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Information storage capacity of discrete spin systems

Yoshida, Beni (2013) Information storage capacity of discrete spin systems. Annals of Physics, 338 . pp. 134-166. ISSN 0003-4916. doi:10.1016/j.aop.2013.07.009.

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Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations.

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Additional Information:© 2013 Elsevier Inc. Received 25 December 2012. Accepted 26 July 2013. Available online 9 August 2013. I thank Eddie Farhi and Peter Shor for support at MIT. I thank Sergey Bravyi, Patrick Hayden, Masahito Ueda and John Preskill for comments and discussion. This work is supported in part by DOE Grant No. DE-FG02-05ER41360 and by Nakajima Foundation.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-05ER41360
Nakajima FoundationUNSPECIFIED
Subject Keywords: Cellular automata; Fractal; Bekenstein bound; Spin glass; Error-correcting code; Information theory
Record Number:CaltechAUTHORS:20131205-082904067
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Official Citation:Beni Yoshida, Information storage capacity of discrete spin systems, Annals of Physics, Volume 338, November 2013, Pages 134-166, ISSN 0003-4916, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:42846
Deposited By: Ruth Sustaita
Deposited On:05 Dec 2013 16:43
Last Modified:10 Nov 2021 16:29

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