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Universal single-qubit operations based on purely geometric phase factors in adiabatic processes are demonstrated by utilizing a four-level system in a trapped single $^{40}$Ca$^+$ ion connected by three oscillating fields. Robustness against parameter variations is studied. The scheme demonstrated here can be employed as a building block for large-scale holonomic quantum computations, which may be useful for large qubit systems with statistical variations in system parameters.
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Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. Here, we experimentally demonstrate a solution scheme, demonstrating nonadiabatic holonomic single qubit quantum gates with optimal control in a trapped Yb ion based on three level systems with resonant drives, which also hold the advantages of fast evolution and convenient implementation. Compared with corresponding previous geometric gates and conventional dynamic gates, the superiority of our scheme is that it is more robust against control amplitude errors, which is confirmed by the measured gate infidelity through both quantum process tomography and random benchmarking methods. In addition, we also outline that nontrivial two qubit holonomic gates can also be realized within current experimental technologies. Therefore, our experiment validates the feasibility for this robust and fast holonomic quantum computation strategy.
For circuit-based quantum computation, experimental implementation of universal set of quantum logic gates with high-fidelity and strong robustness is essential and central. Quantum gates induced by geometric phases, which depend only on global properties of the evolution paths, have built-in noise-resilience features. Here, we propose and experimentally demonstrate nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped $^{171}mathrm{Yb}^{+}$ ion based on four-level systems with resonant drives. We confirm the implementation with measured gate fidelity through both quantum process tomography and randomized benchmarking methods. Meanwhile, we find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies. Compared with previous implementations on three-level systems, our experiment share both the advantage of fast nonadiabatic evolution and the merit of robustness against systematic errors, and thus retains the main advantage of geometric phases. Therefore, our experiment confirms a promising method for fast and robust holonomic quantum computation.
Fully autonomous precise control of qubits is crucial for quantum information processing, quantum communication, and quantum sensing applications. It requires minimal human intervention on the ability to model, to predict and to anticipate the quantum dynamics [1,2], as well as to precisely control and calibrate single qubit operations. Here, we demonstrate single qubit autonomous calibrations via closed-loop optimisations of electron spin quantum operations in diamond. The operations are examined by quantum state and process tomographic measurements at room temperature, and their performances against systematic errors are iteratively rectified by an optimal pulse engineering algorithm. We achieve an autonomous calibrated fidelity up to 1.00 on a time scale of minutes for a spin population inversion and up to 0.98 on a time scale of hours for a Hadamard gate within the experimental error of 2%. These results manifest a full potential for versatile quantum nanotechnologies.
The non-adiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent years. Here, we propose the first scheme for realizing universal single-qubit gates based on an optomechanical system working with the non-adiabatic geometric phases. Our quantum gates are robust to the control errors and the parameter fluctuations, and have unique functions to achieve the quantum state transfer and entanglement generation between cavities. We discuss the corresponding experimental parameters and give some simulations. Our scheme may have the practical applications in quantum computation and quantum information processing.
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier transformation can be obtained with a single loop.
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