Effect of local minima on adiabatic quantum optimization.
Effect of local minima on adiabatic quantum optimization.
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DOI：
10.1103/physrevlett.100.130503
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发表时间：
2007-09
影响因子：
8.6
通讯作者：
M. H. S. Amin
中科院分区：
文献类型：
--
作者：
M. H. S. Amin
我们提出了一种微扰方法来估计绝热量子优化的光谱间隙，基于问题的哈密顿量的能级结构。我们表明，对于具有指数大量的局部极小值接近全局极小值的问题，差距变得指数小，使计算时间指数长。绝热量子计算的量子优势可以仅通过局部绝热演化来获得，这需要在整个演化过程中的相位相干性和谱的知识。这样的问题，因此，不适合绝热量子计算。
We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.