological stabiliser codes can be used to fault-tolerantly implement logical operations. Twists are defects corresponding to the end-points of domain walls and are associated with symmetries of the anyon model of the code. We consider twists in multiple copies of the 2d surface code and identify necessary and sufficient conditions for considering these twists as anyons: namely that they must be self-inverse and that all charges which can be localised by the twist must be invariant under its associated symmetry. If both of these conditions are satisfied the twist and its set of localisable anyonic charges reproduce the behaviour of an anyonic model belonging to a hierarchy which generalises the Ising anyons. We show that the braiding of these twists results in either (tensor products of) the S gate or (tensor products of) the CZ gate. We also show that for any number of copies of the 2d surface code the application of H gates within a copy and CNOT gates between copies is sufficient to generate all possible twists

Immunogold localization of alkaline phosphatase in a human osteosarcoma cell line (SAOS-2)

Laser based NDE techniques offer a potential solution to many of the NDE problems found in the applications of high performance materials and aerospace structures. Typical of these structures and materials are the ones being developed for high speed civil transport as well as the currently used structures such as found in the commercial fleet. The response of the structure to a modulated laser beam can be used to probe both its thermal and mechanical properties which are often critical to its proper performance. Anther often mentioned advantage of laser based inspections is the laser beam can be remotely scanned over the surface of the object enabling the inspection of complex geometries