Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.Comment: 10 pages, 3 figure

Symmetry of anisotropic exchange interactions in semiconductor nanostructures

The symmetry of exchange interaction of charge carriers in semiconductor nanostructures (quantum wells and quantum dots) is analysed. It is shown that the exchange Hamiltonian of two particles belonging to the same energy band can be universally expressed via pseudospin operators of the particles. The relative strength of the anisotropic exchange interaction is shown to be independent of the binding energy and the isotropic exchange constant

Modulation of motor cortical excitability following rapid-rate transcranial magnetic stimulation

Objective: To investigate the effect of high frequency rTMS (25 Hz at 90-100% of resting motor threshold) on the excitability of the motor cortex of healthy human subjects.Methods: Resting and active motor threshold, MEP recruitment curve (I/O curve), short interval intracortical inhibition (SICI) and facilitation (ICF), and the duration of the silent period (SP) were tested in the right first dorsal interosscous muscle (FDI) before and twice after the end of 1500 pulses in 16 normal young adult male volunteers.Results: Twenty-five Hertz rTMS decreased motor thresholds, reduced the duration of the silent period and had a tendency to increase the slope of the I/O curve. Most of these effects lasted for the duration of the two post-testing sessions (at least 30 min) and had returned to normal by 2 h. There were no significant effects on SICI/ICF.Conclusion: Twenty-five Hertz rTMS can produce a long lasting increase in cortical excitability in healthy subjects.Significance: This method may prove useful for the study of normal human physiology and for therapeutic manipulation of brain plasticity. (c) 2006 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved