Heralded High-Dimensional Photon-Photon Quantum Gate

TL;DR

This paper demonstrates a high-dimensional photonic quantum gate using orbital angular momentum encoding, achieving a four-dimensional controlled phase-flip gate with improved stability and fidelity, advancing optical quantum information processing.

Contribution

It introduces a protocol for a high-dimensional entangling gate for photonic qudits and experimentally realizes a four-dimensional CPF gate with enhanced stability.

Findings

Achieved a four-dimensional qudit-qudit CPF gate with fidelity between 0.64 and 0.82.

Developed a high-precision phase-locking technology for stable high-dimensional OAM beam splitting.

Demonstrated that the protocol reduces the complexity compared to decomposing into multiple two-qubit gates.

Abstract

High-dimensional encoding of quantum information holds the potential to greatly increase the computational power of existing devices by enlarging the accessible state space for fixed register size and by reducing the number of required entangling gates. However, qudit-based quantum computation remains far less developed than conventional qubit-based approaches, in particular for photons, which represent natural multi-level information carriers that play a crucial role in the development of quantum networks. A major obstacle for realizing quantum gates between two individual photons is the restriction of direct interaction between photons in linear media. In particular, essential logic components for quantum operations such as native qudit-qudit entangling gates are still missing for optical quantum information processing. Here we address this challenge by presenting a protocol for realizing an entangling gate -- the controlled phase-flip (CPF) gate -- for two photonic qudits in arbitrary dimension. We experimentally demonstrate this protocol by realizing a four-dimensional qudit-qudit CPF gate, whose decomposition would require at least 13 two-qubit entangling gates. Our photonic qudits are encoded in orbital angular momentum (OAM) and we have developed a new active high-precision phase-locking technology to construct a high-dimensional OAM beam splitter that increases the stability of the CPF gate, resulting in a process fidelity within a range of $ [0.64 \pm 0.01, 0.82 \pm 0.01]$. Our experiment represents a significant advance for high-dimensional optical quantum information processing and has the potential for wider applications beyond optical system.