Fig. 3. Precision and run-time attained by noisy quantum simulators.

An erroneous quantum simulator can obtain the thermodynamic limit of the perturbed model to a precision ${\epsilon }^{\prime }$ in time $\text{poly}\left(1/{\epsilon }^{\prime }\right)$—this thermodynamic limit, however, can have an error f(δ) from the target thermodynamic limit in the presence of hardware error δ.