Compiling Quantum Regular Language States

• URL: http://arxiv.org/abs/2602.02698v1
• Date: Mon, 02 Feb 2026 19:11:38 GMT
• Title: Compiling Quantum Regular Language States
• Authors: Armando Bellante, Reinis Irmejs, Marta Florido-Llinàs, María Cea Fernández, Marianna Crupi, Matthew Kiser, J. Ignacio Cirac,
• Abstract summary: We develop a quantum state-preparation compiler for regular language states.<n>Users describe the target state via (i) a finite set of bitstrings, (ii) a regular expression, or (iii) a deterministic finite automaton (DFA)<n>The efficient DFA representation and offloads expensive linear algebra minimization in exchange of simpler automata manipulations.
• Score: 0.08030359871216612
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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