Statistical mechanics of quantum error correcting codes
- URL: http://arxiv.org/abs/2007.03822v4
- Date: Wed, 24 Mar 2021 16:35:31 GMT
- Title: Statistical mechanics of quantum error correcting codes
- Authors: Yaodong Li, Matthew P. A. Fisher
- Abstract summary: We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension.
We propose a statistical mechanical description of the QECC in terms of "entanglement domain walls"
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study stabilizer quantum error correcting codes (QECC) generated under
hybrid dynamics of local Clifford unitaries and local Pauli measurements in one
dimension. Building upon 1) a general formula relating the error-susceptibility
of a subregion to its entanglement properties, and 2) a previously established
mapping between entanglement entropies and domain wall free energies of an
underlying spin model, we propose a statistical mechanical description of the
QECC in terms of "entanglement domain walls". Free energies of such domain
walls generically feature a leading volume law term coming from its "surface
energy", and a sub-volume law correction coming from thermodynamic entropies of
its transverse fluctuations. These are most easily accounted for by
capillary-wave theory of liquid-gas interfaces, which we use as an illustrative
tool. We show that the information-theoretic decoupling criterion corresponds
to a geometric decoupling of domain walls, which further leads to the
identification of the "contiguous code distance" of the QECC as the crossover
length scale at which the energy and entropy of the domain wall are comparable.
The contiguous code distance thus diverges with the system size as the
subleading entropic term of the free energy, protecting a finite code rate
against local undetectable errors. We support these correspondences with
numerical evidence, where we find capillary-wave theory describes many
qualitative features of the QECC; we also discuss when and why it fails to do
so.
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