Exceptional Points and Optimized Encoding in Qubit Stabilizer Codes

Abstract

Continuous blind stabilizer measurements turn stabilizer codes into a Liouvillian spectral problem in which Hamiltonian terms compete with dissipative error channels. We show that this competition generically enables Liouvillian exceptional points, whose occurrence at weak error rates is constrained by the code distance. Exceptional points are detrimental in this regime of error correction as they maximize the decay rate of encoded coherences. We then optimize the encoding of the logical qubit using the eigenmodes of the Lindblad operator. This phase-optimized encoding cancels the linear short-time decay of logical qubit coherences. We apply this encoding to the [[5,1,3]] code and demonstrate that it outperforms naive encoding methods near the exceptional point, improves the fidelity of a logical $π$ rotation and remains effective in the presence of additional weak error channels.