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
The code is written in Python and is organized in a self-contained Jupyter notebook. It can be visualized on GitHub (without execution) by just clicking on its file name.
Jupyter Notebook or JupyterLab should be installed to execute the notebook in your local machine.
The following Python packages are also required numpy, matplotlib and qiskit.