Fast, optimal circuit design of multiplexed readout resonators with individual Purcell filters.*

Multiplexed readout circuits with individual Purcell filters have emerged as a promising architecture satisfying the speed, fidelity, and scalability necessary for large-scale quantum error correction. At relevant system sizes, however, simultaneously designing for all target parameters quickly becomes intractable using typical Finite-Element-Method-based approaches. Instead, we present a circuit-based simulation approach together with a computationally efficient, closed-loop optimization of the entire readout circuit. We further study the hybridization dynamics of the readout and filter resonator and observe parameter regimes where the Purcell protection from the filter breaks down. Finally, we discuss the experimental realization of circuits in different parameter regimes as well as the readout performance of these systems.