Compiling Quantum Regular Language States

Quantum Physics arXiv:2602.02698 (quant-ph) [Submitted on 2 Feb 2026] Title:Compiling Quantum Regular Language States Authors:Armando Bellante, Reinis Irmejs, Marta Florido-Llinàs, María Cea Fernández, Marianna Crupi, Matthew Kiser, J.

Ignacio Cirac View a PDF of the paper titled Compiling Quantum Regular Language States, by Armando Bellante and 6 other authors View PDF HTML (experimental) Abstract:State preparation compilers for quantum computers typically sit at two extremes: general-purpose routines that treat the target as an opaque amplitude vector, and bespoke constructions for a handful of well-known state families. We ask whether a compiler can instead accept simple, structure-aware specifications while providing predictable resource guarantees. We answer this by designing and implementing a quantum state-preparation compiler for regular language states (RLS): uniform superpositions over bitstrings accepted by a regular description, and their complements. Users describe the target state via (i) a finite set of bitstrings, (ii) a regular expression, or (iii) a deterministic finite automaton (DFA), optionally with a complement flag. By translating the input to a DFA, minimizing it, and mapping it to an optimal matrix product state (MPS), the compiler obtains an intermediate representation (IR) that exposes and compresses hidden structure. The efficient DFA representation and minimization offloads expensive linear algebra computation in exchange of simpler automata manipulations. The combination of the regular-language frontend and this IR gives concise specifications not only for RLS but also for their complements that might otherwise require exponentially large state descriptions. This enables state preparation of an RLS or its complement with the same asymptotic resources and compile time. We outline two hardware-aware backends: SeqRLSP, which yields linear-depth, ancilla-free circuits for linear nearest-neighbor architectures via sequential generation, and TreeRLSP, which achieves logarithmic depth on all-to-all connectivity via a tree tensor network. We prove depth and gate-count bounds scaling with the system size and the state's maximal Schmidt rank, and we give explicit compile-time bounds that expose the benefit of our approach. We implement and evaluate the pipeline. Comments: Subjects: Quantum Physics (quant-ph); Formal Languages and Automata Theory (cs.FL) Cite as: arXiv:2602.02698 [quant-ph] (or arXiv:2602.02698v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.02698 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Armando Bellante [view email] [v1] Mon, 2 Feb 2026 19:11:38 UTC (2,661 KB) Full-text links: Access Paper: View a PDF of the paper titled Compiling Quantum Regular Language States, by Armando Bellante and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.FL 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)