[Paper Review] Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion

Ming-Zhong Ai, Sai Li+6 more|arXiv (Cornell University)|Jan 19, 2021

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes and experimentally demonstrates nonadiabatic holonomic single-qubit quantum gates in a trapped 171Yb+ ion using a four-level system with two dark paths, achieving high-fidelity operations via resonant microwave drives. The implementation achieves a gate fidelity above 98.75% via randomized benchmarking and shows enhanced robustness against Rabi frequency errors compared to prior nonadiabatic schemes, validating a promising path toward fast, robust holonomic quantum computation.

ABSTRACT

For circuit-based quantum computation, experimental implementation of 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 $^{171}\mathrm{Yb}^{+}$ 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 on three-level systems, our experiment share both the advantage of fast nonadiabatic evolution and the merit of robustness against systematic errors, and thus retains the main advantage of geometric phases. Therefore, our experiment confirms a promising method for fast and robust holonomic quantum computation.

Motivation & Objective

• To develop a fast and robust method for single-qubit quantum gates in trapped ions that leverages geometric phase properties.
• To overcome the limitations of adiabatic holonomic quantum computation, such as slow operation speed due to decoherence.
• To demonstrate that nonadiabatic holonomic gates with two dark paths preserve noise resilience while enabling faster evolution.
• To validate the feasibility of universal nonadiabatic holonomic quantum computation using current trapped-ion technology.
• To extend the framework to nontrivial two-qubit gates for universal quantum computation.

Proposed method

• Utilizes a four-level system in a 171Yb+ ion with hyperfine levels |0⟩, |1⟩, |2⟩, and |a⟩ to implement nonadiabatic holonomic gates via resonant microwave drives.
• Employs a dressed-state approach to create two degenerate dark states, enabling geometric phase accumulation under nonadiabatic evolution.
• Applies a two-step cyclic evolution protocol where the system evolves along two distinct dark paths, each accumulating a geometric phase.
• Uses quantum process tomography and randomized benchmarking (RB) to characterize gate fidelity and robustness.
• Designs a nontrivial two-qubit control-phase gate using the ion's internal state and motional phonon mode via Raman coupling.
• Applies rotating-wave approximation and transforms the Hamiltonian into an effective interaction picture to realize conditional geometric phases.

Experimental results

Research questions

• RQ1 Can nonadiabatic holonomic single-qubit gates be experimentally realized in a trapped ion with two dark paths while maintaining high fidelity?
• RQ2 Does the proposed scheme achieve enhanced robustness against Rabi frequency errors compared to conventional nonadiabatic holonomic schemes?
• RQ3 Can the same framework be extended to implement nontrivial two-qubit entangling gates for universal quantum computation?
• RQ4 To what extent does decoherence limit gate fidelity in this nonadiabatic holonomic scheme?
• RQ5 Is the use of resonant microwave drives sufficient to achieve high-fidelity geometric gates without requiring complex laser control?

Key findings

• The experiment achieved an average gate fidelity of 98.75% as measured by randomized benchmarking, primarily limited by coherence time.
• The nonadiabatic holonomic gates demonstrated superior robustness against Rabi frequency errors compared to previous nonadiabatic schemes under the same maximum driving amplitude.
• Theoretical and experimental results show excellent agreement, particularly when decoherence effects are included in simulations.
• The two-qubit control-phase gate was realized in a 171Yb+ ion using spin-phonon entanglement, with a gate time of approximately 500 μs and effective Rabi frequency of ~100 μs⁻¹.
• The scheme is compatible with current trapped-ion platforms and enables universal robust nonadiabatic holonomic quantum computation.
• The presence of two dark paths ensures that the geometric phase is protected against certain systematic errors, preserving the noise-resilience feature of holonomic quantum computation.