Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by randomized benchmarking, and the controlled-NOT gate acquires fidelity 0.9782 by quantum process tomography. Our approach is also platform-independent, and thus may open a way to large-scale holonomic quantum computation.
@article{arxiv.2003.09848,
title = {Dynamical-Invariant-based Holonomic Quantum Gates: Theory and Experiment},
author = {Yingcheng Li and Tao Xin and Chudan Qiu and Keren Li and Gangqin Liu and Jun Li and Yidun Wan and Dawei Lu},
journal= {arXiv preprint arXiv:2003.09848},
year = {2020}
}