Fault correction for Clifford circuits

A computer system coupled operatively to a quantum computer, the computer system comprising:

• a processor;
• and
• operatively coupled to the processor, computer memory holding instructions that cause the processor to correct a fault in application of a Clifford circuit to a qubit register of the quantum computer, the instructions comprising:
• instructions (A) for receiving circuit data defining the Clifford circuit;
• instructions (B) for emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register;
• and
• instructions (C) for emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register.

A method to correct a fault in application of a Clifford circuit to a qubit register of a quantum computer, the method comprising:

• receiving circuit data defining the Clifford circuit;
• emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register;
• emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and on the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register;
• emitting low-density parity-check (LDPC) space-time quantum code based on the circuit data, the outcome code, and the space-time quantum code, the LDPC space-time quantum code including connected stabilizers of the space-time quantum code up to a predetermined weight;
• and
• decoding the LDPC space-time quantum code in an LDPC decoder to correct the fault in the application of the Clifford circuit to the qubit register.