  One of the main important features of the noisy intermediate-scale quantum
(NISQ) era is the correct evaluation and consideration of errors. In this
paper, we analyze the main sources of errors in current (IBM) quantum computers
and we present a useful tool (TED-qc) designed to facilitate the total error
probability expected for any quantum circuit. We propose this total error
probability as the best way to estimate a lower bound for the fidelity in the
NISQ era, avoiding the necessity of comparing the quantum calculations with any
classical one. In order to contrast the robustness of our tool we compute the
total error probability that may occur in three different quantum models: 1)
the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover's
algorithm. For each model, the main quantities of interest are computed and
benchmarked against the reference simulator's results as a function of the
error probability for a representative and statistically significant sample
size. The analysis is satisfactory in more than the $99\%$ of the cases. In
addition, we study how error mitigation techniques are able to eliminate the
noise induced during the measurement. These results have been calculated for
the IBM quantum computers, but both the tool and the analysis can be easily
extended to any other quantum computer.
