  Qubit entanglement is a valuable resource for quantum information processing,
where increasing its dimensionality provides a pathway towards higher capacity
and increased error resilience in quantum communications, cluster computation
and quantum phase measurements. Time-frequency entanglement, a continuous
variable subspace, enables the high-dimensional encoding of multiple qubits per
particle, bounded only by the spectral correlation bandwidth and readout timing
jitter. Extending from a dimensionality of two in discrete polarization
variables, here we demonstrate a hyperentangled, mode-locked, biphoton
frequency comb with a time-frequency Hilbert space dimensionality of at least
648. Hong-Ou-Mandel revivals of the biphoton qubits are observed with 61
time-bin recurrences, biphoton joint spectral correlations over 19
frequency-bins, and an overall interference visibility of the high-dimensional
qubits up to 98.4%. We describe the Schmidt mode decomposition analysis of the
high-dimensional entanglement, in both time- and frequency-bin subspaces, not
only verifying the entanglement dimensionality but also examining the
time-frequency scaling. We observe a Bell violation of the high-dimensional
qubits up to 18.5 standard deviations, with recurrent correlation-fringe
Clauser-Horne-Shimony-Holt S-parameter up to 2.771. Our biphoton frequency comb
serves as a platform for dense quantum information processing and
high-dimensional quantum key distribution.
