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Fault-Tolerant Logical Gate Networks for CSS Codes

Andrew M. Steane·Ben Ibinson
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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.

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Andrew M. Steane, Ben Ibinson. 2003-11-04. Fault-Tolerant Logical Gate Networks for CSS Codes. https://doi.org/10.1103/physreva.72.052335

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