Resonance Offset Tailored Composite Pulses

Holly K. Cummins, Jonathan A. Jones

We describe novel composite pulse sequences which act as general rotors and thus are suitable for nuclear magnetic resonance (NMR) quantum computation. The Resonance Offset Tailoring To Enhance Nutations (ROTTEN) approach permits perfect compensation of off-resonance errors at two selected frequencies placed symmetrically around the frequency of the RF source.

Ray Freeman, Thomas A. Frenkiel, Malcolm H. Levitt

Athan J Shaka, Alexander Pines

Jonathan Berkheim, David J. Tannor

Composite Pulses (CPs) are widely used in Nuclear Magnetic Resonance (NMR), optical spectroscopy, optimal control experiments and quantum computing to manipulate systems that are well-described by a two-level Hamiltonian. A careful design of these pulses can allow the refocusing of an ensemble at a desired state, even if the ensemble experiences imperfections in the magnitude of the external field or resonance offsets. Since the introduction of CPs, several theoretical justifications for their robustness have been suggested. In this work, we suggest another justification based on the classical mechanical concept of a stability matrix. The motion on the Bloch Sphere is mapped to a canonical system of coordinates and the focusing of an ensemble corresponds to caustics, or the vanishing of an appropriate stability matrix element in the canonical coordinates. Our approach highlights the directionality of the refocusing of the ensemble on the Bloch Sphere, revealing how different ensembles refocus along different directions. The approach also clarifies when CPs can induce a change in the width of the ensemble as opposed to simply a rotation of the axes. As a case study, we investigate the $90(x)180(y)90(x)$ CP introduced by Levitt, where the approach provides a new perspective into why this CP is effective.

Ghassen Dridi, Mohamed Mejatty, Steffen J. Glaser +1 more

We present a general procedure to implement a not gate by composite pulses robust against both offset uncertainties and control field variations. We define different degrees of robustness in this two-parameter space, namely, along one, two, or all directions. We show that the phases of the composite pulse satisfy a nonlinear system and can be computed analytically or numerically.

I Chikawa, Motooki Ando, Y Asushi K Ondo +1 more