Randomized Benchmarking with Synthetic Quantum Circuits

[2412.18578] Randomized Benchmarking with Synthetic Quantum Circuits Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2412.18578 (quant-ph) [Submitted on 24 Dec 2024 ( v1 ), last revised 30 Jul 2026 (this version, v3)] Title: Randomized Benchmarking with Synthetic Quantum Circuits Authors: Yale Fan , Riley Murray , Thaddeus D. Ladd , Kevin Young , Robin Blume-Kohout View a PDF of the paper titled Randomized Benchmarking with Synthetic Quantum Circuits, by Yale Fan and 4 other authors View PDF HTML (experimental) Abstract: Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the structure of the group representation generated by the set of benchmarked operations. However, existing techniques become prohibitively inefficient for representations that are highly reducible yet decompose into irreducible subspaces of high dimension. These situations prevail when benchmarking high-dimensional systems such as qudits or bosonic modes, where experimental control is limited to implementing a small subset of all possible unitary operations. We introduce a broad framework for enhancing the sample efficiency of RB that is sufficiently powerful to extend the practical reach of RB beyond the multiqubit setting. Our strategy, which applies to any benchmarking group, uses "synthetic" quantum circuits with classical post-processing of both input and output data to leverage the full structure of reducible superoperator representations. To demonstrate the efficacy of our approach, we develop a detailed theory of RB for systems with rotational symmetry. Such systems carry a natural action of the group $\text{SU}(2)$, and they form the basis for several novel quantum error-correcting codes. We show that, for experimentally accessible high-spin systems, synthetic RB protocols can reduce the complexity of measuring rotationally invariant error rates by two orders of magnitude relative to standard approaches such as character RB. Comments: 70 pages, 11 figures; v2: minor updates; v3: close to published version Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2412.18578 [quant-ph] (or arXiv:2412.18578v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2412.18578 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Quantum Sci. Technol. 11, 035052 (2026) Related DOI : https://doi.org/10.1088/2058-9565/ae8b56 Focus to learn more DOI(s) linking to related resources Submission history From: Yale Fan [ view email ] [v1] Tue, 24 Dec 2024 18:10:00 UTC (4,123 KB) [v2] Tue, 14 Apr 2026 05:40:00 UTC (448 KB) [v3] Thu, 30 Jul 2026 08:50:00 UTC (471 KB) Full-text links: Access Paper: View a PDF of the paper titled Randomized Benchmarking with Synthetic Quantum Circuits, by Yale Fan and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-12 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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