Congestion-free routing on quantum chips
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Quantum Physics arXiv:2604.27015 (quant-ph) [Submitted on 29 Apr 2026] Title:Congestion-free routing on quantum chips Authors:Mithilesh Kumar, Yusuf Tahir, Varun Daiya, Sanjana Mattaparthi, Aarav Shaurya View a PDF of the paper titled Congestion-free routing on quantum chips, by Mithilesh Kumar and 4 other authors View PDF HTML (experimental) Abstract:Limited connectivity makes nonlocal quantum gates expensive on near-neighbor hardware, where compilation typically relies on SWAP transport, inheriting both depth overhead and path congestion. We present a swap-free routing framework in which higher levels of a qudit act as orthogonal spectral buses that transport control information without moving the computational state. We show that exact congestion relief in nearest-neighbor architectures requires local Hilbert-space expansion. In this model, a nonlocal operation over a path of length $L$ requires $2L+1$ logical routing primitives, compared to the $3L$ baseline. Overlapping routes remain distinguishable through bus labels encoded in the same physical qudits. This routing algebra extends to Boolean fan-in at a common target: multiple controls arriving on distinct buses trigger a local unitary based on an arbitrary Boolean function of bus digits, yielding multi-control operations of depth $2L + D_g + O(1)$ for fan-in size $K$ and target-synthesis cost $D_g$. We prove decodability, reversibility, and correctness for CNOT and Boolean fan-in, along with a state-count lower bound $d \geq 2^{K+1}$ for exact overlap routing. Cirq simulations confirm single-control correctness and zero crosstalk. Compiler-level benchmarks on QFT, QAOA, and mirror-interaction circuits verify the predicted congestion law and transport reduction. Noisy QuTiP simulations show that the architectural advantage depends on higher-level coherence and speed. These results identify spectral qudit routing as a congestion-relief architecture that separates nonlocal control delivery from local target-side aggregation, providing a minimal mechanism for overcoming qubit routing limitations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.27015 [quant-ph] (or arXiv:2604.27015v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.27015 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mithilesh Kumar [view email] [v1] Wed, 29 Apr 2026 12:01:54 UTC (680 KB) Full-text links: Access Paper: View a PDF of the paper titled Congestion-free routing on quantum chips, by Mithilesh Kumar and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)