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

TL;DR

This paper introduces two optimized photonic architectures for implementing arbitrary high-dimensional quantum state transformations, reducing complexity and enhancing polarization-based applications, with potential benefits for quantum computing and communication.

Contribution

The paper presents two novel architectures that optimize the realization of arbitrary unitary transformations in high-dimensional quantum systems using photonic path and polarization.

Findings

First architecture halves the number of interferometers needed.

Second architecture uses high-dimensional X gate for local polarization operations.

Both architectures maintain symmetric layout and improve implementation efficiency.

Abstract

An arbitrary lossless transformation in high-dimensional quantum space can be decomposed into elementary operations which are easy to implement, and an effective decomposition algorithm is important for constructing high-dimensional 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 high-dimensional 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 high-dimensional transformations and could have potential applications in high-dimensional quantum computation and quantum communication.