Tomas Jochym-O'Connor, Theodore J. Yoder
PRResearch
Stabilizer codes are among the most successful quantum error-correcting codes, yet they have important limitations on their ability to fault tolerantly compute. Here, we introduce a new quantity, the disjointness of the stabilizer code, which, roughly speaking, is the number of mostly nonoverlapping representations of any given nontrivial logical Pauli operator. The notion of disjointness proves useful in limiting transversal gates on any error-detecting stabilizer code to a finite level of the Clifford hierarchy. For code families, we can similarly restrict logical operators implemented by constant-depth circuits. For instance, we show that it is impossible, with a constant-depth but possibly geometrically nonlocal circuit, to implement a logical non-Clifford gate on the standard two-dimensional surface code.
Tomas Jochym-O'Connor, Theodore J. Yoder
PRResearch
Vikesh Siddhu, Dina Abdelhadi, et al.
ISIT 2024
Dax Enshan Koh, Murphy Yuezhen Niu, et al.
Journal of Physics A
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PRX Quantum