Year: 2026
Type: preprint
Abstract: Reliable quantum computation requires methods for verifying quantum circuits. Level-synchronized tree automata (LSTAs) were recently introduced to represent sets of quantum states for this purpose. We study LSTAs along two axes relevant to verification: the complexity of their decision problems and the size of their representations under circuit operations. We prove that acyclic LSTAs have NP-complete nonemptiness and $Π_2^P$-complete language inclusion, and that general language inclusion is EXPSPACE-complete. We further prove inherent quadratic representation growth under individual quantum gates in a fixed qubit order, and give an adjacent-qubit reordering construction that preserves level synchronization. These results clarify the scope of applicability of the automata-theoretic toolbox for quantum circuit verification.
Source: arXiv (Cornell University)
Institutions: Université de Sherbrooke, University of Antwerp
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223053812