Optimized architectures for universal quantum state transformations using photonic path and polarization

Abstract

An arbitrary lossless transformation in high-dimensional (HD) quantum space can be decomposed into elementary operations which are easy to implement, and an effective decomposition algorithm is important for constructing HD systems. Here, we present two optimized architectures to effectively realize an arbitrary unitary transformation by using the photonic path and polarization based on the existing decomposition algorithm. In the first architecture, the number of required interferometers is reduced by half compared with previous works. In the second architecture, by using the HD X gate, all the elementary operations are transferred to the operations which act locally on the photonic polarization in the same path. Such an architecture could be of significance in polarization-based applications. Both architectures maintain the symmetric layout. Our work facilitates the optical implementation of HD transformations and could have potential applications in HD quantum computation and quantum communication.