High fidelity feed-back assisted parity measurement in circuit QED

TL;DR

This paper investigates a high-fidelity two-qubit parity measurement in circuit QED, emphasizing feedback control to mitigate back-action effects and improve measurement accuracy even with unknown initial states.

Contribution

It introduces a feedback-based method to determine phase shifts during measurement, independent of initial states, enhancing parity measurement fidelity in circuit QED.

Findings

The phase rotation can be estimated from the measurement record.

The method is effective even with unknown initial states.

The approach is robust against measurement record errors.

Abstract

We analyze a two qubit parity measurement based on dispersive read-out in circuit quantum electrodynamics. The back-action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record, using the method of state estimation. Our main result is that the outcome of this phase determination process is {\em independent} of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation, where the initial state is unknown. We discuss how this feed-back method can be used to achieve a high fidelity parity measurement for realistic values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feed-back procedure towards errors in the measurement record.