CaltechAUTHORS
  A Caltech Library Service

Local non–Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

Kim, Isaac H. (2011) Local non–Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice. Physical Review A, 83 (5). Art. No. 052308. ISSN 1050-2947. https://resolver.caltech.edu/CaltechAUTHORS:20110602-102059917

[img]
Preview
PDF - Published Version
See Usage Policy.

496Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20110602-102059917

Abstract

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevA.83.052308DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevA.83.052308PublisherUNSPECIFIED
http://pra.aps.org/abstract/PRA/v83/i5/e052308PublisherUNSPECIFIED
Additional Information:© 2011 American Physical Society. Received 3 January 2011; published 12 May 2011. The author thanks Jeongwan Haah for his help in finding the logical operator of the system and John Preskill for many insightful discussions. This research was supported in part by NSF under Grant No. PHY-0803371 and ARO under Grant No. W911NF-09-1-0442.
Funders:
Funding AgencyGrant Number
NSFPHY-0803371
Army Research Office (ARO)W911NF-09-1-0442
Issue or Number:5
Classification Code:PACS: 03.67.Pp, 03.67.Lx, 11.15.−q, 71.10.−w
Record Number:CaltechAUTHORS:20110602-102059917
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110602-102059917
Official Citation:Local non–Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice Isaac H. Kim Published 12 May 2011 (6 pages) 052308
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23870
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:02 Jun 2011 17:53
Last Modified:03 Oct 2019 02:50

Repository Staff Only: item control page