Dynamics of dispersive single qubit read-out in circuit quantum electrodynamics

TL;DR

This paper investigates the dynamics of dispersive single-qubit read-out in circuit QED, demonstrating how transmitted field measurements can accurately infer qubit states and aid in quantum state tomography.

Contribution

It provides a detailed experimental and theoretical analysis of the measurement dynamics, including the development of a measurement operator for state reconstruction.

Findings

Excellent agreement between experiment and Bloch-type equations

Measurement operator accurately infers qubit populations

Method enables quantum state tomography in circuit QED

Abstract

The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements.