Magic composite pulses

I describe composite pulses during which the average dipolar interactions within a spin ensemble are controlled while realizing a global rotation. The construction method used is based on the average Hamiltonian theory and rely on the geometrical properties of the spin-spin dipolar interaction only. I present several such composite pulses robust against standard experimental defects in NRM: static or radio-frequency field miscalibration, fields inhomogeneities. Numerical simulations show that the magic sandwich pulse sequence, a pulse sequence that reverse the average dipolar field while applied, is plagued by defects originating from its short initial and final \pi/2 radio-frequency pulses. Using the magic composite pulses instead of \pi/2 pulses improves the magic sandwich effect. A numerical test using a classical description of NMR allows to check the validity of the magic composite pulses and estimate their efficiency.Comment: 22 pages, 6 figure

Geometric Aspects of Composite Pulses

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by employing a sequence of possibly poor quality pulses. In this article, we demonstrate that two kinds of composite pulses, one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a twoqubit system, have vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.Comment: 20 pages, 4 figures. Accepted for publication in Philosophical Transactions of the Royal Society

A First Principles Theory of Nuclear Magnetic Resonance J-Coupling in solid-state systems

A method to calculate NMR J-coupling constants from first principles in extended systems is presented. It is based on density functional theory and is formulated within a planewave-pseudopotential framework. The all-electron properties are recovered using the projector augmented wave approach. The method is validated by comparison with existing quantum chemical calculations of solution-state systems and with experimental data. The approach has been applied to verify measured J-coupling in a silicophosphate structure, Si5O(PO4)6Comment: 9 page

Phase space spinor amplitudes for spin 1/2 systems

The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-\half is treated in detail, and it is shown that phase space amplitudes on the sphere transform correctly as spinors under under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-\half magnetic dipole in a time-dependent magnetic field.Comment: 19 pages, added new results, fixed typo

Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

Given a group automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that any irreducible lattice in a connected semi simple Lie group having finite centre and rank at least 2 has the $R_\infty$-property.Comment: 6 page

Cultural policies in cities of the ‘global South’: a multi-scalar approach

Building on the literature on global cities and on the worlding of cities, the articles in this special issue chart how cities outside Europe and North America try to reinvent and rescale themselves using culture. They suggest that the fabric of urban cultural policy is embedded in multi-scalar power dynamics. First, the contributions in this special issue reveal the importance of circulating standards across borders in structuring narratives about urban history, heritage and identity, in conjunction with local actors’ interests. Second, the diffusion of hegemonic cultural policy models such as the “creative city” leads to logics of exclusion, gentrification, and has been met with resistance, which suggest that these models can be to the detriment of local residents, despite the progressive values they are often claim to promote. Third, this special issue points to the need to rethink the politics of cultural policy mobility and offers conceptual tools such as vernacularization to make sense of the ways in which urban elites navigate, negotiate and take advantage of circulating cultural policy models

Concomitant medication use and clinical outcome of repetitive Transcranial Magnetic Stimulation (rTMS) treatment of Major Depressive Disorder.

BackgroundRepetitive Transcranial Magnetic Stimulation (rTMS) is commonly administered to Major Depressive Disorder (MDD) patients taking psychotropic medications, yet the effects on treatment outcomes remain unknown. We explored how concomitant medication use relates to clinical response to a standard course of rTMS.MethodsMedications were tabulated for 181 MDD patients who underwent a six-week rTMS treatment course. All patients received 10 Hz rTMS administered to left dorsolateral prefrontal cortex (DLPFC), with 1 Hz administered to right DLPFC in patients with inadequate response to and/or intolerance of left-sided stimulation. Primary outcomes were change in Inventory of Depressive Symptomatology Self Report (IDS-SR30) total score after 2, 4, and 6 weeks.ResultsUse of benzodiazepines was associated with less improvement at week 2, whereas use of psychostimulants was associated with greater improvement at week 2 and across 6 weeks. These effects were significant controlling for baseline variables including age, overall symptom severity, and severity of anxiety symptoms. Response rates at week 6 were lower in benzodiazepine users versus non-users (16.4% vs. 35.5%, p = 0.008), and higher in psychostimulant users versus non-users (39.2% vs. 22.0%, p = 0.02).ConclusionsConcomitant medication use may impact rTMS treatment outcome. While the differences reported here could be considered clinically significant, results were not corrected for multiple comparisons and findings should be replicated before clinicians incorporate the evidence into clinical practice. Prospective, hypothesis-based treatment studies will aid in determining causal relationships between medication treatments and outcome

Quantum information processing using strongly-dipolar coupled nuclear spins

Dipolar coupled homonuclear spins present challenging, yet useful systems for quantum information processing. In such systems, eigenbasis of the system Hamiltonian is the appropriate computational basis and coherent control can be achieved by specially designed strongly modulating pulses. In this letter we describe the first experimental implementation of the quantum algorithm for numerical gradient estimation on the eigenbasis of a four spin system.Comment: 5 pages, 5 figures, Accepted in PR

Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction

We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N=3, but requires N=6 elementary two-qubit gates.Comment: 7 pages, 2 figure

Rhetoric in the language of real estate marketing

“Des. Res.”, “rarely available”, “viewing essential” – these are all part of the peculiar parlance of housing advertisements which contain a heady mix of euphemism, hyperbole and superlative. Of interest is whether the selling agent’s penchant for rhetoric is spatially uniform or whether there are variations across the urban system. We are also interested in how the use of superlatives varies over the market cycle and over the selling season. For example, are estate agents more inclined to use hyperbole when the market is buoyant or when it is flat, and does it matter whether a house is marketed in the summer or winter? This paper attempts to answer these questions by applying textual analysis to a unique dataset of 49,926 records of real estate transactions in the Strathclyde conurbation over the period 1999 to 2006. The analysis opens up a new avenue of research into the use of real estate rhetoric and its interaction with agency behaviour and market dynamics