Abstract
A big open question in the quantum information theory concerns the feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction, if the memory is in contact with a cold enough thermal bath. Here we report analytic and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code. We prove that its memory time is at least , where is the lattice size, is the inverse temperature of the bath, and is a constant coefficient. However, this bound applies only if the lattice size does not exceed a critical value which grows exponentially with . In that sense, the model can be called a partially self-correcting memory. We also report a Monte Carlo simulation indicating that our analytic bounds on the memory time are tight up to constant coefficients. To model the readout step we introduce a new decoding algorithm, which can be implemented efficiently for any topological stabilizer code. A longer version of this work can be found in Bravyi and Haah, arXiv:1112.3252.
- Received 13 June 2013
DOI:https://doi.org/10.1103/PhysRevLett.111.200501
© 2013 American Physical Society