Collective unitary evolution with linear optics by Cartan decomposition

TL;DR

This paper introduces a new iterative method for decomposing general unitary operations and designs compact linear optical architectures for implementing collective two-qubit unitaries, enabling flexible quantum computations with fewer optical elements.

Contribution

It presents a novel decomposition procedure and two optimized optical architectures for deterministic two-qubit collective unitaries, reducing optical elements and enhancing feasibility.

Findings

Reduced optical elements from 25 to 20 and 21 to 20 for the architectures.

Successfully implemented two-dimensional quantum walk and quantum Fourier transform.

Schemes are simple and compatible with current technology.

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.