Counting collisions in random circuit sampling for benchmarking quantum computers
arXiv:2312.04222 · doi:10.1063/5.0219266
Abstract
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 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 (), but not completely out of reach for near-future technology.
Published version. Code available at: https://github.com/unitaryfund/research/
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