Non-Abelian Quantum Codes

Like their classical counterparts, quantum codes are designed to pro- tect quantum in- formation from noise. From the perspective of informa- tion theory one considers the op- erations required to restore the encoded information given a syndrome which diagnoses the noise. From a more physics perspective, one considers systems whose energetically protected groundspace encodes the information. In this work we show that standard error correction procedures can be applied to systems where the noise ap- pears as non- abelian Fibonacci anyons. In the case of a Hamiltonian with non-commuting terms, we build a theory describing the spectrum of these models, with particular focus on the 3D gauge color code model. Numerics support the conjecture that this model is gapped, which one would expect for a self-correcting quantum memory