2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212039It 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 criteriaQuantum Physicstext