{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/counting-collisions-in-random-circuit","title":"Counting collisions in random circuit sampling for benchmarking quantum computers","arxiv_id":"2312.04222","date":"2023-12-07","proceeding":null,"authors":["Andrea Mari"],"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.","url_abs":"https://arxiv.org/abs/2312.04222v2","url_pdf":"https://arxiv.org/pdf/2312.04222v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"counting-collisions-in-random-circuit","repo_url":"https://github.com/unitaryfund/research","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}