Qubit control using quantum Zeno effect: Action principle approach

TL;DR

This paper uses a path-integral formalism to analyze how the quantum Zeno effect can control a two-level quantum system under continuous measurement, revealing complex phase dynamics and potential applications in quantum error correction.

Contribution

It introduces a systematic action principle approach to understand the quantum Zeno effect in driven two-level systems with repeated measurements, highlighting phase space dynamics.

Findings

Oscillations slow down and halt at measurement-resonance conditions.

Dynamics organize around hyperbolic points with reversed stability.

Phase space flow occurs between hyperbolic points via separatrices.

Abstract

We employ the stochastic path-integral formalism and action principle for continuous quantum measurements - the Chantasri-Dressel-Jordan (CDJ) action formalism [1, 2] - to understand the stages in which quantum Zeno effect helps control the states of a simple quantum system. The detailed dynamics of a driven two-level system subjected to repeated measurements unravels a myriad of phases, so to say. When the detection frequency is smaller than the Rabi frequency, the oscillations slow down, eventually coming to a halt at an interesting resonance when measurements are spaced exactly by the time of transition between the two states. On the other hand, in the limit of large number of repeated measurements, the dynamics organizes itself in a rather interesting way about two hyperbolic points in phase space whose stable and unstable directions are reversed. Thus, the phase space flow occurs from one hyperbolic point to another, in different ways organized around the separatrices. We believe that the systematic treatment presented here paves the way for a better and clearer understanding of quantum Zeno effect in the context of quantum error correction.