Toward fault-tolerant quantum computation without concatenation
Abstract
Description
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features-improved accuracy threshold, local operations-have also been studied. By iteratively distilling a certain two-qubit entangled state it is shown how to perform an encoded Toffoli gate, important for universal computation, on CSS codes that are either unconcatenated or, for a range of very large block sizes, singly concatenated.
12 pages, 2 figures, replaced: new stuff on error models, numerical example for concatenation criteria
12 pages, 2 figures, replaced: new stuff on error models, numerical example for concatenation criteria