We describe an interdisciplinary experiment concept featuring a novel technique for detecting gravitational waves (GWs) at the millihertz frequencies with circular particle accelerators like the Large Hadron Collider (LHC) at CERN, using ultrafast single photon detectors. We find that if technological development allows, then millihertz GWs could be detected on Earth at the LHC, possibly even before the launch of the LISA mission, which is a space-based laser interferometer searching for millihertz GWs, to be launched in 2034. The network of such an earth-based LHC-GW detector with LISA would significantly improve localizing the GW source in the sky, aiding astronomers to look for light signals from the detected GW event (electromagnetic follow-up studies).