The new field of quantum error correction has developed spectacularly since
its origin less than two years ago. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment. Recovery from errors can work effectively even if occasional
mistakes occur during the recovery procedure. Furthermore, encoded quantum
information can be processed without serious propagation of errors. Hence, an
arbitrarily long quantum computation can be performed reliably, provided that
the average probability of error per quantum gate is less than a certain
critical value, the accuracy threshold. A quantum computer storing about 10^6
qubits, with a probability of error per quantum gate of order 10^{-6}, would be
a formidable factoring engine. Even a smaller, less accurate quantum computer
would be able to perform many useful tasks. (This paper is based on a talk
presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18
December 1996.)Comment: 24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
