Programmable photonic circuits (PPCs) have garnered substantial interest in
achieving deep learning accelerations and universal quantum computations.
Although photonic computation using PPCs offers critical advantages, including
ultrafast operation, energy-efficient matrix calculation and room-temperature
quantum states, its poor scalability impedes the integration required for
industrial applications. This challenge arises from the temporally one-shot
operation using propagating light in conventional PPCs, which leads to the
light-speed increase of device footprints. Here we propose a concept of
programmable photonic time circuits, which employ time-cycle-based computations
analogous to the gate cycling in the von Neumann architecture and quantum
computation. As a building block, we develop a reconfigurable SU(2) time gate
composed of two resonators, which have tunable resonances and are coupled
through time-coded dual-channel gauge fields. We demonstrate universal U(N)
operations with high fidelity using the systematic assembly of the SU(2) time
gates, achieving improved scalability from O(N^2) to O(N) in both the footprint
and gate number. This result opens a pathway to industrial-level PPC
implementation in very large-scale integration.Comment: 46 pages, 6 figure