Abstract
In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-quantum-bit code.
- Received 18 February 1997
DOI:https://doi.org/10.1103/PhysRevA.57.127
©1998 American Physical Society