Generalization of short coherent control pulses: extension to arbitrary rotations

Abstract

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.

6 pages, no figures; published version

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• Optimized Dynamical Decoupling via Genetic Algorithms
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• Modulated Continuous Wave Control for Energy-efficient Electron-nuclear Spin Coupling
• Shaped Pulses for Energy Efficient High-Field NMR at the Nanoscale
• Numerical Analysis of Optimized Coherent Control Pulses
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• Frequency modulated pulses for quantum bits coupled to time-dependent baths
• Symmetry-Enhanced Performance of Dynamical Decoupling
• Anomalous behavior of control pulses in presence of noise with singular autocorrelation
• Short coherent control pulse with small random errors in its direction