{"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/simulation-of-quantum-circuits-by-low-rank","title":"Simulation of quantum circuits by low-rank stabilizer decompositions","arxiv_id":"1808.00128","date":"2018-08-01","proceeding":null,"authors":["Sergey Bravyi","Dan Browne","Padraic Calpin","Earl Campbell","David Gosset","Mark Howard"],"abstract":"Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a pure state $\\psi$ is defined to be the smallest integer $\\chi$ such that $\\psi$ is a superposition of $\\chi$ stabilizer states. Here we develop a comprehensive mathematical theory of the stabilizer rank and the related approximate stabilizer rank. We also present a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art. A new feature is the capability to simulate circuits composed of Clifford gates and arbitrary diagonal gates, extending the reach of a previous algorithm specialized to the Clifford+T gate set. We implemented the new simulation methods and used them to simulate quantum algorithms with 40-50 qubits and over 60 non-Clifford gates, without resorting to high-performance computers. We report a simulation of the Quantum Approximate Optimization Algorithm in which we process superpositions of $\\chi\\sim10^6$ stabilizer states and sample from the full n-bit output distribution, improving on previous simulations which used $\\sim 10^3$ stabilizer states and sampled only from single-qubit marginals. We also simulated instances of the Hidden Shift algorithm with circuits including up to 64 T gates or 16 CCZ gates; these simulations showcase the performance gains available by optimizing the decomposition of a circuit's non-Clifford components.","url_abs":"https://arxiv.org/abs/1808.00128v2","url_pdf":"https://arxiv.org/pdf/1808.00128v2.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":"simulation-of-quantum-circuits-by-low-rank","repo_url":"https://github.com/or1426/Clifford-T-estimator","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"simulation-of-quantum-circuits-by-low-rank","repo_url":"https://github.com/or1426/pscs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}