Entanglement Sharing Across a Damping-Dephasing Channel
Vikesh Siddhu, Dina Abdelhadi, et al.
ISIT 2024
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.
Vikesh Siddhu, Dina Abdelhadi, et al.
ISIT 2024
Rahul Sarkar, Theodore J. Yoder
J. Comput. Appl. Math.
Sergey Bravyi, Theodore J. Yoder, et al.
IEEE TC
Shilin Huang, Tomas Jochym-O'Connor, et al.
PRX Quantum