Transversal operations are an elegant way to realize fault-tolerant quantum gates. Fault-tolerant quantum computation has been studied in detail over a finite field. In this paper, we derive transversal Clifford operations for CSS codes over nice rings, including Fourier transforms, SUM gates, and phase gates. Transversal operations alone cannot provide a computationally universal set of gates. As an example of a non-transversal gate, we derive fault-tolerant implementations of doubly-controlled Z gates for triorthogonal stabilizer codes over nice rings.
['Sangjun Lee', 'Andreas Klappenecker']
Generalized fault-tolerant quantum computation over nice rings