Observable-Conditioned Backaction in Dynamic Circuits: A Higher-Order Context-Conditioned Kernel for Local Dynamics

Quantum Physics [Submitted on 19 Mar 2026] Observable-Conditioned Backaction in Dynamic Circuits: A Higher-Order Context-Conditioned Kernel for Local Dynamics Petr Sramek Mid-circuit measurements are essential primitives for dynamic circuits and quantum error correction, yet characterizing their induced disturbance on spectator qubits remains a central practical problem. Device-level benchmarking often compresses this disturbance into low-order proxy metrics such as T_1, T_2, readout assignment error, and pairwise crosstalk. We argue that these proxies can be operationally incomplete for multiscale dynamic circuits. We introduce a higher-order context-conditioned kernel, \Gamma_{\mathrm{eff}}[Y,O] = \Gamma_{\mathrm{loc}}[O] + \Gamma_{\mathrm{proxy}}[O] + \Gamma_{\mathrm{rel}}[Y,O], where Y is a global context label and O a local observable. The term \Gamma_{\mathrm{rel}}[Y,O] is a phenomenological compression ansatz isolating residual context dependence unexplained by standard proxies. To avoid impossibility issues of quantum partial-information decompositions on non-commuting algebras, the Möbius weights entering this ansatz are evaluated operationally on classical measurement outcomes. We present evidence in three steps. First, earlier GHZ-versus-clock hardware results motivate an observable-class split. Second, we present dynamical evidence using the A6 synthetic hardware harness. A6 injects a pure higher-order context dependence via a programmed conditional interaction. Because the (C_0,C_1,C_2) parity context is invisible to singles and pairs by construction, standard low-order diagnostics are fundamentally blind to the source of the probe's disturbance. Third, we demonstrate coherent controllability through the A6.2 quantum-eraser experiment. Programmable MARK interactions suppress unconditional fringes while eraser-basis conditioning restores them, consistent with complementarity bounds. These results validate a context-conditioned description of backaction over proxy-only null models. Comments: 11 pages, 4 figures, 2 tables. Includes empirical data, rigorous passive controls, and a hardware-native quantum eraser validation on IBM superconducting processors. Open-source Qiskit artifacts available via Zenodo Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.18381 [quant-ph]   (or arXiv:2603.18381v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.18381 Focus to learn more Submission history From: Petr Sramek [view email] [v1] Thu, 19 Mar 2026 00:59:11 UTC (1,357 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 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?)