Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon*

In this work, we report an experimental realization of a qudit-based PEA on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. The controlled-unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. We also proposed a systematic scheme to decompose an arbitrary unitary matrix into smaller d-level unitary matrices. Representing and connecting these d-level unitary matrices with photonic qudit gates is our plan for future research.