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On the General Class of Models of Adiabatic Evolution

机译：关于绝热演化的一般模型

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摘要

The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.
机译：提出了绝热演化的一般模型，以加快量子搜索问题中的绝热计算速度。结果表明，通过将随时间变化的哈密顿量的基态能量暂时增加到适当的数量，量子计算可以执行时间复杂度为O（1）的计算。但是还知道，如果系统的初始状态和最终状态之间的重叠为零，则基于绝热演化的广义模型的计算可能会完全崩溃。在本文中，我们发现了此类绝热演化算法的另一个严重局限性，应在应用程序中加以考虑。也就是说，如果系统中哈密顿量的插值路径选择不当，则这种为解决量子搜索问题而设计的演化仍然有可能完全失败，而通常的绝热演化可以相对有效地完成相同的工作。这意味着在绝热计算中并不总是建议使用非线性路径。相反，通常简单的绝热演变可能足以有效使用。

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  • 来源
    《Open Systems & Information Dynamics》 |2016年第3期|1650016.1-1650016.9|共9页
  • 作者

    Jie Sun; Songfeng Lu; Fang Liu;

  • 作者单位

    School of Computer Science and Technology Huazhong University of Science and Technology Wuhan 430074, China,College of Educational Information and Technology Hubei Normal University Huangshi 435002, China;

    School of Computer Science and Technology Huazhong University of Science and Technology Wuhan 430074, China;

    School of Computer Science and Technology Huazhong University of Science and Technology Wuhan 430074, China;

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  • 正文语种 eng
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  • 关键词

    Quantum computing; adiabatic evolution; interpolating paths;

    机译：量子计算;绝热演化插补路径;

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