Geometric aspects of composite pulses

Holly K. Cummins, Jonathan A. Jones

Sami Husain, Minaru Kawamura, Jonathan A. Jones

Tsubasa Ichikawa, Masamitsu Bando, Yasushi Kondo +1 more

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 realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, 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 two-qubit system-have a 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.

Athan J Shaka, Alexander Pines

Yukihiro Ota, Yasushi Kondo

We show that some composite pulses widely employed in NMR experiments are regarded as nonadiabatic geometric quantum gates with Aharanov-Anandan phases. Thus, we reveal the presence of a fundamental issue on quantum mechanics behind a traditional technique. To examine the robustness of such composite pulses against fluctuations, we present a simple noise model in a two-level system. Then, we find that the composite pulses possesses purely geometrical nature even under a certain type of fluctuations.

P. Gordon