We report a novel digital coherent receiver based on sampling the signal in the optical domain to overcome the speed limitations of electronic analog-to-digital converters. Digital coherent receivers with aggregate optical sampling rates of up to 112 GHz are realized experimentally. The performance of such receivers is investigated in transmission experiments. Transmission of 56 GBd quadrature phase-shift keying signals over 610 km standard single-mode fiber and coherent detection with electronic impairment mitigation is demonstrated. The employed electrical analog-to-digital converters have only 20 GHz bandwidth and a sampling rate of 50 GHz.