  Quantum information is the next frontier in information science, promising
unconditionally secure communications, enhanced channel capacities, and
computing capabilities far beyond their classical counterparts. And as quantum
information processing devices continue to transition from the lab to the
field, the demand for the foundational infrastructure connecting them with each
other and their users---the quantum internet---will only increase. Due to the
remarkable success of frequency multiplexing and control in the classical
internet, quantum information encoding in optical frequency offers an
intriguing synergy with state-of-the-art fiber-optic networks. Yet coherent
quantum frequency operations prove extremely challenging, due to the
difficulties in mixing frequencies efficiently, arbitrarily, in parallel, and
with low noise. Here we implement an original approach based on a
reconfigurable quantum frequency processor, designed to perform arbitrary
manipulations of spectrally encoded qubits. This processor's unique tunability
allows us to demonstrate frequency-bin Hong-Ou-Mandel interference with
record-high 94% visibility. Furthermore, by incorporating such tunability with
our method's natural parallelizability, we synthesize independent quantum
frequency gates in the same device, realizing the first high-fidelity flip of
spectral correlations on two entangled photons. Compared to quantum frequency
mixing approaches based on nonlinear optics, our linear method removes the need
for additional pump fields and significantly reduces background noise. Our
results demonstrate multiple functionalities in parallel in a single platform,
representing a huge step forward for the frequency-multiplexed quantum
internet.
