We show that any $N$-dimensional unitary matrix can be realized using a finite sequence of concatenated identical fixed multiport beam splitters (MBSs) and phase shifters (PSs). Our construction is based on a Lie group theorem applied to existing decompositions. Using the Bell-Walmsley-Clements framework, we prove that any $N$-dimensional unitary requires $N+2$ phase masks, $N-1$ fixed MBSs, and $N-1$ BSs. Our scheme requires only $O\left(N\right)$ fixed, identical components (MBSs and BSs) compared with the $O\left(N^2\right)$ fixed BSs required by conventional schemes (e.g., Clements), all while keeping the same number of PSs. Experimentally, these MBSs can be realized as a monolithic element via femtosecond laser writing, offering superior performance through reduced insertion losses. As an application, we present a reconfigurable linear optical circuit that implements a three-dimensional unitary emerging in the unambiguous discrimination of two nonorthogonal qubit states.

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• Classical optics
• Photonics
• Quantum optics