Tradeoffs for Reliable Quantum Information Storage in 2D Systems

Sergey Bravyi, David Poulin, and Barbara Terhal
Phys. Rev. Lett. 104, 050503 – Published 5 February 2010

Abstract

We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits k, the distance of the code d, and the number of particles n. It is shown that kd2=O(n) where the coefficient in O(n) depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. The analogous tradeoff for the classical information storage is kd=O(n).

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  • Received 16 October 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.050503

©2010 American Physical Society

Authors & Affiliations

Sergey Bravyi1, David Poulin2, and Barbara Terhal1

  • 1IBM Watson Research Center, Yorktown Heights New York 10598, USA
  • 2Département de Physique, Université de Sherbrooke, Québec, Canada

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Vol. 104, Iss. 5 — 5 February 2010

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