In order to ensure that our quantum bits remain protected, we have to perform error-detecting measurements very frequently. However, the circuits we use to perform these measurements, if poorly designed, may introduce more errors than the code can correct. Designing circuits which perform fault-tolerant quantum error correction is a cutting-edge field of research, and Professor Terhal will focus in on the surface code, the favoured candidate for near-term quantum error correction. This discussion concludes with the introduction of the fault-tolerant threshold, the physical error rate which must be reached in order for quantum error correction to be effective.

Main takeaways

• To detect errors in most quantum error-correcting codes, it is necessary to measure stabilisers using parity check circuits, which couple the qubits affected by the stabiliser to one or more nearby ancilla qubits.
• The order in which gates are executed in these circuits, and the arrangement of ancilla qubits can have drastic effects on the logical error rate.
• Every operation which can be performed on a physical qubit can, in principle, be performed on a logical qubit, though there are typically only a few such operations which can be implemented fault-tolerantly, introducing only correctable errors with high probability.
• Fault tolerance systems have threshold error rates. If the physical operations used in a fault-tolerant quantum error correction protocol have error rates which are smaller than this value, then increasing the redundancy of the underlying code will decrease the logical error rate.