A mid-circuit erasure check on a dual-rail cavity qubit using the joint-photon number-splitting regime of circuit QED

Erasure qubits promise low logical error rates with fewer physical qubits, but require a key new element not present in traditional schemes, a mid-circuit erasure detector (MCED). An effective MCED must balance three competing requirements: (1) a low missed-erasure rate, (2) a low added-erasure rate, and (3) a low added-Pauli-error rate. Furthermore, to take advantage of the hardware efficiency of erasure schemes, this measurement should place as few additional requirements on the hardware as possible.

I will show how this can be solved for dual-rail cavity qubits by combining two already-present control elements: a high-fidelity tunable beamsplitter coupling between cavities (used for gates) and a static dispersive coupling between just one cavity and an ancillary transmon (used for SPAM). When the beamsplitter strength exceeds the dispersive shift (made possible by a SNAIL parametric coupler) the frequency shift of the transmon depends only on the joint photon number in both cavities. This ‘joint-photon number-splitting regime’ provides a powerful way to extend single-oscillator control methods to two-oscillators. This enables a hardware-efficient erasure check which clearly distinguishes leakage and logical states (missed-erasure rate 9×10^-4) while remaining minimally invasive on the logical states themselves (added-Pauli-error rate 3×10^-3, added-erasure-rate 3×10^-2, both dominated by intrinsic cavity errors).

I will compare this scheme to other erasure check methods, discuss how pulse shapes can be optimized in light of system error rates, and provide examples of where the joint-photon number-splitting regime could further be applied.