The probabilistic nature of single-photon sources and photon–photon interactions encourages encoding as much quantum information as possible in every photon for the purpose of photonic quantum information processing. Here, by encoding high-dimensional units of information (qudits) in time and frequency degrees of freedom using on-chip sources, we report deterministic two-qudit gates in a single photon with fidelities exceeding 0.90 in the computational basis. Constructing a two-qudit modulo SUM gate, we generate and measure a single-photon state with nonseparability between time and frequency qudits. We then employ this SUM operation on two frequency-bin entangled photons—each carrying two 32-dimensional qudits—to realize a four-party high-dimensional Greenberger–Horne–Zeilinger state, occupying a Hilbert space equivalent to that of 20 qubits. Although high-dimensional coding alone is ultimately not scalable for universal quantum computing, our design shows the potential of deterministic optical quantum operations in large encoding spaces for practical and compact quantum information processing protocols.

单光子源和光子-光子相互作用的概率性质鼓励以光子量子信息处理为目的，在每个光子中尽可能多地编码量子信息。在这里，通过使用片上源在时间和频率自由度上对信息（量子数）的高维单元进行编码，我们在计算基础上报告了单个光子中确定性二维量子门，其保真度超过0.90。构造一个两模取模SUM门，我们生成并测量一个单光子状态，时间与频率之间不可分离。然后，我们对两个频点纠缠的光子（每个都携带两个32维qudits）进行此SUM运算，以实现四方高维Greenberger-Horne-Zeilinger态，占据相当于20量子比特的希尔伯特空间。