Adaptive Shor Scheme for fault tolerance on repetition code

Quantum error correction schemes are essential for reaching fault-tolerant quantum computing. However, fault-tolerant schemes require significant overhead that by itself introduces additional errors. The Shor scheme tackles this problem by repeating syndromes, which can reach (t+1)^2 measurement rounds for a stabilizer code that can correct up to t errors. A recent proposal of adaptive syndrome measurement for Shor schemes [1] suggests a protocol that requires no more than (t+3)^2/4-1 measurement rounds, significantly less than the regular Shor scheme. The adaptive measurement determines the syndrome for error correction based on the difference between consecutive rounds while keeping fault tolerance criteria. Thus, the adaptive scheme reaches its superiority by including classical calculation and decision-making during quantum calculation. In this work, we present the first simulation results of the adaptive Shor scheme and verify that it is indeed fault tolerant. We exemplify these results with a repetition code and indicate the requirements for implementing such fault-tolerant schemes in a physical system.

[1] Theerapat Tansuwannont, Kenneth R. Brown, arXiv:2208.05601 (2022)