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.
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) based on non-Abelian geometric phases can possess potential robustness advantages due to its intrinsic error-resilient features. However, rigorous geometric conditions, including cyclic evolution and parallel transport conditions, typically demand complex and error-prone control and also involve additional auxiliary resources. Moreover, the limitations of optional evolution paths in previous NHQC schemes make it difficult to avoid path segments that are heavily affected by systematic errors, thereby weakening the error resilience of holonomic gates. To address this problem, we propose a multipath NHQC scheme, which can sufficiently improve the robustness of quantum gates by flexibly correcting geometric evolution paths. Numerical simulation results show that our scheme surpasses previous NHQC schemes in suppressing systematic errors for arbitrary gate types. In addition, we provide a physical implementation based on superconducting quantum circuits, with the decoherence-free-subspace encoding and an experiment-friendly two-body exchange interaction, demonstrating the excellent compatibility of our scheme. Therefore, our scheme offers a promising alternative for future fault-tolerant quantum computation.
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a new set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.
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.
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.
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.
Nonadiabatic holonomic quantum computation provides a promising approach toward fault-tolerant quantum control, due to its simple requirements for energy level structure and intrinsic robustness stemming from non-Abelian geometric phases. However, conventional nonadiabatic holonomic quantum computation relies on segmented evolution along a specific trajectory, which not only complicates experimental control but also exacerbates decoherence effects. Meanwhile, minor deviations in systematic parameters can directly disrupt the cyclic evolution process necessary to construct holonomic gates, leading to degraded gate robustness. To address these disadvantages, we here propose a general strategy to incorporate cyclic evolution protection into the holonomic gate construction. The aim is to design on-demand trajectories by modulating pulse shapes, thereby circumventing the detrimental impact of systematic errors on cyclic evolution. Consequently, universal holonomic gates implemented through a stable cyclic evolution process can maintain lower error sensitivity. Meanwhile, in our scheme, compressing the state population in the ancillary state ensures less energy consumption, resulting in higher gate fidelity. Therefore, our work serves as a practical solution for achieving high-fidelity and robust universal quantum gates, paving the way for large-scale quantum computation.