A note on threshold theorem of fault-tolerant quantum computation

TL;DR

This paper examines the optimal timing for error correction in fault-tolerant quantum computing, revealing that the best correction interval depends on the code's concatenation level, challenging the common practice of correcting after each gate.

Contribution

It demonstrates that the optimal error-correction period varies with the concatenation level, providing insights for improving quantum error correction strategies.

Findings

Optimal correction period depends on concatenation level k

Correcting after each gate may not be optimal

Error correction timing should consider code level

Abstract

Error-correction process has to be carried out periodically to prevent accumulation of errors in fault-tolerant quantum computation. It is believed that the best choice to get maximum threshold value is carrying out an error-correction process after each quantum gate operation. Result of this note shows that the optimal error-correction period depends on the value of k which is the level number of concatenated quantum error-correction code.