Integrated high-dimensional quantum gates using two-dimensional multimode interference waveguides

The concept of high-dimensional multiphotonic gates has many potential applications. As an example, encoding qubit information in high-dimensional systems has significant advantages in terms of robustness against errors and can reduce quantum circuit complexities, and high-dimensional error-correction codes have shown advantages in terms of resources. Furthermore, high-dimensional multiphoton gates can be used for Bell-state or Greenberger–Horne–Zeilinger-state measurements, which are an essential requirement of quantum communication protocols. As a high-dimensional degree of freedom, the orbital angular momentum (OAM) of photons can be used for this purpose.

In this work, integrated high-dimensional quantum gates are proposed for the first time. The structure of the proposed integrated quantum gates includes properly designed multimode interference (MMI) waveguides. In MMI waveguides, an input field profile can be reproduced in single or multiple images at periodic intervals along the propagation direction of the waveguide. This property is called self-imaging. Using the beam propagation method (BPM) for simulating OAM modes in MMI waveguides, it has been shown that at the shortest length for self-imaging occurrence, the sign of the topological charge of the even OAM modes is reversed, while the odd OAM modes remain unchanged. The charge conversion property of the MMI waveguides for even higher-order OAM modes can be used to implement the integrated quantum gates in a simple way. For instance, for an input state of (-2, -1, 0, 1), the quantum logic gate of X can be implemented using the proposed MMI waveguide followed by a first-order spiral phase plate (SPP), in that the SPP adds +1 to the mode, leading to (-1,0,1,2). Afterwards, the MMI waveguide reverses the sign of the even modes without any change in the odd modes, which leads to the correct output modes: (-1,0,1, -2).