Quantum encoding is suitable for matched filtering

Matched filtering is a powerful signal searching technique used in several employments from radar and communications applications to gravitational-wave detection. Here we devise a method for matched filtering with the use of quantum bits. Our method's asymptotic time complexity does not depend on template length and, including encoding, is $\mathcal{O}(L(\log_2L)^2)$ for a data with length $L$ and a template with length $N$, which is classically $\mathcal{O}(NL)$. Hence our method has superior time complexity over the classical computation for long templates. We demonstrate our method with real quantum hardware on 4 qubits and also with simulations.