Symmetry‐Protected Quantum Adiabatic Evolution in Spontaneous Symmetry‐Breaking Transitions,Annalen Der Physik

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Symmetry‐Protected Quantum Adiabatic Evolution in Spontaneous Symmetry‐Breaking Transitions
Annalen Der Physik ( IF 2.2 ) Pub Date : 2020-02-24 , DOI: 10.1002/andp.201900471
Min Zhuang _{1,

2} , Jiahao Huang ₁ , Yongguan Ke ₁ , Chaohong Lee _{1,

2,

3}

Affiliation

Quantum adiabatic evolution describes the dynamical evolution of a slowly driven Hamiltonian. In most systems undergoing spontaneous symmetry‐breaking transitions, the symmetry‐protected quantum adiabatic evolution can still appear, even when the two lowest eigenstates become degenerate. Here, a general derivation to revisit the symmetry‐dependent transition and the symmetry‐dependent adiabatic condition (SDAC) is given. Further, based on the SDAC, an adiabatic‐parameter‐fixed sweeping scheme is used for achieving fast adiabatic evolution, which is more efficient than the linear sweeping scheme. In the limit of small adiabatic parameter, an analytic inequality is obtained for the ground state fidelity only dependent on the adiabatic parameter. The general statements are then demonstrated via two typical systems. Besides, the robustness of the symmetry‐dependent adiabatic evolution against weak symmetry‐breaking sources is studied. The findings can be tested via the techniques in quantum annealing and may provide promising applications in practical quantum technologies.

中文翻译：

自发对称突破跃迁中受对称保护的量子绝热演化

量子绝热演化描述了缓慢驱动的哈密顿量的动力学演化。在大多数经历自发对称破坏跃迁的系统中，即使两个最低本征态退化，对称保护的量子绝热演化仍会出现。在此，给出了重新推导对称依赖性跃迁和对称依赖性绝热条件（SDAC）的一般推导。此外，基于SDAC，使用绝热参数固定的扫描方案来实现快速绝热演化，这比线性扫描方案更有效。在小绝热参数的范围内，仅依赖于绝热参数获得了基态保真度的解析不等式。然后通过两个典型的系统演示一般性陈述。除了，研究了对称依赖绝热演化对弱对称破坏源的鲁棒性。这些发现可以通过量子退火技术进行测试，并可以在实际的量子技术中提供有希望的应用。

更新日期：2020-02-24

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