FAULT-TOLERANT FIDELITY BASED ON FEW-QUBIT CODES: PARITY-CHECK CIRCUITS FOR BIASED ERROR OPERATORS

In the shallow sub-threshold regime, fault-tolerant quantum computation requires a tremendous amount of qubits. In this paper, we study the error correction in the deep sub-threshold regime. We estimate the physical error rate for achieving the logical error rates of 10(-6) - 10(-15) using few-qubit codes, i.e. short repetition codes, small surface codes and the Steane code. Error correction circuits that are efficient for biased error operators are identified. Using the Steane code, when error operators are biased with a ratio of 10(-3) the logical error rate of 10(-15) can be achieved with the physical error rate of 10(-5) which is much higher than the physical error rate of 10(-9) for depolarising errors.

Automated summary

In this paper, the authors study error correction in the deep sub-threshold regime and estimate the physical error rate required to achieve low logical error rates using few-qubit codes. They also identify error correction circuits that are efficient for biased error operators.