Hardware Efficient Universal Linear Transformations for Optical Modes in the Synthetic Time Dimension

Efficiently encoding and extracting time-serial information of a light field favors large-scale programmable time-domain unitary operations. The current state-of-the-art designs of universal discrete unitary operation of light using multiport interferometers require integrating $\mathcal{O}(N^2)$ beamsplitters and phase shifters or stabilizing $N-1$ phases between path-paralleled optical components, in order to arbitrarily mix $N$ input modes. We present a compact design that only relies on $\mathcal{O}(\log_2N)$ basic components and phase-stabilization to efficiently realize any unitary operations over $N$ modes encoded within $N$ time bins, that we term the ‘generalized Green Machine’ [1]. By programming coupling between the modes, arbitrary unitary transformations decomposed using the Sine-Cosine Fractal (SCF) [2] can be implemented by the generalized Green Machine. We demonstrate the versatility of this design by boosting the success probability of Bell-state measurements over time-serial encoded photonic cluster states. This architecture enables large-scale time-bin encoded unitary transformations for near-term quantum information processing tasks.

[1] Cui, C., Postlewaite, J., Saif, B. N., Fan, L., & Guha, S. (2023). Superadditive communications with the green machine: a practical demonstration of nonlocality without entanglement. arXiv preprint arXiv:2310.05889.

[2] Basani, J. R., Vadlamani, S. K., Bandyopadhyay, S., Englund, D. R., & Hamerly, R. (2023). A self-similar sine–cosine fractal architecture for multiport interferometers. Nanophotonics, 12(5), 975-984.