[Paper Review] Universally shortcuts to adiabatic passage for generation of Greenberger-Horne-Zeilinger states by transitionless quantum driving

Ye‐Hong Chen, Yan Xia+2 more|arXiv (Cornell University)|Nov 25, 2014

Quantum Information and Cryptography3 citations

TL;DR

This paper proposes a fast, robust scheme to generate Greenberger-Horne-Zeilinger (GHZ) states in a three-atom system using transitionless quantum driving combined with quantum Zeno dynamics and non-resonant lasers. By constructing shortcuts to adiabatic passage, the method achieves high-fidelity GHZ state preparation in significantly reduced time while maintaining resilience against decoherence and operational errors.

ABSTRACT

Berry's approach on quantum driving shows how to set a Hamiltonian which drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final result of an adiabatic process in a shorter time. In this paper, motivated by transitionless quantum driving, we construct shortcuts to adiabatic passage in a three-atom system to create the Greenberger-Horne-Zeilinger states with the help of quantum Zeno dynamics and of non-resonant lasers. The influence of various decoherence processes is discussed by numerical simulation and the result proves that the scheme is fast and robust against decoherence and operational imperfection.

Motivation & Objective

• To overcome the slow speed of conventional adiabatic processes in preparing entangled Greenberger-Horne-Zeilinger (GHZ) states.
• To mitigate decoherence and operational imperfections that limit the fidelity of quantum state preparation in practice.
• To develop a shortcut-based approach that accelerates adiabatic state preparation while preserving the final state fidelity.
• To integrate quantum Zeno dynamics and non-resonant lasers to enhance control and stability in the state generation protocol.

Proposed method

• Adopt Berry's transitionless quantum driving framework to design a Hamiltonian that drives the system along instantaneous eigenstates of a reference Hamiltonian.
• Implement quantum Zeno dynamics to suppress unwanted transitions and stabilize the target state during evolution.
• Utilize non-resonant lasers to mediate interactions between atoms and enable precise control over the system's dynamics.
• Construct shortcuts to adiabatic passage that eliminate the need for slow evolution while maintaining the final state of the adiabatic process.
• Formulate the effective Hamiltonian and control fields to ensure fast and accurate evolution toward the desired GHZ state.
• Perform numerical simulations to evaluate the scheme’s performance under realistic decoherence and operational imperfection models.

Experimental results

Research questions

• RQ1 Can transitionless quantum driving be effectively applied to generate GHZ states in a three-atom system with high fidelity?
• RQ2 How does the combination of quantum Zeno dynamics and non-resonant lasers improve the robustness of GHZ state preparation?
• RQ3 To what extent does the proposed scheme mitigate decoherence and operational errors compared to standard adiabatic protocols?
• RQ4 What is the minimum evolution time required to achieve high-fidelity GHZ state generation using this shortcut approach?
• RQ5 How does the system's fidelity scale under realistic noise and control imperfections in the proposed scheme?

Key findings

• The proposed scheme achieves high-fidelity preparation of Greenberger-Horne-Zeilinger states in a significantly shorter time than conventional adiabatic processes.
• Numerical simulations confirm that the scheme remains robust against various decoherence processes, including spontaneous emission and dephasing.
• The integration of quantum Zeno dynamics effectively suppresses unwanted transitions, enhancing state stability during evolution.
• Non-resonant lasers enable effective coupling between atoms without inducing unwanted transitions, improving control precision.
• The method maintains high fidelity even under operational imperfections, demonstrating practical feasibility for experimental realization.
• The shortcut-based approach successfully replicates the final state of adiabatic evolution while drastically reducing the required evolution time.