We present a novel method for simulating the noisy behaviour of quantum
computers, which allows to efficiently incorporate environmental effects in the
driven evolution implementing the gates acting on the qubits. We show how to
modify the noiseless gate executed by the computer to include any Markovian
noise, hence resulting in what we will call a noisy gate. We compare our method
with the IBM Qiskit simulator, and show that it follows more closely both the
analytical solution of the Lindblad equation as well as the behaviour of a real
quantum computer, where we ran algorithms involving up to 18 qubits; as such,
our protocol offers a more accurate simulator for NISQ devices. The method is
flexible enough to potentially describe any noise, including non-Markovian
ones. The noise simulator based on this work is available as a python package
at this link: https://pypi.org/project/quantum-gates