Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis

TL;DR

This paper develops a simplified and accurate stochastic master equation framework for homodyne measurement of multi-qubit observables in circuit QED, enabling better analysis of multi-qubit measurement dynamics.

Contribution

It introduces a new technique that simplifies deriving stochastic master equations for multi-qubit measurements, avoiding complex transformations used previously.

Findings

Derived a family of stochastic master equations for multi-qubit measurements.

Showed that larger registers evolve under non-Markovian dynamics.

Achieved ~94% fidelity in three-qubit, two-mode simulations.

Abstract

We derive a family of stochastic master equations describing homodyne measurement of multi-qubit diagonal observables in circuit quantum electrodynamics. In the regime where qubit decay can be neglected, our approach replaces the polaron-like transformation of previous work, which required a lengthy calculation for the physically interesting case of three qubits and two resonator modes. The technique introduced here makes this calculation straightforward and manifestly correct. Using this technique, we are able to show that registers larger than one qubit evolve under a non-Markovian master equation. We perform numerical simulations of the three-qubit, two-mode case from previous work, obtaining an average post-measurement state fidelity of $\sim 94\%$, limited by measurement-induced decoherence and dephasing.