  We show that counting the number of collisions (re-sampled bitstrings) when
measuring a random quantum circuit provides a practical benchmark for the
quality of a quantum computer and a quantitative noise characterization method.
We analytically estimate the difference in the expected number of collisions
when sampling bitstrings from a pure random state and when sampling from the
classical uniform distribution. We show that this quantity, if properly
normalized, can be used as a "collision anomaly" benchmark or as a "collision
volume" test which is similar to the well-known quantum volume test, with
advantages (no classical computing cost) and disadvantages (high sampling
cost). We also propose to count the number of cross-collisions between two
independent quantum computers running the same random circuit in order to
obtain a cross-validation test of the two devices. Finally, we quantify the
sampling cost of quantum collision experiments. We find that the sampling cost
for running a collision volume test on state-of-the-art processors (e.g.~20
effective clean qubits) is quite small: less than $10^5$ shots. For large-scale
experiments in the quantum supremacy regime the required number of shots for
observing a quantum signal in the observed number of collisions is currently
infeasible ($>10^{12}$), but not completely out of reach for near-future
technology.
