Resource requirements for fault-tolerant quantum simulation: The ground state of the transverse Ising model

We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground-state energy of a one-dimensional quantum transverse Ising model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the quantum logic array architecture. Our results show that a significant amount of error correction is required to implement the TIM problem due to the exponential scaling of the computational time with the desired precision of the energy. Comparison of our results to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.