Frequency-bin quantum information encoding offers an intriguing synergy with classical optical networks, with the ability to support many qubits in a single fiber. Yet, coherent quantum frequency operations prove extremely challenging due to the difficulties in mixing frequencies arbitrarily and with low noise. In this paper, we address such challenges and implement distinct quantum gates in parallel on two entangled frequency-bin qubits in the same optical fiber. Our basic quantum operation controls the spectral overlap between adjacent spectral bins, allowing us to observe frequency-bin Hong–Ou–Mandel interference with a visibility of 0.971 ± 0.007. By integrating this tunability with frequency parallelization, we synthesize independent gates on entangled qubits and flip their spectral correlations, allowing us to observe strong violation of the separability bound. Our realization of closed, user-defined gates on frequency-bin qubits in parallel should find application in the development of fiber-compatible quantum information processing and quantum networks.