A universal quantum circuit for two-qubit transformations with three CNOT gates

We consider the implementation of two-qubit unitary transformations by means of CNOT gates and single-qubit unitary gates. We show, by means of an explicit quantum circuit, that together with local gates three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates.Comment: 3 pages, 7 figures. One theorem, one author and references added. Change of notational conventions. Minor correction in Theorem

Experimentally determined flutter from two- and three-bladed model bearingless rotors in hover

A series of experiments was performed on a 1.8-m-diam model rotor in hover for the principal purpose of investigating the lead-lag stability of isolated bearingless rotors. Incidental to those tests, at least three types of pitch-flap flutter were encountered. Type 1 flutter occurred approximately at the second flap-mode frequency on both two-and three-bladed rotors for both small and large pitch angles and appeared to be a classic pitch-flap flutter. Type 2 flutter showed mostly torsional motion and was seen on both two- and three-bladed rotors. Type 3 flutter was a regressing flap flutter that occurred for only the three-bladed rotor configurations and appears to be a wake excited flutter. Although flutter occurred on a number of different configurations, no rotor parameters were identified that were clearly stabilizing or destabilizing

Transience and recurrence of random walks on percolation clusters in an ultrametric space

We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)}, \delta>-1$, with $c_k=C_0+C_1\log k+C_2k^\alpha$, non-negative constants $C_0, C_1, C_2$, and $\alpha>0$. Percolation was proved in Dawson and Gorostiza (2013) for $\delta0$, with $\alpha>2$. In this paper we improve the result for the critical case by showing percolation for $\alpha>0$. We use a renormalization method of the type in the previous paper in a new way which is more intrinsic to the model. The proof involves ultrametric random graphs (described in the Introduction). The results for simple (nearest neighbour) random walks on the percolation clusters are: in the case $\delta<1$ the walk is transient, and in the critical case $\delta=1, C_2>0,\alpha>0$, there exists a critical $\alpha_c\in(0,\infty)$ such that the walk is recurrent for $\alpha<\alpha_c$ and transient for $\alpha>\alpha_c$. The proofs involve graph diameters, path lengths, and electric circuit theory. Some comparisons are made with behaviours of random walks on long-range percolation clusters in the one-dimensional Euclidean lattice.Comment: 27 page

GDL: a model infrastructure for a regional digital library

This brief article describes the early days of the Glasgow Digital Library (GDL), when it was a cross-sectoral and city-wide collaborative initiative involving Strathclyde, Glasgow and Caledonian Universities, as well as Glasgow City Libraries and Archives and the Glasgow Colleges Group