2005/04/30 by Panos Aliferis, Daniel Gottesman, John Preskill · 4 citations
Physics and Astronomy · #quant-ph
published as Quant. Inf. Comput. 6 (2006) 97-165 · 58 pages, 15 figures, uses qic.sty. (v2): New proof of the main lemma; generalized analysis of local non-Markovian noise. (v3): minor revisions
arxiv created 2005/10/21 · arxiv updated 2009/12/01
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon0. Our proof also applies to concatenation of higher-distance codes, and to noise models that allow faults to be correlated in space and in time. The proof uses new criteria for assessing the accuracy of fault-tolerant circuits, which are particularly conducive to the inductive analysis of recursive simulations. Our lower bound on the threshold, epsilon0 > 2.73 × 10-5 for an adversarial independent stochastic noise model, is derived from a computer-assisted combinatorial analysis; it is the best lower bound that has been rigorously proven so far.