  Most quantum gate errors can be characterized by two error models, namely the
probabilistic error model and the Kraus error model. We proved that for a
quantum circuit with either of those two models or a mix of both, the
propagation error in terms of Frobenius norm is upper bounded by $2(1 - (1 -
r)^m)$, where $0 \le r < 1$ is a constant independent of the qubit number and
circuit depth, and $m$ is the number of gates in the circuit. Numerical
experiments of synthetic quantum circuits and quantum Fourier transform
circuits are performed on the simulator of the IBM Vigo quantum computer to
verify our analytical results, which show that our upper bound is tight.
