Quantum Information Processing by Weaving Quantum Talbot Carpets

TL;DR

This paper proposes a novel method for quantum information processing using the Talbot effect, enabling the implementation of universal quantum gates through light's wave interference in free space.

Contribution

It introduces a new approach to quantum computing with linear optics by leveraging the Talbot effect for single and two-quDit gates, expanding the toolkit for quantum information processing.

Findings

Single quDit gates realized via Talbot effect

Complete set of single quDit gates demonstrated

Controlled operations enabled with spatially-dependent beam splitters

Abstract

Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled operations between two quDits. A new form of universal quantum information processing can then be implemented with linear optics and ancilla photons. Though we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.