Investigating the quantum non-demolition character of the longitudinal transmon readout

Standard dispersive readout of a transmon induces several unwanted effects which are detrimental to fast high-fidelity measurements. This includes Purcell decay, and a breakdown of the quantum non-demolition (QND) character of the measurement [1,2]. An alternative approach to this standard setup is to couple the readout resonator and qubit longitudinally [3]. This generates a qubit-state dependent 180 degree out-of-phase displacement of the resonator field, and the lack of state dressing implies the deleterious effects should be absent. In a real circuit which implements longitudinal coupling, however, the multi-level nature of the transmon does not imply that one is protected against leakage out of the qubit code space.

Here we extend the work from [3] by utilizing recently developed theoretical and numerical tools for studying transmon ionization to study whether fast readout of longitudinally coupled transmon-resonator system leads to significant leakage. Using a realistic circuit that realizes longitudinal coupling introduced in Ref. [3], we explore how the multi-level nature of a transmon affects this readout, the impact of chaos in the system, and whether longitudinal readout leads to transmon ionization [2]. We show that we are in principle able to achieve fast, high-fidelity QND readout of transmon qubits with longitudinal coupling.

[1] T Walter, et al., Phys. Rev. Appl. 7, 054020 (2017).

[2] Ross Shillito, et al., Phys. Rev. Applied 18, 034031(2022)

[3] Nicolas Didier, et al., Phys. Rev. Lett. 115, 203601 (2015)