Dynamical-Invariant-based Holonomic Quantum Gates: Theory and Experiment

Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer the decoherence error, while the non-adiabatic HQGs require additional Hilbert space. Here, we report a new dynamical-invariant-based approach to realize HQG. Our approach is free of the dechoherence error and the need of additional Hilbert space. In addition to 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 fidelity is in average 0.9972 by randomized benchmarking, and the controlled-NOT gate fidelity is 0.9782 by quantum process tomography. Our approach is scalable and platform-independent, and thus may open a way to large-scale holonomic quantum computation in the near future.