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Applied Optics and Photonics China (AOPC)

Reverse engineering of high-fidelity nonadiabatic holonomic quantum gates in the ensemble-ions system

Hong Yan Peng, Jiamin Qiu, Ying Lin Yan

Published Jan 23, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2652041

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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.
Nonadiabatic holonomic quantum computation (NHQC) provides an essential way to construct robust and high-fidelity quantum gates due to its geometric features. However, NHQC is more sensitive to decay and dephasing errors than a conventional dynamical gate since it requires an ancillary intermediate state. Here, we utilize the Hamiltonian reverse engineering technique to study the influence of intermediate-state decoherence on NHQC gate fidelity, and propose schemes to construct an arbitrary single-qubit holonomic gate and nontrivial two-qubit holonomic gate with high fidelity and robustness to the decoherence. Although the proposed method is generic and can be applied to many experimental platforms, such as superconducting qubits, trapped ions, and quantum dots, here we take a nitrogen-vacancy center as an example to show that the gate fidelity can be significantly enhanced from 89% to 99.6% in contrast to recent experimental NHQC schemes [Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017); Opt. Lett. 43, 2380 (2018)], and the robustness against decoherence can also be significantly improved. All in all, our scheme provides a promising way for fault-tolerant geometric quantum computation.
Holonomic quantum computation (HQC) offers an inherently robust approach to quantum gate implementation by exploiting quantum holonomies. While adiabatic HQC benefits from robustness against certain control errors, its long runtime limits practical utility due to increased exposure to environmental noise. Nonadiabatic HQC addresses this issue by enabling faster gate operations but compromises robustness. In this work, we propose a scheme for fast holonomic quantum gates based on the π -pulse method, which accelerates adiabatic evolution while preserving its robustness. By guiding the system Hamiltonian along geodesic paths in the parameter space and applying phase-modulating π pulses at discrete points, we realize a universal set of holonomic gates beyond the conventional adiabatic limit. Our scheme allows for arbitrary single-qubit and two-qubit controlled gates within a single-loop evolution and provides additional tunable parameters for flexible gate design. These results demonstrate a promising path toward high-fidelity, fast, and robust quantum computation .
Nonadiabatic holonomic quantum computation (NHQC) offers intrinsic resilience to certain control imperfections. However, conventional nonadiabatic holonomic protocols are constrained by the fixed-pulse-area condition, which limits flexibility and prolongs duration of small-angle gates. Here we experimentally demonstrate a universal brachistochrone nonadiabatic holonomic quantum gate scheme in a trapped 40Ca+ ion, and realized the construction of pX gate under the conventional NHQC, brachistochrone NHQC (BNHQC) and composite BNHQC (CBNHQC) protocols. By characterizing the performance of gate performance in the presence of dissipation, Rabi-frequency errors and detuning errors, we show that BNHQC and CBNHQC outperform conventional NHQC, and BNHQC can offer a favorable balance between operation speed and robustness. It further shows that keeping high fidelity and strong robustness need decrease the accumulated population of excited state in the evolution process. These results highlight nonadiabatic holonomic computation as a practical route toward fast and robust quantum gates in trapped-ion platforms.
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost functional which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.
In this paper, we propose a one-step scheme for implementing the nonadiabatic holonomic swap gate with Rydberg atoms. By applying invariant-based reverse engineering to design the effective Hamiltonian of the system, a suitable evolution path for implementing nonadiabatic holonomic quantum computation is found. In addition, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, so that the scheme is insensitive to the systematic error of pulses. We also estimate the effects of random noise, the random initial phase of the pulses, the Doppler shift, and decoherence on the scheme. The numerical results show that the scheme exhibits fairly good performance against these negative factors. Finally, we generalize the scheme to realize the non-Clifford swap gates. Therefore, this scheme can provide a feasible framework for implementing high-fidelity and robust swap gates and non-Clifford swap gates with Rydberg atoms.