IQI Weekly Seminar

Abstract: We present a fault-tolerant universal gate set, consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Circuits for logical CCZ on these codes are intriguing in that their depth decreases as the code becomes more asymmetric. For instance, Bacon-Shor codes on an m-by-m² lattice have depth-1 (i.e. transversal) CCZ. Moreover, Bacon-Shor codes on an m-by-m^k lattice have transversal k-qubit-controlled-Z. We discuss the consequences in the context of Eastin-Knill and Bravyi-Koenig type no-go theorems. Finally, through a variety of fault-tolerant circuit design tricks, including non-Pauli recovery, we reduce the size of our logical gates and calculate pseudothresholds under circuit depolarizing noise for CCZ on the 3x3 Bacon-Shor code.