Soft-pulse dynamical decoupling in a cavity

Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a single ``soft'' pi-pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be turned to zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters, and use the results to analyze the structure of error operators for controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly-suppressed oscillator heating.Comment: 9pages, 5eps figure

Soft-Pulse Dynamical Decoupling with Markovian Decoherence

We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape, and for several sequences of $\pi$- and $\pi/2$-pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\delta$-pulses, it can be substantially improved by shaping.Comment: New version contains minor content clarification

The 'Beeching Axe' and Electoral Support in Britain

Policy implementation has important electoral effects, but there is often a problem in determining if policy changes drive electoral behaviour or if the process works in reverse. To address this issue we exploit a unique natural experiment in Britain: the closure of thousands of train stations, known as the Beeching Cuts, on the eve of General Election of 1964. We use several statistical methods to show that policy implementation was unaffected by partisan considerations and therefore it can be regarded as an exogenous intervention. An individual level model of voting intentions from the first British Election Study conducted in 1963, and an aggregate model of party vote shares in the General Election of 1964 show that the closures significantly changed voting support for the Conservative party. The 1964 election was very competitive and the closures clearly contributed to the defeat of the incumbent government after 13 years of uninterrupted rule

High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling

We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.Comment: 5 pages, 4 figure

Could Formononetin of Red Clover (\u3cem\u3eTrifolium pratense\u3c/em\u3e L.) be Enhanced by Phosphorus and Arbuscular Mycorrhizal Fungi Management?

Red clover is a forage legume of importance in the world with limited persistency; in Chile this is due mainly to the root borer (Hylastinus obscurus Marsham) infestation. Our previous studies have shown that there is a strong relationship between the root borer and the formononetin content in roots of the plants; therefore, studying factors that enhance the concentration of formononetin in the plant could help to decrease the negative effect of the root borer. The purpose of this research was to assess the relationship between phosphorus availability (P) in the soil interacting with arbuscular mycorrhizal fungi (AMF) over the concentration of formononetin in shoots and roots of red clover. One trial was carried out in a growth chamber at Carillanca Research Center, INIA-Chile, using 6.000 cc pots filled with an Andisol soil. Three levels of soil available phosphorus (10 ppm Olsen-P; 17 ppm Olsen-P; 24 ppm Olsen-P) and two levels of arbuscular mycorrhizal fungi (inoculated and non-inoculated with a commercial mixture) were implemented in a factorial arrangement in a completely randomized design. Soil water was maintained between 50 and 100% of the readily available soil water (RAW) by weighting each pot. Formononetin concentration of shoots and roots was evaluated in two sampling dates by extracting with a methanol solution and relative quantifications based on HPLC. Shoot and root biomass were affected significantly by P and not by AMF, being higher with increased P; however, formononetin concentration was higher with reduced P. On the other hand, there was a significant increase of formononetin concentration both in shoots and roots in the treatments inoculated with AMF. The medium level of P (17 ppm) with AMF inoculation shows a good compromise between biomass production and formononetin concentration

Characterizing and recognizing exact-distance squares of graphs

For a graph $G=(V,E)$, its exact-distance square, $G^{[\sharp 2]}$, is the graph with vertex set $V$ and with an edge between vertices $x$ and $y$ if and only if $x$ and $y$ have distance (exactly) $2$ in $G$. The graph $G$ is an exact-distance square root of $G^{[\sharp 2]}$. We give a characterization of graphs having an exact-distance square root, our characterization easily leading to a polynomial-time recognition algorithm. We show that it is NP-complete to recognize graphs with a bipartite exact-distance square root. These two results strongly contrast known results on (usual) graph squares. We then characterize graphs having a tree as an exact-distance square root, and from this obtain a polynomial-time recognition algorithm for these graphs. Finally, we show that, unlike for usual square roots, a graph might have (arbitrarily many) non-isomorphic exact-distance square roots which are trees.Comment: 15 pages, 6 figure