A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.
Recently,Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution,which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one.Later,they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database.In the present paper,following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys.Rev.A 65 042308],if within the small symmetric evolution interval defined by Zhang et al.,a local adiabatic evolution is performed instead of the original "global" one,this "new" algorithm exhibits slightly better performance,although they are progressively equivalent with M increasing.In addition,the proof of the optimality for this partial evolution based local adiabatic search when M=1 is also presented.Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search,which are found to have the same phenomenon above,are also discussed.
In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial and final Hamiltonians are one-dimensional projector Hamiltonians on the corresponding ground state.After some simple analysis,we find the time complexity improvement is always accompanied by the increase of some other "complexities" that should be considered.But this just gives the implication that more feasibilities can be achieved in adiabatic evolution based quantum algorithms over the circuit model,even though the equivalence between the two has been shown.In addition,we also give a rough comparison between these different models for the speedup of the problem.
为了解决目前的关键蛋白质预测方法对生物功能的分析不够深入的情况,利用蛋白质复合物信息,提出1种基于随机游走模型,结合蛋白质相互作用网络中的边聚集系数等数据来预测关键蛋白质的RWP(random walk method for predicting essential proteins)算法。在酿酒酵母(Saccharomyces cerevisiae)蛋白质相互作用网络上,以敏感度、特异性、阳性预测值、阴性预测值、准确率等5个统计学指标为评价标准,将RWP与介数中心性、度中心性、信息中心性、CSC算法及LIDC算法等5种用于预测关键蛋白质的方法进行对比实验。结果表明:RWP在关键蛋白质识别率等方面优于这5种测度方法,它具有较好的预测关键蛋白质的性能。
