Experimental realization of high-dimensional quantum gates with ultrahigh fidelity and efficiency

Qudit, a high-dimensional quantum system, can provide a larger Hilbert space, and it has been shown that the larger Hilbert space has remarkable advantages over the smaller one in quantum information processing. However, it is a great challenge to realize the high-fidelity quantum gates with qudits. Here we theoretically propose and experimentally demonstrate the four-dimensional quantum gates (including the generalized Pauli X4 gate, Pauli Z4 gate, and all of their integer powers) with optical qudits based on the polarization-spatial degree of freedom of the single photon. Furthermore, we also realize the polarization-controlled eight-dimensional controlled-X4 gate and all of its integer powers. The experimental results achieve both the ultrahigh average gate fidelity 99.73% and efficiency 99.47%, which are above the error threshold for fault-tolerant quantum computation. Our work paves the way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.