Qudit, a high-dimensional quantum system, provides a larger Hilbert space to process the quantum information and has shown remarkable advantages over the qubit counterparts. It is a great challenge to realize the high fidelity universal quantum gates with qudits. Here we theoretically propose and experimentally demonstrate a set of universal quantum gates for a single optical qudit with four dimensions (including the generalized Pauli X4 gate, Pauli Z4 gate, and all of their integer powers), which are encoded in the polarization-spatial degree of freedom without multiple unstable cascaded interferometers. Furthermore, we also realize the controlled-X4 gate and all of its integer powers. We have achieved both the ultra-high average gate fidelity 99.73% and efficiency 99.47%, which are above the the error threshold for fault-tolerant quantum computation. Our work paves a way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.
@article{arxiv.2311.18179,
title = {Experimental realization of universal high-dimensional quantum gates with ultra-high fidelity and efficiency},
author = {Zhe Meng and Wen-Qiang Liu and Bo-Wen Song and Xiao-Yun Wang and An-Ning Zhang and Zhang-Qi Yin},
journal= {arXiv preprint arXiv:2311.18179},
year = {2023}
}