Geometric aspects of composite pulses

Abstract

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.

Control of the spin geometric phase in semiconductor quantum rings

“…To the best of our knowledge, this is the first experimental demonstration of the pure geometric-phase control of an electron spin in solid-state devices. We conclude that this multiparameter control of the spin geometric phase may pave the way for future spintronic applications, such as geometric-gate operation29 of a solid-state flying qubit or control of persistent spin currents in a mesoscopic ring1130, which may have potential applications for non-volatile memory devices.…”

Non-Adiabatic Universal Holonomic Quantum Gates Based on Abelian Holonomies

“…In this work, we have implemented a universal set of non-adiabatic geometric quantum gates based on abelian holonomies by making use of the dynamical invariants (8) and (18). Our implementation does not require secondary techniques such as double-loop or spin-echo technique and is expected to be physically straightforward on NMR.…”

“…Implementation of high-precision gates is an urgent subject to be solved. Composite gates originally proposed in NMR measurement are one of such strategies although composite gates require many elementary gates and hence longer execution time [8,9].…”

Nuclear magnetic resonance quantum information processing

“…The NMR technique uses a sequence composed of pulses especially designed in order to achieve some desired unitary evolution. Ichikawa et al [9] studied some geometrical aspects of such a composed evolution. They show some possibilities to implement geometric quantum gates in NMR systems.…”