  We estimate the resource requirements for the quantum simulation of the
ground state energy of the one dimensional quantum transverse Ising model
(TIM), based on the surface code implementation of a fault tolerant quantum
computer. The surface code approach has one of the highest known tolerable
error rates (1%) which makes it currently one of the most practical quantum
computing schemes. Compared to results of the same model using the concatenated
Steane code, the current results indicate that the simulation time is
comparable but the number of physical qubits for the surface code is 2-3 orders
of magnitude larger than that of the concatenation code. Considering that the
error threshold requirements of the surface code is four orders of magnitude
higher than the concatenation code, building a quantum computer with a surface
code implementation appears more promising given current physical hardware
capabilities.
