  This work provides a nonasymptotic error analysis of quantum Krylov
algorithms based on real-time evolutions, subject to generic errors in the
outputs of the quantum circuits. We prove upper and lower bounds on the
resulting ground state energy estimates, and the error in the upper bound is
linear in the input error rates. This resolves a misalignment between known
numerics, which exhibit approximately linear error scaling, and prior
theoretical analysis, which only provably obtained square-root scaling. Our
main technique is to express generic errors in terms of an effective target
Hamiltonian studied in an effective Krylov space. These results provide a
theoretical framework for understanding the main features of quantum Krylov
errors.
