  In this Letter, we propose a new approach to process high-dimensional quantum
information encoded in a photon frequency domain. In contrast to previous
approaches based on nonlinear optical processes, no active control of photon
energy is required. Arbitrary unitary transformation and projection measurement
can be realized with passive photonic circuits and time-resolving detection. A
systematic circuit design for a quantum frequency comb with arbitrary size has
been given. The criteria to verify quantum frequency correlation has been
derived. By considering the practical condition of detector's finite response
time, we show that high-fidelity operation can be readily realized with current
device performance. This work will pave the way towards scalable and
high-fidelity quantum information processing based on high-dimensional
frequency encoding.
