Citation: Gidney, Craig, Noah Shutty, and Cody Jones. "Magic state cultivation: growing T states as cheap as CNOT gates." arXiv preprint arXiv:2409.17595 (2024).
Web: https://arxiv.org/abs/2409.17595
Tags: Computer-scientific, Error-correcting-codes, Toric-code, Color-code
In this paper, the authors improve on previous work on T-state preparation. They introduce a method for quickly and efficiently preparing a T-state which they call "magic state cultivation". Their circuit is amazingly efficient. The spacetime volume comparison at the beginning of the paper is striking.
The idea is as follows. First, the magic state is injected onto a distance 3 color code, and grown slowly to a distance 5 surface code. These steps involve postselection exponential in the distance of the code, and thus it is important that they are being performed on small distances. The code is then suddenly grown into a large code, in what the authors call an "escape procedure".
This escape procedure works by realizing the color code as a folded corner of a large surface code. The color code is included into the large surface code, a large number of rounds of error correction are performed to spread the entanglement from the boundary of the corner to the whole surface code path, and then the corner is unfolded.
This elegant idea underscores the importance of the fact that the surface code and color code are topological, and are not just random LDPC codes. There are a lot of insights and algorithms that can be made by exploiting the topological features of the code (i.e. realizing codes as doubled copies of other codes).