Abstract
Mark Howard (NUI Maynooth)
Universal Quantum Computation using Protected Operations and Distillation
The stabilizer formalism is a mathematical technique, for describing
quantum states and quantum processes, which gives special prominence to
a subset of all quantum states (stabilizer states) and a subset of all
operations (stabilizer operations). A crucial result in quantum
information theory says that, whilst stabilizer states and operations
are extremely important (they underpin most error-correcting codes, for
example), a quantum computer using only this restricted set of states
and operations can never be more powerful than a classical computer. The
immediate implication is that any useful quantum computer must make use
of non-stabilizer states or non-stabilizer operations (i.e., this non-
stabilizer resource ``unlocks'' the power of the quantum
computer).
Motivated by some proposals for fault-tolerant quantum computing,
wherein stabilizer operations are effectively perfect, we analyze the
utility of an additional non-stabilizer resource -- in particular
when this non-stabilizer resource is highly imperfect.