Universal multi-mode linear optical quantum operation in the time domain

Universal multi-mode linear optical operations are essential for almost all optical quantum information protocols (QIPs) for both qubits and continuous variables. Thus far, large-scale implementation of such operations has been pursued mainly by developing photonic chips that contain large interferometers for path-encoded optical modes. However, such encoding requires larger circuits for larger-scale operations, possibly limiting scalability. Here, we realize a scalable dual-loop optical circuit that can programmably perform universal three-mode linear optical operations in the time domain. The programmability, validity, and quantum feature of our circuit are demonstrated by performing nine different three-mode operations on squeezed-state pulses, fully characterizing their output states via homodyne detection, and confirming their entanglement. Our circuit can be straightforwardly scaled up by making the outer loop longer and also extended to universal quantum computers by incorporating measurement and feedforward systems. Thus, our work paves the way to large-scale QIPs which exhibit quantum advantage.