Efficient qudit based scheme for photonic quantum computing

TL;DR

This paper proposes an efficient linear optics-based scheme for photonic quantum computing using qudits, demonstrating reduced resource requirements and applying it to solve the k-coloring problem.

Contribution

It introduces a method to construct non-deterministic multi-qudit gates with linear optics and photon detectors, and shows qudit cluster states need fewer resources than qubit ones.

Findings

Qudit cluster states require fewer optical modes.

The scheme enables non-deterministic multi-qudit gates.

Application to the k-coloring problem demonstrates practical benefits.

Abstract

Linear optics is a promising alternative for the realization of quantum computation protocols due to the recent advancements in integrated photonic technology. In this context usually qubit based quantum circuits are considered, however, photonic systems naturally allow also for d-ary, i.e., qudit based, algorithms. This work investigates qudits defined by the possible photon number states of a single photon in d > 2 optical modes. We demonstrate how to construct locally optimal non-deterministic many-qudit gates using linear optics and photon number resolving detectors, and explore the use of qudit cluster states in the context of a d-ary optimization problem. We find that the qudit cluster states require less optical modes and are encoded by a fewer number of entangled photons than the qubit cluster states with similar computational capabilities. We illustrate the benefit of our qudit scheme by applying it to the k-coloring problem.