  In this paper we introduce a universal operator theoretic framework for
quantum fault tolerance. This incorporates a top-down approach that implements
a system-level criterion based on specification of the full system dynamics,
applied at every level of error correction concatenation. This leads to more
accurate determinations of error thresholds than could previously be obtained.
This is demonstrated both formally and with an explicit numerical example. The
basis for our approach is the Quantum Computer Condition (QCC), an inequality
governing the evolution of a quantum computer. We show that all known coding
schemes are actually special cases of the QCC. We demonstrate this by
introducing a new, operator theoretic form of entanglement assisted quantum
error correction, which incorporates as special cases all known error
correcting protocols, and is itself a special case of the QCC.
