This technique aims to detect errors in quantum circuits by analyzing the relationship between input and output sets of quantum states. By utilizing tree automata to compactly represent quantum state sets and avoiding the inaccuracies of floating-point calculations, this approach significantly improves the accuracy and efficiency of quantum circuit verification. Connecting quantum program verification with automata theory, it opens new possibilities for using automata theory in the future development of quantum computing verification and bug detection.

     This study addresses whether parallel computing can achieve fast-forwarding in Hamiltonian simulation, focusing on time-independent and sparse Hamiltonian quantum systems. We demonstrate that in various settings, Hamiltonian simulation cannot be fast-forwarded using low-depth circuits, revealing the limitations of parallel computing in this context. These findings highlight fundamental constraints that must be considered in the design of efficient quantum algorithms, offering critical insights for future quantum computing research and applications.