Fault-tolerant quantum computation with a soft-decision decoder for error correction and detection by teleportation

Fault-tolerant quantum computation with quantum error-correcting codes has been considerably developed over the past decade. However, there are still difficult issues, particularly on the resource requirement. For further improvement of fault-tolerant quantum computation, here we propose a soft-decision decoder for quantum error correction and detection by teleportation. This decoder can achieve almost optimal performance for the depolarizing channel. Applying this decoder to Knill's C(4)/C(6) scheme for fault-tolerant quantum computation, which is one of the best schemes so far and relies heavily on error correction and detection by teleportation, we dramatically improve its performance. This leads to substantial reduction of resources.