Method comparison: Time-independent and time-dependent coupling on qubitdyne protocol with higher photon states

The qubitdyne protocol allows for quadrature detection of bosonic modes in stationary systems via repeated weak interactions with an auxiliary qubit. This approach circumvents the loss of photons in the cavity. While the earlier implementation of qubitdyne protocol utilizes constant coupling, Strandberg, et al. [<em>PRL</em> <strong>133</strong>, 063601 (2024)], suggests time-dependent coupling can significantly enhance the measurement process.