Protected measurements for protected superconducting qubits

Protected superconducting qubits, such as the 0-π qubit, promise to substantially decrease error rates. However, their protection comes at the cost of controllability since they are intentionally decoupled from their environment. In particular, there are a lack of strategies to measure these qubits. Here we propose QND measurement schemes for the 0-π qubit in the protected regime. Our approach utilizes the internal harmonic mode of the 0-π qubit, and makes use of measurement protocols for GKP states based on conditional displacement gates. We quantify how these measurements retain the protection of the qubit and discuss their experimental implementation.