Fig. 4: Temperature-dependent bounds for magic distillation.
From: Constraints on magic state protocols from the statistical mechanics of Wigner negativity
Shown are two contour plots of the bound on R(ϵ, β) for the case \(H\,=\,H^{\prime} \,=\,{\sum }_{k\,\in\, {{\mathbb{Z}}}_{3}}k\left|k\right\rangle \left\langle k\right|\) and \(\epsilon ^{\prime} \,=\,0\), where β is the inverse temperature and ϵ is the depolarizing error of the input magic state. The top figure (a) does not use any changes of Clifford basis, and the form of the bound depends on both the error parameter and temperature. The curved dashed line is ϵ⋆(β) and given by Eq. 86 in Supplementary Note 4 and \({\beta }_{\star }\,=\,{(k{T}_{\star })}^{-1}\) is given by \({E}_{2}\,-\,\phi \,=\,k{T}_{\star }\ln 2\). In the bottom figure (b) Clifford processing is used resulting in a smoother bound. In both figures the β = 0 line correspond to the unital bounds.
