Środowiskowe Seminarium z Informacji i Technologii Kwantowych

Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. In the talk, I will discuss a new metric for these codes, the disjointness, and use it to prove that transversal gates are necessarily in a finite level of the Clifford hierarchy. I will also derive similar bounds on constant-depth circuits for topological codes, regardless of geometric locality of the gates. Based on arXiv:1710.07256.