Fault-tolerant quantum error correction with a surface GKP code

A method of performing error corrected measurements for a surface code comprising Gottesman, Kitaev Preskill (GKP) qubits, the method comprising:

• for respective ones of the GKP qubits of the surface code:
• determining a position operator ({circumflex over (q)}) or a momentum operator ({circumflex over (p)}) shift for one or more stabilizers of the respective GKP qubit;
• determining analog information indicating a relative amount the determined position operator ({circumflex over (q)}) or the determined momentum operator ({circumflex over (p)}) is shifted relative to a decision boundary;
• error-correcting the respective GKP qubit based on the determined position operator ({circumflex over (q)}) or the momentum operator ({circumflex over (p)}) shift;
• determining, based on the analog information, a confidence value for the respective error corrections, wherein an error correction performed for a position or momentum shift further from the measurement decision boundary is given a higher confidence value than an error correction performed for a position or momentum shift closer to the measurement decision boundary;
• and
• providing error-corrected measurement values for the respective ones of the GKP qubits of the surface code and corresponding respective confidence values for the error-corrected measurement values, wherein the confidence values indicate respective levels of confidence in the error corrections for the GKP qubits of the surface code, wherein the confidence values are provided for use in decoding the error-corrected measurement values for the respective ones of the GKP qubits of the surface code.

One or more non-transitory computer-readable media storing program instructions, that when executed on or across one or more processors, cause the one or more processors to:

• determine a position operator ({circumflex over (q)}) or a momentum operator ({circumflex over (p)}) shift for one or more stabilizers of a respective Gottesman, Kitaev Preskill (GKP) qubit of a surface code;
• determine analog information indicating a relative amount the determined position operator ({circumflex over (q)}) or the determined momentum operator ({circumflex over (p)}) is shifted relative to a decision boundary;
• error-correct the respective GKP qubit based on the determined position operator ({circumflex over (q)}) or the momentum operator ({circumflex over (p)}) shift;
• determine, based on the analog information, a confidence value for the respective error corrections, wherein an error correction performed for a position or momentum shift further from the measurement decision boundary is given a higher confidence value than an error correction performed for a position or momentum shift closer to the measurement decision boundary;
• and
• provide error-corrected measurement values for the respective ones of the GKP qubits of the surface code and corresponding respective confidence values for the error-corrected measurement values, wherein the confidence values indicate respective levels of confidence in the error corrections for the GKP qubits of the surface code.