Real output in Switzerland: new estimates for 1914-47

In this article, Felix A, Andrist, Richard G. Anderson, and Marcela Williams provide, for the first time, an estimate of the real gross domestic product of Switzerland between 1914 and 1947. The estimate is obtained from published data on three other measures of Swiss economic activity during this period: net national product, industrial production, and the transport volume of Swiss railroads. These underlying series closely represent the economic growth of Switzerland; but, they also seem unreasonably volatile as proxy measures of total production, and hence, are filtered by moving averages. Although such smoothing might reduce the accuracy of the estimates, comparisons to U.S. data suggest any such loss is small.Gross national product ; Switzerland

Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random 3-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have similar error stability than color codes on triangular lattices, as well as the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code demonstrate the inherent robustness of this implementation.Comment: 8 pages, 4 figures, 1 tabl

Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes

We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a statistical-mechanical three-dimensional disordered Ising lattice gauge theory, we estimate via large-scale Monte Carlo simulations that color codes are stable against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson loop distributions, we introduce a very sensitive probe to locate first-order phase transitions in lattice gauge theories.Comment: 12 pages, 5 figures, 1 tabl

オオサカダイガク カンゴガク ザッシ 13カン 1ゴウ タイショク キネン トクシュウ

退職記念特

Generalized Toric Codes Coupled to Thermal Baths

We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. As a consequence, we find that for qutrits new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension $d$ of the qudits. Although we provide an explicit proof that the system relax to the Gibbs state for arbitrary qudits, we also prove that above a certain crossing temperature, qutrits initial decay rate is smaller than the original case for qubits. Surprisingly this behavior only happens with qutrits and not with other qudits with $d>3$.Comment: Revtex4 file, color figures. New Journal of Physics' versio

Structure of 2D Topological Stabilizer Codes

We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can be understood in terms of the homology of string operators that carry a certain topological charge. In the case of subspace codes, we prove that two codes are equivalent under a suitable set of local transformations if and only they have equivalent topological charges. Our approach emphasizes local properties of the codes over global ones.Comment: 54 pages, 11 figures, version accepted in journal, improved presentation and result