dorsal/arxiv
View SchemaPhase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
| Authors | Takuya Ohno, Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401101 |
| URL | https://arxiv.org/abs/quant-ph/0401101 |
| DOI | 10.1016/j.nuclphysb.2004.07.003 |
| Journal | Nucl.Phys. B697 (2004) 462 |
Abstract
We study the phase structure of the random-plaquette Z_2 lattice gauge model in three dimensions. In this model, the "gauge coupling" for each plaquette is a quenched random variable that takes the value \beta with the probability 1-p and -\beta with the probability p. This model is relevant for the recently proposed quantum memory of toric code. The parameter p is the concentration of the plaquettes with "wrong-sign" couplings -\beta, and interpreted as the error probability per qubit in quantum code. In the gauge system with p=0, i.e., with the uniform gauge couplings \beta, it is known that there exists a second-order phase transition at a certain critical "temperature", T(\equiv \beta^{-1}) = T_c =1.31, which separates an ordered(Higgs) phase at T<T_c and a disordered(confinement) phase at T>T_c. As p increases, the critical temperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects with the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The value p_c is just the accuracy threshold for a fault-tolerant quantum memory and associated quantum computations. By the Monte-Carlo simulations, we calculate the specific heat and the expectation values of the Wilson loop to obtain the phase-transition line T_c(p) numerically. The accuracy threshold is estimated as p_c \simeq 0.033.
{
"annotation_id": "57b21efc-a9af-420b-95f4-786eee1a2203",
"date_created": "2026-03-02T18:02:05.746000Z",
"date_modified": "2026-03-02T18:02:05.746000Z",
"file_hash": "59587a2cdd94665abce06ab69a01432fbbe9d41831319b0a5f80dac8de78f59a",
"private": false,
"record": {
"abstract": "We study the phase structure of the random-plaquette Z_2 lattice gauge model\nin three dimensions. In this model, the \"gauge coupling\" for each plaquette is\na quenched random variable that takes the value \\beta with the probability 1-p\nand -\\beta with the probability p. This model is relevant for the recently\nproposed quantum memory of toric code. The parameter p is the concentration of\nthe plaquettes with \"wrong-sign\" couplings -\\beta, and interpreted as the error\nprobability per qubit in quantum code. In the gauge system with p=0, i.e., with\nthe uniform gauge couplings \\beta, it is known that there exists a second-order\nphase transition at a certain critical \"temperature\", T(\\equiv \\beta^{-1}) =\nT_c =1.31, which separates an ordered(Higgs) phase at T\u003cT_c and a\ndisordered(confinement) phase at T\u003eT_c. As p increases, the critical\ntemperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects\nwith the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The\nvalue p_c is just the accuracy threshold for a fault-tolerant quantum memory\nand associated quantum computations. By the Monte-Carlo simulations, we\ncalculate the specific heat and the expectation values of the Wilson loop to\nobtain the phase-transition line T_c(p) numerically. The accuracy threshold is\nestimated as p_c \\simeq 0.033.",
"arxiv_id": "quant-ph/0401101",
"authors": [
"Takuya Ohno",
"Gaku Arakawa",
"Ikuo Ichinose",
"Tetsuo Matsui"
],
"categories": [
"quant-ph",
"cond-mat.dis-nn",
"hep-lat"
],
"doi": "10.1016/j.nuclphysb.2004.07.003",
"journal_ref": "Nucl.Phys. B697 (2004) 462",
"title": "Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory",
"url": "https://arxiv.org/abs/quant-ph/0401101"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "62ca4bde-b8b3-42e7-beaf-7c72fa184b5c",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}