Persistent level-resolved transmon population after dispersive readout, and the limits of its open-system description

Sinan Bugu

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arXiv · 2611.08235

Persistent level-resolved transmon population after dispersive readout, and the limits of its open-system description

Sinan Bugu

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Abstract

We calculate the level-resolved transmon population remaining after dispersive readout with a converged open-system model. The drive and qubit-cavity coupling use the rotating-wave approximation, while the cavity is a quantized mode in a frame displaced by its classical trajectory. At a readout occupation of 80, the model leaves a persistent distribution across the first transmon levels, with p2 = 1.02 x 10^-3 and p3 = 4.10 x 10^-5 at the end of readout. These populations survive an additional drive-off wait: over 73 ns each level decays by less than 3 percent and follows its own relaxation rate, not the near-factor-of-two drop in residual cavity photons. This identifies the population as bare-level occupation rather than coherent dressing. Channel-removal and bath-model controls attribute p2 mainly to dephasing and p3 and above mainly to relaxation, unchanged across bath models though absolute values vary by up to 15 percent. We also test the coherent drive truncation. In dissipation-free transmon-only benchmarks driven by the classical cavity trajectory, the nearest-neighbour RWA drive underestimates the full charge-operator result while the drive is on. At switch-off for occupation 80, where coherent populations are hundreds of times larger than the residual values, p2(RWA)/p2(full) = 0.905 and p3(RWA)/p3(full) = 0.759, with larger discrepancies at deeper levels. One source is a parity-allowed non-nearest-neighbour charge matrix element omitted by the drive operator. A naive beyond-RWA extension with bare-basis Lindblad dissipators fails a zero-drive ground-state test and serves only as a diagnostic. A dressed-basis (secular) construction instead leaves the dressed ground state stationary at zero drive. The result is a converged RWA prediction of readout-induced population plus direct tests of where the approximation loses quantitative reliability.

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Sinan Bugu. 2026-11-05. Persistent level-resolved transmon population after dispersive readout, and the limits of its open-system description. https://arxiv.org/abs/2611.08235

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