In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial, local, independent noise. It is found that the gate operations must be subject to less than 5.3% error. An existing proof that purification is equivalent to error correction is used to show that this bound can also be applied to concatenated error correcting codes in the presence of noisy gates, and hence gives a limit to the tolerable error rate for a fault-tolerant quantum computer formed by concatenation. This is shown to apply also to the case where error detection and postselection, as proposed by Knill, is used to enhance the threshold. We demonstrate the trade-off between gate and environmentally induced faulty rotations and qubit loss errors.
Physical Review A
- Pub Date:
- May 2008
- Quantum error correction and other methods for protection against decoherence;
- Entanglement production characterization and manipulation;
- Quantum Physics
- 8 pages, 6 figures. published version