To ensure that our quantum bits remain protected, we have to perform error-detecting and correcting measurements very frequently. However, these error-correcting circuits themselves are also prone to errors, which can cause the efficiency of the algorithm to go down eventually. That’s not what we want!
Designing circuits which perform fault-tolerant quantum error correction is a cutting-edge field of research. In this video, we will discuss one of the most promising candidate-algorithms that does just this: surface codes. Professor Barbara Terhal concludes with the introduction of the fault-tolerant threshold, the physical error rate which must be reached for quantum error correction to be effective.
Stabilizer codes perform parity checks in order to detect errors. We have seen a general idea of how to detect X and Z errors. Based on this idea, how would you detect a Y-type error?
A bit philosophical, but still interesting is this paper by prof. Barbara Terhal herself, addressing the question of whether there is a fundamental reason why quantum information is more fragile than classical information.
This paper was written by A. Fowler et al. as an introduction to surface codes.
Here is a paper by M.H. Devoret and R. Schoelkopf, describing the different stages to reach before achieving fault-tolerant quantum computation.