Julien Bréhier, "Understanding Stabilizer Codes Under Local Decoherence Through A General Statistical Mechanics Mapping"

Wednesday 5 Feb 2025, 12:00 → 13:00 Europe/Berlin

We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches— (i) Haah’s polynomial formalism [1] and (ii) the CSS-to-homology correspondence— we construct a mapping from the nth moment of the decohered ground state density matrix to a classical statistical mechanics model. We demonstrate that various measures of information capacity– (i) quantum relative entropy, (ii) coherent information, and (iii) entanglement negativity— map to thermodynamic quantities in the statistical mechanics model and can be used to characterize the decoding phase transition.