Analysis of Error Propagation in Quantum Computers

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.