State of the art quantum computers have very limited applicability for accurate calculations. Here we report the first experimental demonstration of qubit-based matched filtering for a detection of the gravitational-wave signal from a binary black hole merger. With our implementation on noisy superconducting qubits, we obtained a similar signal-to-noise ratio for the binary black hole merger as achievable with classical computation, providing evidence for the utility of qubits for practically relevant tasks. The algorithm we invented for this application is a Monte Carlo algorithm which uses quantum and classical computation together. It provides a quasi-quadartic speed-up for time-domain convolution, similar to achievable with fast Fourier transform.