Deterministic optical quantum logic with multiple high-dimensional degrees of freedom in a single photon

Amongst the myriad quantum systems suitable for information processing, photons have the critical advantage of extremely low decoherence, with minimal interaction with their surrounding environment. This isolation, however, has the downside of also making photon-photon interactions for two-qubit gates difficult and, with linear optics, inherently probabilistic. Such a situation poses a formidable roadblock for photonics in scaling up quantum computing. An intriguing answer to this problem is to encode multiple qubits in a single photon's different degrees of freedom. While this solution ultimately suffers from exponential resource scaling, it enables deterministic two-qubit gates and thus offers significant encoding potential in the current generation of quantum circuits. So far, though, experiments in this paradigm have utilized two-dimensional encoding per each degree of freedom, thus failing to exploit the full information capacity of single photons. Qudits, high-dimensional units of quantum information, can be encoded in photonic time and frequency degrees of freedom using on-chip sources like microresonators, which can easily expand the Hilbert space in a scalable way. Here, we demonstrate the first high-dimensional, single-photon two-qudit gates in time and frequency bins. By exploiting fast optical switching, we realize the cyclic shift operation (generalized X gate) for three time bins and confirm this operation's coherence through an interference measurement. By incorporating the frequency-bin degree of freedom as well, we build on this X gate and implement the two-qudit controlled increment (CINC) and modulo sum (SUM) gates, either of which are sufficient, along with single-qudit operations, for universal quantum computing. Our scheme thus shows the potential of deterministic optical quantum computing for practical and compact quantum information processing.