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26 April 2024 |
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Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory | | Takuya Ohno
; Gaku Arakawa
; Ikuo Ichinose
; Tetsuo Matsui
; | | Date: |
19 Dec 2003 | | Journal: | Nucl.Phys. B697 (2004) 462 | | Subject: | Quantum Physics; Disordered Systems and Neural Networks | quant-ph cond-mat.dis-nn hep-lat | | 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 eta with the probability 1-p and -eta 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 -eta, 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 eta, it is known that there exists a second-order phase transition at a certain critical "temperature", T(equiv eta^{-1}) = T_c =1.31, which separates an ordered(Higgs) phase at TT_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. | | Source: | arXiv, quant-ph/0401101 | | Services: | Forum | Review | PDF | Favorites | |
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