Low-depth two-unitary design of programmable photonic circuits

The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses, hardware errors, and difficulties in programmability. We propose an enhanced architecture for programmable photonic circuits that minimizes circuit depth and offers analytical programmability, properties that have not been simultaneously achieved in previous circuit designs. Our proposal exploits a previously overlooked representation of general nonunitary matrices as sums of two unitaries. Furthermore, similar to the traditional singular value decomposition-based circuits, the circuits in our unitary-sum-based architecture inherit the advantages of the constituent unitary circuits. Overall, our proposal provides a significantly improved solution for matrix-vector multiplication compared to the established approaches.