Experimental Equivalence Checking of Quantum Circuits by Nonlocality
Hao Tang, Yu Guo, Weixiao Sun, Xiao‐Min Hu, Bi‐Heng Liu, Zhaohui Wei, Yun‐Feng Huang, Yong‐Jian Han, Chuan‐Feng Li, Guang‐Can Guo · Physical Review Letters · 2024
The quantum circuit model is the most widely used theoretical model for quantum computing. Therefore, determining whether two quantum circuits whose internal structures cannot be seen have the same functionality will be a fundamental problem in future quantum industries, which however turns out to be QMA-hard. Here, based on a photonic system we experimentally implement the equivalence checking of two unknown quantum circuits with real unitary matrix representations, where quantum nonlocality plays a key role and allows us to measure an "average-case" distance between the two quantum circuits very efficiently. Particularly, we also experimentally apply such protocols to verify the correctness of quantum circuit optimizations, which is another crucial topic in future quantum industries. Our work constitutes a proof of concept for the equivalence checking of quantum circuits without relying on their detailed structures.