Heralded high-dimensional photon–photon quantum gate

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 a 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, particularly for photons, which represent natural multilevel 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 gate—for two photonic qudits in an arbitrary dimension. We experimentally demonstrate this protocol by realizing a four-dimensional qudit–qudit controlled phase-flip gate, whose decomposition would require at least 13 two-qubit entangling gates. Our photonic qudits are encoded in orbital angular momentum, and we have developed a new active high-precision phase-locking technology to construct a high-dimensional orbital angular momentum beamsplitter that increases the stability of the controlled phase-flip gate, resulting in a process fidelity within a range of [0.71 ± 0.01, 0.85 ± 0.01]. Our experiment represents an important advance for high-dimensional optical quantum information processing and has the potential for wider applications beyond optical system.