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.
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.
The nonadiabatic holonomic quantum computation (NHQC) has received great attention for decades, however, there are many challenges to its implementation in experiments. To further shorten the evolution time is the first challenge to be conquered to realize high-fidelity quantum gates in NHQC. In this paper, we propose a controlled two-qubit model in Rydberg atoms to realize nonadiabatic holonomic quantum gates, where the evolution time is extremely decreased and the influences of several kinds of noises are minimized by utilizing the time-optimal-control technique on the target atom. In addition, we can construct arbitrary geometric gates by selecting the appropriate parameters in our model. Furthermore, numerical simulations for the $\mathrm{C}\ensuremath{-}T$ gate and $\mathrm{C}\ensuremath{-}\sqrt{H}$ gate based on the master equation show that the fidelities of geometric gates obtained in our model are still very high even though noises are considered, which demonstrates the robustness of our protocol. It is worth noting that the controlled two-qubit model may pave the way to realize fault-tolerant quantum computation in the future.
We propose a one-step scheme to implement the time-optimal nonadiabatic holonomic three-qubit controlled gates in Rydberg atoms by modulating Rabi frequencies of driving fields on the target atom. We perform the time-optimal operations following the brachistochrone curve, after which the scheme manifests completely different characteristics in contrast to the conventional nonadiabatic holonomic quantum computation (NHQC) that all operations require exactly the same evolution time, even for small angular rotations. Since the present three-qubit controlled-gate scheme significantly reduces the evolution time, the influence of decoherence can be greatly reduced. On the other hand, the robustness on the systematic error can also be guaranteed by the feature of geometric phase. The simulation through master equation verifies the high fidelity and robustness of our scheme. Although we use the Rydberg-atom system to verify the feasibility of our scheme, any quantum platforms capable of achieving the same form of effective Hamiltonian is feasible, which means the proposed three-qubit time-optimal-control nonadiabatic holonomic gates is independent of the particular physical platform and may have the potential for wider application.
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.
Nonadiabatic holonomic quantum computation (NHQC) is implemented by fast evolution processes in a geometric way to withstand local noises. However, recent works of implementing NHQC are sensitive to the systematic noise and error. Here, we present a path-optimized NHQC (PONHQC) scheme based on the non-Abelian geometric phase, and find that a geometric gate can be constructed by different evolution paths, which have different responses to systematic noises. Due to the flexibility of the PONHQC scheme, we can choose an optimized path that can lead to excellent gate performance. Numerical simulation shows that our optimized scheme can greatly outperform the conventional NHQC scheme, in terms of both fidelity and robustness of the gates. In addition, we propose to implement our strategy on superconducting quantum circuits with decoherence-free subspace encoding with the experiment-friendly two-body exchange interaction. Therefore, we present a flexible NHQC scheme that is promising for the future robust quantum computation.
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.
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus faster gate operations are highly desired. Here, we propose a nonadiabatic holonomic quantum-computation (NHQC) scheme with detuned interactions on a $\mathrm{\ensuremath{\Delta}}$-type three-level system, which combines the time-optimal control technique with the time-independent detuning adjustment to further accelerate universal gate operations, so that the gate time can be greatly shortened within the hardware limitation, and thus high-fidelity gates can be obtained. Meanwhile, our numerical simulations show that the gate robustness is also stronger than previous schemes. Finally, we present an implementation of our proposal on superconducting quantum circuits, with a decoherence-free subspace encoding, based on the experimentally demonstrated parametrically tunable coupling technique, which simplifies previous investigations. Therefore, our protocol provides a more promising alternative for future fault-tolerant quantum computation.