Counting collisions in random circuit sampling for benchmarking quantum computers

• URL: http://arxiv.org/abs/2312.04222v1
• Date: Thu, 7 Dec 2023 11:12:30 GMT
• Title: Counting collisions in random circuit sampling for benchmarking quantum computers
• Authors: Andrea Mari
• Abstract summary: We show that counting the number of collisions when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer. We show that this quantity, if properly normalized, can be used as a "collision anomaly" benchmark or as a "collision volume" test.
• Score: 0.7252027234425332
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $10^5$ 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.

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