Fault tolerant syndrome extraction and decoding in Bacon-Shor quantum error correction

A method for quantum error correction comprising:

• extracting a syndrome from an array of qubits;
• determining if the extracted syndrome is a valid syndrome;
• computing a bitwise exclusive OR between the extracted syndrome and a most recent valid syndrome if the extracted syndrome is valid;
• decoding the computed bitwise exclusive OR to determine the locations of qubits whose error states have changed;
• and
• updating an error register, implemented on an integrated circuit, representing locations within the array of qubits with the determined locations.

A quantum system comprising:

• an array of qubits configured to store an item of quantum information, the array of qubits including a plurality of data qubits and a plurality of measurement qubits configured to extract a first syndrome representing agreement among the plurality of data qubits with respect to a first basis and a second syndrome representing agreement among the plurality of data qubits with respect to the first basis;
• an integrated circuit comprising:
• validation logic configured to determine if the syndrome is valid and to compare the first syndrome to the second syndrome and reject the extracted syndromes if the first syndrome does not match the second syndrome;
• decoding logic configured to evaluate the syndrome to determine location of errors within the plurality of data qubits;
• and
• an error register configured to store locations of the determined errors.