Scheme for constructing graphs associated with stabilizer quantum codes

We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code; second, the canonical form of the CWS code is uncovered; third, the input vertices are attached to the graphs. To check the effectiveness of the scheme, we discuss several graphical constructions of various useful stabilizer codes characterized by single and multi-qubit encoding operators. In particular, the error-correcting capabilities of such quantum codes are verified in graph-theoretic terms as originally advocated by Schlingemann and Werner. Finally, possible generalizations of our scheme for the graphical construction of both (stabilizer and nonadditive) nonbinary and continuous-variable quantum codes are briefly addressed.Comment: 42 pages, 12 figure

Dynamic actions on bridge slabs due to heavy vehicle impact on roadside barriers

The use of roadside safety barriers in Italy has changed in recent years: the number of installed devices has increased, and so have their stiffness and resistance. These changes were necessary because early barrier design was inadequate to contain and redirect heavy vehicles. The change in barrier design led to an increase in stiffness and resistance; consequently, the action transferred to the structure by the device increased. The need for resistance on the bridge slabs can be too high because the peculiar action of the roadside barriers was not adequately taken into account in the oldest bridge design codes. In addition, characterizing the actions transferred to the bridge slab is difficult because of the dynamic nature of vehicle impacts on roadside barriers. Given the impossibility of performing a full-scale laboratory test for every bridge deck, the use of computational mechanics applied to dynamic impact/interaction problems is one of the best ways to establish these actions in the project phase. Research was conducted into the use of a three-dimensional finite element model of the bridge slab-barrier-vehicle system to perform a numerical simulation of the impact, according to the procedure used for the roadside barrier homologation crash test, described in the European Standard EN 1317

Protected gates for topological quantum field theories

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons; in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.Comment: 50 pages, many figures, v3: updated to match published versio

Randomized benchmarking in measurement-based quantum computing

Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.Comment: 10 pages, 4 figures, comments welcome; v2 published versio