Wang, Chenyang and Harrington, Jim and Preskill, John (2003) ConfinementHiggs transition in a disordered gauge theory and the accuracy threshold for quantum memory. Annals of Physics, 303 (1). pp. 3158. ISSN 00034916. http://resolver.caltech.edu/CaltechAUTHORS:20111017135406894

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Abstract
We study the ±J randomplaquette Z_2 gauge model (RPGM) in three spatial dimensions, a threedimensional analog of the twodimensional ±J randombond Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly chosen plaquettes (occurring with concentration p) have couplings with the “wrong sign” so that magnetic flux is energetically favored on these plaquettes. Excitations of the model are onedimensional “flux tubes” that terminate at “magnetic monopoles” located inside lattice cubes that contain an odd number of wrongsign plaquettes. Electric confinement can be driven by thermal fluctuations of the flux tubes, by the quenched background of magnetic monopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced symmetry along a “Nishimori line” in the p–T plane (where T is the temperature). The critical concentration p_c of wrongsign plaquettes at the confinementHiggs phase transition along the Nishimori line can be identified with the accuracy threshold for robust storage of quantum information using topological errorcorrecting codes: if qubit phase errors, qubit bitflip errors, and errors in the measurement of local check operators all occur at rates below p_c, then encoded quantum information can be protected perfectly from damage in the limit of a large code block. Through MonteCarlo simulations, we measure p_(c0), the critical concentration along the T=0 axis (a lower bound on p_c), finding p_(c0)=.0293±.0002. We also measure the critical concentration of antiferromagnetic bonds in the twodimensional RBIM on the T=0 axis, finding p_(c0)=.1031±.0001. Our value of p_(c0) is incompatible with the value of p_c=.1093±.0002 found in earlier numerical studies of the RBIM, in disagreement with the conjecture that the phase boundary of the RBIM is vertical (parallel to the T axis) below the Nishimori line. The model can be generalized to a rankr antisymmetric tensor field in d dimensions, in the presence of quenched disorder.
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Additional Information:  © 2002 Elsevier Science. Received 18 July 2002; Available online 8 January 2003. We gratefully acknowledge helpful discussions and correspondence with John Chalker, Tom Gottschalk, Alexei Kitaev, Hidetsugu Kitatani, Andreas Ludwig, Paul McFadden, Hidetoshi Nishimori, and Frank Porter. We particularly thank Andrew Landahl, Nathan Wozny, and Zhaosheng Bao for valuable advice and assistance. This work has been supported in part by the Department of Energy under Grant No. DEFG0392ER40701, by the National Science Foundation under Grant No. EIA0086038, by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD190010374, and by Caltech’s Summer Undergraduate Research Fellowship (SURF) program.  
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Record Number:  CaltechAUTHORS:20111017135406894  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20111017135406894  
Official Citation:  Chenyang Wang, Jim Harrington, John Preskill, ConfinementHiggs transition in a disordered gauge theory and the accuracy threshold for quantum memory, Annals of Physics, Volume 303, Issue 1, January 2003, Pages 3158, ISSN 00034916, 10.1016/S00034916(02)000192.  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  27258  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  18 Oct 2011 17:56  
Last Modified:  26 Dec 2012 14:17 
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