Universal Fault-Tolerant Computing with Bacon-Shor Codes

Опубликовано 11 декабря 2017, 3:32

We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford hierarchy become accessible as the code becomes more asymmetric. For instance, in an appropriate gauge, Bacon-Shor codes on an m-by-mk lattice have transversal k-qubit-controlled Z. We also describe how, for any stabilizer code, logical operator asymmetry is a necessary condition for transversal gates in high levels of the Clifford hierarchy. For Bacon-Shor CCZ, through a variety of tricks, including intermediate error-correction and non-Pauli recovery, we reduce the overhead required for fault-tolerant implementation. We calculate pseudothresholds for our universal gate set on the smallest 3-by-3 Bacon-Shor code and also compare our gates with magic-states within the framework of a proposed ion trap architecture.

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