Verifying Quantum Circuits with Level-Synchronized Tree Automata (Technical Report)

TL;DR

This paper introduces level-synchronized tree automata (LSTAs) for the symbolic verification of quantum circuits, enabling efficient, automated, and scalable analysis of large and parameterized quantum systems.

Contribution

The paper presents LSTAs, a novel automata model with enhanced expressive power and decidability, and develops an automated verification algorithm that outperforms existing methods in efficiency and scalability.

Findings

LSTAs support complex quantum gate operations with at most quadratic complexity.

The verification algorithm can handle quantum circuits much larger than previous tools.

LSTAs are effective for parameterized verification of families of quantum circuits.

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.