Preparation of Qunaught States for a Surface GKP Code using a Three (or higher) Level Ancilla System

A fault tolerant quantum error correction protocol is implemented for a surface code comprising Gottesman Kitaev Preskill (GKP) qubits. Analog information is determined when measuring position or momentum shifts, wherein the analog information indicates a closeness of the shift to a decision boundary. The analog information is further used to determine confidence values for error corrected measurements from the GKP qubits of the surface code. These confidence values are used to dynamically determine edge weights in a matching graph used to decode syndrome measurements of the surface code, wherein the confidence values are obtained using a maximum-likelihood decoding protocol for two-qubit gates. Also, a three-level ancilla is used to more reliably squeeze the GKP qunaught states.