Publication detail

Verifying Quantum Circuits with Level-Synchronized Tree Automata

ABDULLA, P. CHEN, Y. CHEN, Y. HOLÍK, L. LENGÁL, O. LIN, J. LO, F. TSAI, W.

Original Title

Verifying Quantum Circuits with Level-Synchronized Tree Automata

Type

journal article in Scopus

Language

English

Original Abstract

We present a new method for the verification of quantum circuits based on a novel symbolic representation of sets of quantum states using level-synchronized tree automata (LSTAs). LSTAs extend classical tree automata by labeling each transition with a set of choices, which are then used to synchronize subtrees of an accepted tree. Compared to the traditional tree automata, LSTAs have an incomparable expressive power while maintaining important properties, such as closure under union and intersection, and decidable language emptiness and inclusion. We have developed an efficient and fully automated symbolic verification algorithm for quantum circuits based on LSTAs. The complexity of supported gate operations is at most quadratic, dramatically improving the exponential worst-case complexity of an earlier tree automata-based approach. Furthermore, we show that LSTAs are a promising model for parameterized verification, i.e., verifying the correctness of families of circuits with the same structure for any number of qubits involved, which principally lies beyond the capabilities of previous automated approaches. We implemented this method as a C++ tool and compared it with three symbolic quantum circuit verifiers and two simulators on several benchmark examples. The results show that our approach can solve problems with sizes orders of magnitude larger than the state of the art.

Keywords

quantum circuits,tree automata, verification

Authors

ABDULLA, P.; CHEN, Y.; CHEN, Y.; HOLÍK, L.; LENGÁL, O.; LIN, J.; LO, F.; TSAI, W.

Released

19. 1. 2025

ISBN

2475-1421

Periodical

Proceedings of the ACM on Programming Languages

Year of study

9

Number

1

State

United States of America

Pages from

923

Pages to

953

Pages count

31

URL

https://dl.acm.org/doi/10.1145/3704868

BibTex

@article{BUT193377,
  author="ABDULLA, P. and CHEN, Y. and CHEN, Y. and HOLÍK, L. and LENGÁL, O. and LIN, J. and LO, F. and TSAI, W.",
  title="Verifying Quantum Circuits with Level-Synchronized Tree Automata",
  journal="Proceedings of the ACM on Programming Languages",
  year="2025",
  volume="9",
  number="1",
  pages="923--953",
  doi="10.1145/3704868",
  issn="2475-1421",
  url="https://dl.acm.org/doi/10.1145/3704868"
}