  Dissipative collective effects are ubiquitous in quantum physics, and their
relevance ranges from the study of entanglement in biological systems to noise
mitigation in quantum computers. Here, we put forward the first fully quantum
simulation of dissipative collective phenomena on a real quantum computer,
based on the recently introduced multipartite collision model. First, we
theoretically study the accuracy of this algorithm on near-term quantum
computers with noisy gates, and we derive some rigorous error bounds that
depend on the timestep of the collision model and on the gate errors. These
bounds can be employed to estimate the necessary resources for the efficient
quantum simulation of the collective dynamics. Then, we implement the algorithm
on some IBM quantum computers to simulate superradiance and subradiance between
a pair of qubits. Our experimental results successfully display the emergence
of collective effects in the quantum simulation. In addition, we analyze the
noise properties of the gates that we employ in the algorithm by means of full
process tomography, with the aim of improving our understanding of the errors
in the near-term devices that are currently accessible to worldwide
researchers. We obtain the values of the average gate fidelity, unitarity,
incoherence and diamond error, and we establish a connection between them and
the accuracy of the experimentally simulated state. Moreover, we build a noise
model based on the results of the process tomography for two-qubit gates and
show that its performance is comparable with the noise model provided by IBM.
Finally, we observe that the scaling of the error as a function of the number
of gates is favorable, but at the same time reaching the threshold of the
diamond errors for quantum fault tolerant computation may still be orders of
magnitude away in the devices that we employ.
