Optimized master-equation simulations of strongly-driven transmon-resonator systems

We demonstrate that combining a time-dependent displacement transformation [1] with a matrix-free implementation of operators and superoperators enables efficient master-equation simulations of a strongly driven transmon–resonator system on commodity hardware (CPU servers with ~100 cores and ~500 GiB memory). While close-to-coherent resonator states have been studied previously in the strongly driven dispersive measurement regime [1], we show that it is possible to handle even stronger drives that lead to significant deviations from coherent resonator states. As an example, we simulate the high-power transmon measurement of Ref. [2], where the two qubit states differ by thousands of resonator photons on average, and the resonator states become non-Gaussian due to complex transmon–resonator interactions. It is simultaneously possible to simulate transitions to highly-excited states of a transmon, arbitrarily large number of photons on average in the resonator, and significant deviations of the resonator state from a coherent one. We expect that these techniques will also be useful for studying measurement-induced state transitions of a transmon in the dispersive regime.

[1] Phys. Rev. A 108, 033722 (2023)

[2] Phys. Rev. Lett. 105, 173601 (2010)