Dynamical Regimes of Two Qubits Coupled through a Transmission Line

Quantum Physics [Submitted on 23 Apr 2026] Dynamical Regimes of Two Qubits Coupled through a Transmission Line Fabio Borrelli, Giovanni Miano, Carlo Forestiere We investigate the reduced dynamics of two identical superconducting qubits capacitively coupled through a finite-length transmission line. Starting from circuit quantization, we derive a circuit Hamiltonian that naturally separates the line modes into even- and odd-parity sectors coupled to collective qubit operators. Depending on the hierarchy between the qubit frequency \omega_q, the mode spacing \omega_{TL}, and the coupling scale \omega_g, the line acts either as a structured reservoir or as a discrete few-mode coupler. In the long-line continuum limit, each sector is described by a Drude--Lorentz spectral density and the dynamics is solved with the hierarchical equations of motion. Using the Breuer--Laine--Piilo measure, we identify the parameter region in which the reduced dynamics exhibits non-Markovian relaxation. In the short-line limit, the continuum description breaks down and the dynamics becomes respectively multimode or single-mode. This establishes a unified cQED picture of the dynamical regimes of finite-length transmission lines in superconducting-circuit architectures. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.21463 [quant-ph]   (or arXiv:2604.21463v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.21463 Focus to learn more Submission history From: Carlo Forestiere [view email] [v1] Thu, 23 Apr 2026 09:17:09 UTC (4,073 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?)