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

TL;DR

This paper integrates a hierarchical-equations-of-motion solver into superconducting-qubit calibration to reveal non-Markovian bath signatures often hidden by traditional Markovian models.

Contribution

It introduces a novel calibration framework that explicitly reports bath structure as a diagnostic, contrasting with conventional methods that absorb it into residuals.

Findings

HEOM recovers physical revival envelopes with significantly higher T2* than Markovian fits.

Rabi contrast shows minor deviation (~2.17%) from mesolve, indicating consistency.

Bath-dressed contamination remains stable under increased densification.

Abstract

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.