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.
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.
In quantum control, geometrical operations could provide an extra layer of robustness against control errors. However, the conventional non-adiabatic holonomic quantum computation (NHQC) is limited by the fact that all of the operations require exactly the same amount of evolution time, even for a small-angle rotation. Furthermore, NHQC confines the driving part of the Hamiltonian to strictly cover a fixed pulse area, making it sensitive to control errors. Here we present an unconventional approach of NHQC, termed brachistochronic NHQC, for bypassing these limitations. Specifically, with B-NHQC, non-Abelian geometric gates can be time-optimized by following the brachistochrone curve, minimizing the impact from the environmental decoherence. Additionally, we demonstrate that B-NHQC is compatible with composed pulses, which can further enhance the robustness against pulse errors. For benchmarking, we provide a thorough analysis on the performance of B-NHQC under experimental conditions; we found that the gate error can be reduced by as much as 64% compared with NHQC.
Abstract Nonadiabatic holonomic quantum computation (NHQC) has attracted significant interest due to its intrinsic robustness against local parameter fluctuations. However, conventional NHQC schemes are constrained by long evolution times, with all gate operations requiring the same duration regardless of the rotation angle, leading to increased susceptibility to decoherence. In this paper, we propose a time-optima NHQC (TONHQC) scheme in the Rydberg atomic system, which minimizes gate operation time while maintaining geometric robustness. By solving the quantum brachistochrone equation (QBE), we derive an optimal trajectory for state evolution. We demonstrate the feasibility of TONHQC using87Rb atoms by constructing high-fidelity geometric two-qubit gates. Numerical simulations for controlled-Hadamard (C-H), controlled-π/4 (C-S) and controlled-π/8 (C-T) gates confirm that TONHQC outperforms conventional NHQC protocols, achieving higher fidelity and enhanced resilience against spontaneous emission and Rabi frequency fluctuations. These findings suggest that TONHQC as a promising approach for realizing high-fidelity holonomic quantum gates in Rydberg atom systems, paving the way for scalable and fault-tolerant quantum computation.
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.
Nonadiabatic holonomic quantum computation (NHQC) has attracted significant attention due to its fast evolution and the geometric nature-induced resilience to local noises. However, its long operation time and complex physical implementation make it hard to surpass the dynamical scheme, and thus hindering its wide application. Here, we present to implement NHQC with the shortest path under some conditions, through the inverse Hamiltonian engineering technique, which posseses higher fidelity and stronger robustness than previous NHQC schemes. Meanwhile, the gate performance in our scheme can be further improved by using the proposed composite dynamical decoupling pulses, which can efficiently improve both the gate fidelity and robustness, making our scheme outperform the optimal dynamical scheme in a certain parameter range. Remarkably, our scheme can be readily implemented with Rydberg atoms, and a simplified implementation of the controlled-not gate in the Rydberg blockade regime can be achieved. Therefore, our scheme represents a promising progress towards future fault-tolerant quantum computation in atomic systems.
Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault-tolerant quantum computation, owing to its robustness against operational noise. However, because of the parametric restrictions in previous schemes, the main robust advantage of holonomic quantum gates is reduced. Here, we experimentally demonstrate a solution scheme, obtaining nonadiabatic holonomic single-qubit quantum gates with optimal control in a trapped 171Yb+ ion based on a three-level system with resonant driving, which also has the advantages of rapid evolution and convenient implementation. Compared with previous geometric gates and conventional dynamical gates, the superiority of our scheme is that it is more robust against control amplitude errors, which is confirmed by the gate infidelity as measured by both quantum-process tomography and random benchmarking methods. In addition, we outline how nontrivial two-qubit holonomic gates can also be realized using currently available experimental technology. Thus, our experiment confirms the feasibility of this robust and fast holonomic quantum-computation strategy.
For circuit-based quantum computation, experimental implementation of a 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 171Yb+ 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, our experiments share both the advantages of fast nonadiabatic evolution and robustness against systematic errors. Therefore, our experiments confirm a promising method for fast and robust holonomic quantum computation.