  Analog quantum simulation is a promising path towards solving classically
intractable problems in many-body physics on near-term quantum devices.
However, the presence of noise limits the size of the system and the length of
time that can be simulated. In our work, we consider an error model in which
the actual Hamiltonian of the simulator differs from the target Hamiltonian we
want to simulate by small local perturbations, which are assumed to be random
and unbiased. We analyze the error accumulated in observables in this setting
and show that, due to stochastic error cancellation, with high probability the
error scales as the square root of the number of qubits instead of linearly. We
explore the concentration phenomenon of this error as well as its implications
for local observables in the thermodynamic limit.
