HEOM-in-Calibration-Loop: Exposing Non-Markovian Bath Signatures That Markovian Calibration Elides in Superconducting-Qubit Tune-Up

Quantum Physics [Submitted on 23 Apr 2026] HEOM-in-Calibration-Loop: Exposing Non-Markovian Bath Signatures That Markovian Calibration Elides in Superconducting-Qubit Tune-Up Jun Ye Closed-loop superconducting-qubit calibration has matured into DAG-orchestrated protocol chains, yet published frameworks treat the bath via a Markovian master equation or a phenomenological likelihood, absorbing bath structure into fit residuals instead of reporting it as a diagnostic. We integrate a QuTiP 5.x hierarchical-equations-of-motion (HEOM) solver driven by a Tier-1 1/f Burkard bath into a multi-protocol calibration DAG (Rabi -> {Ramsey || T1}) and benchmark it against sesolve and mesolve on a frozen platform in a pulse-level simulator (no hardware validation). The Ramsey channel carries the headline: the Markovian fit is censored by its exponential-family numerical ceiling, while HEOM recovers a physical revival envelope whose primary T2* separates from the Markovian reference by at least 13x at 95% independent-bootstrap confidence within the HEOM-feasible budget; the point-estimate ratio reaches >=28x on the 50-point primary-t1 grid and ~72x on the 30-point biexp-family tau_aw pivot at L=5. Rabi contrast falls 2.17% below mesolve on a noise-limited 30-point grid; the paired-bootstrap CI crosses zero, so this channel corroborates rather than independently establishes the non-Markovian signature. T1 decay shape matches across backends (beta=1.000), yet HEOM's initial occupation drops from 1.000 to 0.879 -- a bath-dressed contamination stable under a 16-point densification. The DAG adds 9.62 us average per-protocol scheduling overhead, no meaningful latency penalty at protocol granularity. HEOM-in-loop thereby changes what calibration reports: bath structure appears as a quantifiable residual rather than a hidden confound. Comments: 6 pages + 1 page reference, 3 figures. Comments/suggestions are welcome Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.21458 [quant-ph]   (or arXiv:2604.21458v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.21458 Focus to learn more Submission history From: Jun Ye [view email] [v1] Thu, 23 Apr 2026 09:15:13 UTC (141 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)