High‐Dimensional Photonic Quantum Computing with a Measurement‐Free Auxiliary System.

Enhancing the capabilities of quantum computing relies heavily on harnessing the power of qudit‐based high‐dimensional quantum gates. In the study, single‐qudit 4D X$ X$, X2$ X^{2}$, and X†$ X^{\dagger }$ gates tailored for a two‐photon system in polarization states are presented. Furthermore, a two‐qudit 4×4$4\times 4$‐dimensional controlled‐not (CNOT) gate designed for a four‐photon system is introduced. These high‐dimensional gates can offer versatile and straightforward optical implementations, ensuring them to fulfill in a deterministic way. To facilitate these processes, an auxiliary system in the form of a Λ$\Lambda$‐type atom residing in a cavity is employed. Remarkably, the auxiliary system retains its original state after the operation process ends, so it is not required to measure and plays a pivotal role in promoting effective interactions among distinct photons in its extended coherence time. Importantly, the in‐depth analysis of the fidelities and efficiencies of these quantum gates showcase remarkable outcomes, affirming the superiority of the proposed protocols. Therefore, these high‐dimensional gates not only amplify quantum parallelism, but also bolster the speed of quantum computations, fortify resilience against errors, and foster scalability for executing intricate quantum operations. [ABSTRACT FROM AUTHOR]