We sample 1,000 random initial states and apply the QMPS circuit framework in the presence of depolarizing noise with error parameter λ 2/3 for all two-and three-qubit gates. Note that the noise parameter for all single-qubit gates is always fixed to λ 1 = 10 −4 . We set the number of measurement shots to 4,096 and plot the percentage of runs in which the target state is successfully reached against the noise strength. The success rate under exact, noise-free computation (without sampling) is shown as a black dashed line. The success probability when acting completely random is always zero. We provide both, the results for the full χ = 4 QMPS circuit (purple solid line) and the truncated χ = 2 QMPS (orange dash-dotted line). Insets: the corresponding average number of protocols steps \bar{T} as a function of the noise strength λ . The standard deviation is indicated by the shaded areas.