Bravyi, Sergey and Haah, Jeongwan (2011) Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120522-120847872
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A big open question in the quantum information theory concerns 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 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 self-correcting behavior. Assuming that dynamics of the memory system can be described by a Markovian master equation of Davies form, we prove that T_(mem) ≥ L^c^b for some constant c > 0, where L is the lattice size and B is the inverse temperature of the bath. However, this bound applies only if the lattice size does not exceed certain critical value L* ~ e^(b/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.
|Item Type:||Report or Paper (Working Paper)|
|Additional Information:||December 11, 2011. We would like to thank David DiVincenzo, John Preskill, and Barbara Terhal for helpful discussions. SB is supported in part by the DARPA QuEST program under contract number HR0011-09- C-0047, and IARPA QCS program under contract number D11PC20167. JH is supported in part by the Korea Foundation for Advanced Studies and by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center. Computational resources for this work were provided by IBM Blue Gene Watson supercomputer center.|
|Group:||Institute for Quantum Information and Matter, IQIM|
|Subject Keywords:||PACS numbers: 03.67.Pp, 03.67.Ac, 03.65.Ud|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Joy Painter|
|Deposited On:||22 May 2012 22:34|
|Last Modified:||26 Dec 2012 15:14|
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