{"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/the-t-complexity-costs-of-error-correction","title":"The T-Complexity Costs of Error Correction for Control Flow in Quantum Computation","arxiv_id":"2311.12772","date":"2023-11-21","proceeding":null,"authors":["Charles Yuan","Michael Carbin"],"abstract":"Numerous quantum algorithms require the use of quantum error correction to overcome the intrinsic unreliability of physical qubits. However, error correction imposes a unique performance bottleneck, known as T-complexity, that can make an implementation of an algorithm as a quantum program run more slowly than on idealized hardware. In this work, we identify that programming abstractions for control flow, such as the quantum if-statement, can introduce polynomial increases in the T-complexity of a program. If not mitigated, this slowdown can diminish the computational advantage of a quantum algorithm. To enable reasoning about the costs of control flow, we present a cost model that a developer can use to accurately analyze the T-complexity of a program and pinpoint the sources of slowdown. We also present a set of program-level optimizations, that a developer can use to rewrite a program to reduce its T-complexity, predict the T-complexity of the optimized program using the cost model, and then compile it to an efficient circuit via a straightforward strategy. We implement the program-level optimizations in Spire, an extension of the Tower quantum compiler. Using a set of 11 benchmark programs that use control flow, we show that the cost model is accurate, and that Spire's optimizations recover programs that are asymptotically efficient, meaning their runtime T-complexity under error correction is equal to their time complexity on idealized hardware. Our results show that optimizing a program before it is compiled to a circuit can yield better results than compiling the program to an inefficient circuit and then invoking a quantum circuit optimizer found in prior work. For our benchmarks, only 2 of 8 tested circuit optimizers recover circuits with asymptotically efficient T-complexity. Compared to these 2 optimizers, Spire uses 54x to 2400x less compile time.","url_abs":"https://arxiv.org/abs/2311.12772v2","url_pdf":"https://arxiv.org/pdf/2311.12772v2.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":"the-t-complexity-costs-of-error-correction","repo_url":"https://github.com/psg-mit/spire-artifact","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}