Realization of quantum computing requires the development of high-fidelity quantum gates that are resilient to decoherence, control errors, and environmental noise. While non-adiabatic holonomic quantum computation (NHQC) offers a promising approach, it often necessitates system-specific adjustments. This work presents a versatile scheme for implementing NHQC gates across multiple qubit systems by optimizing multiple degrees of freedom using a genetic algorithm. The scheme is applied to three qubit systems: ensemble rare-earth ion (REI) qubits, single REI qubits, and superconducting transmon qubits. Numerical simulations demonstrate that the optimized gate operations are robust against frequency detuning and induce low off-resonant excitations, making the scheme effective for advancing fault-tolerant quantum computation across various platforms.
Realization of quantum computing requires the development of high-fidelity quantum gates that are resilient to decoherence, control errors, and environmental noise. While non-adiabatic holonomic quantum computation (NHQC) offers a promising approach, it often necessitates system-specific adjustments. This work presents a versatile scheme for implementing NHQC gates across multiple qubit systems by optimizing multiple degrees of freedom using a genetic algorithm. The scheme is applied to three qubit systems: ensemble rare-earth ion (REI) qubits, single REI qubits, and superconducting transmon qubits. Numerical simulations demonstrate that the optimized gate operations are robust against frequency detuning and induce low off-resonant excitations, making the scheme effective for advancing fault-tolerant quantum computation across various platforms.
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.
ABSTRACT Nonadiabatic holonomic quantum computation (NHQC) leverages non‐Abelian geometric phases within a nonadiabatic framework to achieve fast and robust quantum gate operations. However, the practical implementation of NHQC is challenged by the imperfect control inherent in experimental environments. Ensuring deep suppression of control error is critical. In this work, we propose a dynamically optimized NHQC scheme to construct universal super‐robust holonomic quantum gates. The proposed scheme is implemented by strategically designing a set of dynamically correcting pulses to achieve cyclic evolution, while ensuring that unwanted and disruptive dynamical phase elements, including previously neglected cross‐coupling terms, are not accumulated. This constructed super‐robust NHQC scheme efficiently safeguards the cyclic evolution process and makes the holonomic gate immune to control error by effectively correcting the error up to the fourth order. Furthermore, when integrated with decoherence‐free subspace (DFS) encoding in superconducting quantum circuits, our scheme can achieve high‐fidelity holonomic gates, and demonstrate robust resilience against both control errors and collective dephasing errors. Consequently, our work offers a promising pathway toward the realization of scalable and fault‐tolerant holonomic 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.
The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all qubits so that high-fidelity and robust quantum manipulations on them can be achieved. One of the promising approaches is to use geometric phases in the construction of universal quantum gates, due to their intrinsic robustness against certain types of local noise. However, due to limitations in previous implementations, the noise-resilience feature of nonadiabatic holonomic quantum computation (NHQC) still needs to be improved. Here, in combination with the dynamical-correction technique, we propose a general protocol of universal NHQC with simplified control, which can greatly suppress the effect of the accompanied X errors, retaining the main merit of geometric quantum operations. Numerical simulation shows that the performance of our gate can be much better than that of previous protocols. Remarkably, when incorporating a decoherence-free subspace encoding for the collective dephasing noise, our scheme can also be robust against the involved Z errors. In addition, we also outline the physical implementation of the protocol, which is insensitive to both X and Z errors. Therefore, our protocol provides a promising strategy for scalable fault-tolerant quantum computation.
Holonomic quantum gates offer a promising approach for achieving high fidelity and robustness in quantum computation by leveraging geometric phases to suppress the influence of noise. However, existing schemes often suffer from limitations such as complex segmented evolution paths and an inability to implement certain gates, including those with a geometric phase of 𝜋𝜋. In this work, we propose a circular-path holonomic quantum gate scheme with multiple degrees of freedom, which enables the realization of any single-qubit gate, including gates with a geometric phase of 𝜋𝜋. The scheme allows for the optimization of pulse performance, effectively mitigating control errors in both the addressing frequency and Rabi frequency. Applied to a Rydberg-atoms system, numerical simulations demonstrate high fidelity and robustness against control errors, with fidelities exceeding 99.97% under various conditions. This work addresses the limitations of previous schemes and provides a flexible framework for implementing robust quantum gates in three-level quantum systems.
The schmeme of nonadiabatic holonomic quantum computation (NHQC) offers an error-resistant method for implementing quantum gates, capable of mitigating certain errors. However, the conventional NHQC schemes often entail longer operations concerning standard gate operations, making them more vulnerable to the effects of quantum decoherence. In this research, we propose an implementation of the Super-Robust NHQC scheme within the Decoherence-Free Subspace (DFS). SR-NHQC has demonstrated robustness against Global Control Errors (GCEs). By utilizing capacitance-coupled transmon qubits within a DFS, our approach enables universal gate operations on a scalable two-dimensional square lattice of superconducting qubits. Numerical simulations demonstrate the practicality of SR-NHQC in DFS, showcasing its superiority in mitigating GCEs and decoherence effects compared to conventional NHQC schemes. Our work presents a promising strategy for advancing the reliability of quantum computation in real-world applications.