Beni Yoshida: Classifying Fault-tolerant Logical Gates by Group Cohomology (or SPT Phases)
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0Beni Yoshida (Caltech)
Classifying Fault-tolerant Logical Gates by Group Cohomology (or SPT Phases)
QuICS Workshop on the Frontiers of Quantum Information and Computer Science (September 29, 2015)
We present a systematic framework of finding/classifying fault-tolerantly implementable logical gates in topological quantum codes by using the duality map between topological gauge theories and bosonic SPT phases. As a concrete application of the framework, we demonstrate that the transversal R_d in the d-dimensional color code, belonging to the d^th level of the Clifford hierarchy, can be constructed from a d-cocycle function.
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