Fault-Tolerant Logical Gate Networks for CSS Codes
Abstract
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can be prepared by a single recovery operation in any state whose stabilizer generator separates into X and Z parts. Optimized methods to move logical qubits around and to achieve controlled-not and Toffoli gates are discussed. It is found that the number of time-steps required to complete a fault-tolerant quantum computation is the same when k>1 as when k=1.
Cite
@article{arxiv.quant-ph/0311014,
title = {Fault-Tolerant Logical Gate Networks for CSS Codes},
author = {Andrew M. Steane and Ben Ibinson},
journal= {arXiv preprint arXiv:quant-ph/0311014},
year = {2013}
}
Comments
13 pages, 16 figures. The material in the appendix was included in a previous quant-ph eprint, but not yet published; it has been corrected and clarified. The rest is new. Replacement version: various small corrections and clarifications