Full quantum treatment of Rabi oscillation driven by a pulse train and its application in ion-trap quantum computation

TL;DR

This paper provides a comprehensive quantum analysis of Rabi oscillations driven by pulse trains, revealing exponential decay and no revival, with implications for ion-trap quantum computing fidelity.

Contribution

It introduces a full quantum model of pulse-driven Rabi oscillations and applies it to assess error bounds in ion-trap quantum computation schemes.

Findings

Population inversion collapses exponentially without revival.

Failure probability in ion-trap schemes is around 1% after 100 gates.

Wavelength of the driving field significantly affects quantum computation fidelity.

Abstract

Rabi oscillation of a two-level system driven by a pulse train is a basic process involved in quantum computation. We present a full quantum treatment of this process and show that the population inversion of this process collapses exponentially, has no revival phenomenon, and has a dual-pulse structure in every period. As an application, we investigate the properties of this process in ion-trap quantum computation. We find that in the Cirac--Zoller computation scheme, when the wavelength of the driving field is of the order $10^{-6}$ m, the lower bound of failure probability is of the order $10^{-2}$ after about $10^2$ controlled-NOT gates. This value is approximately equal to the generally-accepted threshold in fault-tolerant quantum computation.