Analytic and numerical demonstration of quantum selfcorrection in the 3D Cubic Code
Abstract
A big open question in the quantum information theory concerns feasibility of a selfcorrecting 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 put in contact with a cold enough thermal bath. In this paper we derive a rigorous lower bound on the memory time $T_{mem}$ of the 3D Cubic Code model which was recently conjectured to have a selfcorrecting behavior. Assuming that dynamics of the memory system can be described by a Markovian master equation of Davies form, we prove that $T_{mem}\ge L^{c\beta}$ for some constant $c>0$, where $L$ is the lattice size and $\beta$ is the inverse temperature of the bath. However, this bound applies only if the lattice size does not exceed certain critical value $L^*\sim e^{\beta/3}$. We also report a numerical Monte Carlo simulation of the studied memory indicating that our analytic bounds on $T_{mem}$ are tight up to constant coefficients. In order to model the readout step we introduce a new decoding algorithm which might be of independent interest. Our decoder can be implemented efficiently for any topological stabilizer code and has a constant error threshold under random uncorrelated errors.
 Publication:

arXiv eprints
 Pub Date:
 December 2011
 arXiv:
 arXiv:1112.3252
 Bibcode:
 2011arXiv1112.3252B
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 40 pages, 6 figures