Equivalence Checking of Sequential Quantum Circuits

We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is state machine, which natural generalization Mealy machines. A major difficulty in circuits (but not present classical circuits) that the spaces are continuums. This resolved by our main theorem showing two machines can be done with input sequences taken from some chosen basis (which finite) and have length quadratic dimensions Hilbert Based on this theoretical result, develop an (and to best knowledge, first) algorithm running time $\mathcal {O}(2^{3m+5l}(2^{3m}{\,+\,}2^{3l}))$ , where notation="LaTeX">$m$ notation="LaTeX">$l$ denote numbers internal qubits, respectively. complexity comparable known algorithms sense both exponential number (qu)bits. Several case studies experiments presented.