Collective unitary evolution with linear optics by Cartan decomposition

¹ School of Mathematics and Physics, University of Science and Technology Beijing - Beijing 100083, China
² Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology - Beijing 100081, China

^(a) hrwei@ustb.edu.cn (corresponding author)

Received: 16 September 2021
Accepted: 5 January 2022

Abstract

Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based on the results of decomposition, we design two compact architectures to deterministically implement arbitrary two-qubit polarization-spatial and spatial-polarization collective unitary operations, respectively. The involved linear optical elements are reduced from 25 to 20 and 21 to 20, respectively. Moreover, the parameterized quantum computation can be flexibly manipulated by wave plates and phase shifters. As an application, we construct the specific quantum circuits to realize two-dimensional quantum walk and quantum Fourier transformation. Our schemes are simple and feasible with the current technology.