Computing physical representation matrix of logical Clifford operation

A method for use with a computing system, the method comprising:

• receiving an extended stabilizer form of a quantum error correction code;
• receiving a logical Clifford operation specification of a logical Clifford operation;
• based at least in part on the extended stabilizer form, computing a stabilizer tableau of the quantum error correction code;
• based at least in part on the stabilizer tableau and the logical Clifford operation specification, computing a physical representation matrix of the logical Clifford operation based at least in part on an invertible bit matrix and an additional bit matrix;
• and
• outputting the physical representation matrix.

A computing system comprising:

• one or more processing devices configured to:
• receive an extended stabilizer form of a quantum error correction code;
• receive a logical Clifford operation specification of a logical Clifford operation;
• based at least in part on the extended stabilizer form, compute a stabilizer tableau of the quantum error correction code at least in part by:
• computing a plurality of destabilizer check rows of the quantum error correction code;
• and
• further extending the extended stabilizer form with the destabilizer check rows;
• based at least in part on the stabilizer tableau and the logical Clifford operation specification, compute a physical representation matrix of the logical Clifford operation;
• compute a quantum circuit based at least in part on the physical representation matrix;
• and
• control a quantum computing device to implement the logical Clifford operation by executing the quantum circuit.