Counterdiabatic formalism of shortcuts to adiabaticity.

A pedagogical introduction to counterdiabatic formalism of shortcuts to adiabaticity is given so that readers can access some of the more specialized articles in the rest of this theme issue without any barriers. A guide to references is given so that this article also serves as a mini-review. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Concatenated Composite Pulses Applied to Liquid-State Nuclear Magnetic Resonance Spectroscopy.

The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.

Geometric aspects of composite pulses.

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.