Compiling Quantum Regular Language States
Armando Bellante, Reinis Irmejs, Marta Florido-Llin\`as, Mar\'ia Cea Fern\'andez, Marianna Crupi, Matthew Kiser, J. Ignacio Cirac

TL;DR
This paper introduces a structure-aware quantum state-preparation compiler for regular language states, enabling efficient and predictable resource use by leveraging automata and matrix product states.
Contribution
It presents a novel compiler that translates regular language specifications into optimized quantum states using automata minimization and matrix product states, providing predictable resource guarantees.
Findings
Efficient compilation of regular language states and their complements.
Linear and logarithmic depth circuit implementations for different hardware architectures.
Explicit bounds on depth and gate count demonstrating resource efficiency.
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…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Parallel Computing and Optimization Techniques · Quantum many-body systems
