We proposed a theoretical protocol to generate robust pulses for executing an arbitrary nonadiabatic holonomic quantum gate operations via reverse engineering. Compared with the traditional scheme that the pulse area needs to satisfy the condition 0 Ω dt = π, the reverse engineering scheme no longer requires this constraint, which greatly improves the flexibility of pulse designing. By optimizing the envelope of the pulses, we show that the gate operations are more robust against the frequency detuning than the traditional scheme. In the meanwhile, we also improve the robustness of the pulse against Rabi frequency fluctuations by utilizing the perturbation theory. The robust pulses can be applied to other ensemble qubit systems to realize quantum error correction, qubit initialization, and quantum gate operations, such as ensemble nitrogen-vacancy center systems, superconducting qubit systems, and other systems where qubits are addressed in frequency.
A theoretical model is proposed to construct high-fidelity arbitrary single qubit gates with geometric phase via a pair of non-adiabatic two-color pulses (TCP) with multiple degrees of freedom interacting with a resonant Λ system. The amplitudes and phases of the TCP are divided into three segments under specific conditions. Compared with the traditional gate operations via single-loop multiple pulses, our model provides a shorter evolution path for small rotation gates, reduces the population in the excited state by 40%, and increases the robustness against the Rabi error. The model is applicable to a single-ion rare-earth-ions (REI) system, where Eu3+ ions doped in an Y2SiO5 crystal is considered. Simulations show that the operational fidelities of NOT gate and Hadamard gate are both above 99.8% with an evolution time of 3 μs.
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