  A fundamental challenge in digital quantum simulation (DQS) is the control of
inherent errors. These appear when discretizing the time evolution generated by
the Hamiltonian of a quantum many-body system as a sequence of quantum gates,
called Trotterization. Here, we show that quantum localization-by constraining
the time evolution through quantum interference-strongly bounds these errors
for local observables. Consequently, for generic quantum many-body
Hamiltonians, Trotter errors can become independent of system size and total
simulation time. For local observables, DQS is thus intrinsically much more
robust than what one might expect from known error bounds on the global
many-body wave function. This robustness is characterized by a sharp threshold
as a function of the Trotter step size. The threshold separates a regular
region with controllable Trotter errors, where the system exhibits localization
in the space of eigenstates of the time-evolution operator, from a quantum
chaotic regime where the trajectory is quickly scrambled throughout the entire
Hilbert space. Our findings show that DQS with comparatively large Trotter
steps can retain controlled Trotter errors for local observables. It is thus
possible to reduce the number of quantum gate operations required to represent
the desired time evolution faithfully, thereby mitigating the effects of
imperfect individual gate operations
