Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published November 12, 2013 | Published + Submitted + Supplemental Material
Journal Article Open

Quantum Self-Correction in the 3D Cubic Code Model

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 L^(cβ), where L is the lattice size, β is the inverse temperature of the bath, and c>0 is a constant coefficient. However, this bound applies only if the lattice size L does not exceed a critical value which grows exponentially with β. 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.

Additional Information

© 2013 American Physical Society. Received 13 June 2013; published 12 November 2013. We would like to thank David DiVincenzo, John Preskill, and Barbara Terhal for helpful discussions. S. B. is supported in part by the DARPA QuEST program under Contract No. HR0011-09-C-0047 and IARPA QCS program under Contract No. D11PC20167. J.H. is supported in part by the Korea Foundation for Advanced Studies and by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation. Computational resources for this work were provided by IBM Blue Gene Watson supercomputer center.

Attached Files

Published - PhysRevLett.111.200501.pdf

Submitted - Bravyi.pdf

Supplemental Material - README.TXT

Supplemental Material - memorytimePRLSM.pdf

Files

Bravyi.pdf
Files (1.2 MB)
Name Size Download all
md5:c4fc8b442eea434279406328a261e3a5
671.9 kB Preview Download
md5:0893b84779647c8f594ce178a2db9fb7
318.9 kB Preview Download
md5:eb1dbbb3b40fcec65de7509985321717
578 Bytes Preview Download
md5:e047c07d7d480c82f87b2d6af7837c0e
252.2 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 17, 2023