  The Krylov subspace method is a standard approach to approximate quantum
evolution, allowing to treat systems with large Hilbert spaces. Although its
application is general, and suitable for many-body systems, estimation of the
committed error is involved. This makes it difficult to automate its use. In
this paper, we solve this problem by realizing that such error can be regarded
as a Loschmidt echo in a tight-binding Hamiltonian. We show that the different
time-regimes of the approximation can be understood using simple physical
ideas. More importantly, we obtain computationally cheap error bounds that
describe with high precision the actual error in the approximation.
