Fault-Tolerant Logical Gate Networks for CSS Codes
arXiv:quant-ph/0311014 · doi:10.1103/PhysRevA.72.052335
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.
arXiv comment13 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
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