QUANTUM ERROR CORRECTION AND FAULT-TOLERANT QUANTUM COMPUTING

We review the theories of quantum error correction, and of fault-tolerant quantum computing, and show how these powerful tools are combined to prove the accuracy threshold theorem for a particular error model. One of the theorem's assumptions is the availability of a universal set of unencoded quantum gates whose error probabilities P-e fall below a value known as the accuracy threshold P-a. For many, P-a similar to 10(-4) has become a rough estimate for the threshold so that quantum gates are anticipated to be approaching the accuracies needed for fault-tolerant quantum computing when P-e < 10(-4). We show how controllable quantum interference effects that arise during a type of non-adiabatic rapid passage can be used to produce a universal set of quantum gates whose error probabilities satisfy P-e < 10(-4). We close with a discussion of the current challenges facing an experimental implementation of this approach to reliable universal quantum computation.