CONDITIONAL GENERATION OF ERROR SYNDROMES IN FAULT-TOLERANT ERROR-CORRECTION

In this paper we show how the fault-tolerant quantum error-correction scheme recently proposed by DiVincenzo and Shor [Phys. Rev. Lett. 77, 3260 (1996)] can be made more efficient. Our scheme, unlike the earlie r one, can deal with a single error between the quantum gate operation s that are required for the implementation of the quantum error correc tion without repeated generation of error syndromes. For errors during gate operations we have to produce fewer error syndromes as we genera te them conditionally on the previous one. We show how to generalize t he method to arbitrary error-correcting codes.