无序规范理论中的禁闭-Higgs跃迁与量子存储的准确度阈值
Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
摘要：
本文研究了三维空间的+/- J无规格元Z_2规范模型（RPGM），它是二维+/- J无规键伊辛模型（RBIM）的三维模拟.该模型是一个纯粹的Z_2规范理论，其中随机选择的格元（浓度为p）与"错误符号“耦合，因此磁通量在这些格元上是有利的。该模型的激励是一维的“磁通管”，终止于“磁单极子”。电约束可以由通量管的热波动、磁单极子的淬灭背景或两者的组合来驱动。像RBIM一样，RPGM在p-T平面（其中T是温度）中沿着“西森线”增强了对称性。利用拓扑纠错码，可以确定限制-Higgs相变时沿Nishimori线的错误符号斑的临界浓度p_c，并给出量子信息稳健存储的精度阈值：如果量子比特相位误差、量子比特比特翻转误差和局部校验算子的测量中的误差都以低于P_c的速率发生，那么编码的量子信息可以在大码块的限制下被完美地保护免受损害。在数值上，我们测量了p_{c0}，即沿T=0轴的临界浓度（p_c的下限），发现p_{c0} = 0.0293 +/-0.0002。我们还测量了T=0轴上二维RBIM中反铁磁键的临界浓度，发现p_{c0} = 0.1031 +/-0.0001。我们的值p_{c0}与早期数值研究中发现的值p_c=.1093 +/-.0002不一致，与RBIM相界垂直于（平行于T轴）西森线以下的猜想不一致。
英文摘要：
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.
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