Arbitrarily accurate variable rotations on the Bloch sphere by composite pulse sequences

Abstract

Composite pulse sequences, which produce arbitrary pre-defined rotations of a two-state system at an angle $\theta$ on the Bloch sphere, are presented. The composite sequences can contain arbitrarily many pulses and can compensate experimental errors in the pulse amplitude and duration to any desired order. A special attention is devoted to two classes of $\pi /2$ sequences --- symmetric and asymmetric --- the phases of which are given by simple formulas in terms of rational multiples of $\pi$ for any number of constituent pulses. This allows one to construct arbitrarily accurate $\pi /2$ composite rotations. These $\pi /2$ composite sequences are used to construct three classes of arbitrarily long composite $\theta$ sequences by pairing two $\pi /2$ composite sequences, one of which is shifted by a phase $\pi -\theta$ with respect to the other one.

11 pages, 6 figures

References in corpus (4)

• Quantum computing with trapped ions
• Realization of the quantum Toffoli gate with trapped ions
• Correction of Arbitrary Errors in Population Inversion of Quantum Systems by Universal Composite Pulses
• Variable Ultra-broadband and Narrowband Composite Polarization Retarders

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