Phase-space theory for dispersive detectors of superconducting qubits

TL;DR

This paper develops a phase-space theoretical framework to analyze the dynamics and measurement backaction of superconducting qubits coupled to dispersive harmonic oscillator detectors, considering various measurement protocols.

Contribution

It introduces a complex-environment approach using Floquet state master equations to model qubit-oscillator interactions and measurement processes.

Findings

Pointer becomes measurable before complete qubit information loss

Analysis of backaction effects on qubit dynamics

Comparison of long-term and short-term measurement schemes

Abstract

Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full read-out cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.