dorsal/arxiv
View SchemaConfinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
| Authors | Chenyang Wang, Jim Harrington, John Preskill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207088 |
| URL | https://arxiv.org/abs/quant-ph/0207088 |
| DOI | 10.1016/S0003-4916(02)00019-2 |
| Journal | Annals of Physics 303, 31-58 (2003) |
Abstract
We study the +/- J random-plaquette Z_2 gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional +/- J random-bond Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly chosen plaquettes (occuring with concentration p) have couplings with the ``wrong sign'' so that magnetic flux is energetically favored on these plaquettes. Excitations of the model are one-dimensional ``flux tubes'' that terminate at ``magnetic monopoles.'' 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 wrong-sign plaquettes at the confinement-Higgs phase transition along the Nishimori line can be identified with the accuracy threshold for robust storage of quantum information using topological error-correcting codes: if qubit phase errors, qubit bit-flip 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. Numerically, 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 two-dimensional 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.
{
"annotation_id": "5096b053-a6b5-4ac5-b49f-a99db5ae5716",
"date_created": "2026-03-02T18:01:52.682000Z",
"date_modified": "2026-03-02T18:01:52.682000Z",
"file_hash": "37a02f791242371cf3f1f3ca2e31d8a54e672fb269d561401f32240327dd5daa",
"private": false,
"record": {
"abstract": "We study the +/- J random-plaquette Z_2 gauge model (RPGM) in three spatial\ndimensions, a three-dimensional analog of the two-dimensional +/- J random-bond\nIsing model (RBIM). The model is a pure Z_2 gauge theory in which randomly\nchosen plaquettes (occuring with concentration p) have couplings with the\n``wrong sign\u0027\u0027 so that magnetic flux is energetically favored on these\nplaquettes. Excitations of the model are one-dimensional ``flux tubes\u0027\u0027 that\nterminate at ``magnetic monopoles.\u0027\u0027 Electric confinement can be driven by\nthermal fluctuations of the flux tubes, by the quenched background of magnetic\nmonopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced\nsymmetry along a ``Nishimori line\u0027\u0027 in the p-T plane (where T is the\ntemperature). The critical concentration p_c of wrong-sign plaquettes at the\nconfinement-Higgs phase transition along the Nishimori line can be identified\nwith the accuracy threshold for robust storage of quantum information using\ntopological error-correcting codes: if qubit phase errors, qubit bit-flip\nerrors, and errors in the measurement of local check operators all occur at\nrates below p_c, then encoded quantum information can be protected perfectly\nfrom damage in the limit of a large code block. Numerically, we measure p_{c0},\nthe critical concentration along the T=0 axis (a lower bound on p_c), finding\np_{c0}=.0293 +/- .0002. We also measure the critical concentration of\nantiferromagnetic bonds in the two-dimensional RBIM on the T=0 axis, finding\np_{c0}=.1031 +/-.0001. Our value of p_{c0} is incompatible with the value of\np_c=.1093 +/-.0002 found in earlier numerical studies of the RBIM, in\ndisagreement with the conjecture that the phase boundary of the RBIM is\nvertical (parallel to the T axis) below the Nishimori line.",
"arxiv_id": "quant-ph/0207088",
"authors": [
"Chenyang Wang",
"Jim Harrington",
"John Preskill"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-lat",
"hep-th"
],
"doi": "10.1016/S0003-4916(02)00019-2",
"journal_ref": "Annals of Physics 303, 31-58 (2003)",
"title": "Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory",
"url": "https://arxiv.org/abs/quant-ph/0207088"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5b92e580-720e-4d8f-8d95-855004b3bd5a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}