Enhanced Decoding Against Coherent Errors in the Surface Code by Excited-State Encoding

We propose that encoding quantum information in excited states of the surface code can enhance the threshold against coherent errors. In particular, we consider the surface code under coherent errors that create electric anyon excitations. We show that a random background of magnetic fluxes reduce the ability of coherent errors in creating far-separated excitations, thus improving the decoding fidelity. Specifically, in the statistical mechanics model that governs the maximum-likelihood decoder, the improved fidelity stems from the interactions induced by the random flux background that favor the decodable phase. We corroborate our arguments with numerical simulations which demonstrate an improved decoding fidelity within the decodable phase, as well as an increased threshold for coherent errors.