Quantum universality by distilling certain one- and two-qubit states with stabilizer operations
Ben W. Reichardt · arXiv (Cornell University) · 2006
Quantum universality can be achieved using stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? We extend the range of single-qubit mixed states which are known to give universality, by using a simple parity-checking operation. Additionally, we display a two-qubit mixed state which is not a mixture of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. The main application of these techniques is to quantum fault tolerance. Our results imply that recent fault-tolerance threshold upper bounds based on the Gottesman-Knill theorem are tight.