用星分解模拟稀疏哈密顿算子
Simulating sparse Hamiltonians with star decompositions
摘要：
我们提出了一个有效的算法来模拟由于稀疏哈密顿量的时间演化。根据哈密顿量H作用于时间t的空间的最大次数d和维数N，该算法使用（d^2（d + log * N））||Ht||）^{1 + o（1）}查询。这提高了Berry、Ahokas、Cleve和Sanders的稀疏哈密顿模拟算法的复杂性，其尺度类似于（d^4（log * N））||Ht||）^{1 + o（1）}。为了实现这一点，我们分解成一个小的哈密尔顿的非零条目的图形具有的属性，每个连接的组件是一个明星，并有效地模拟这些作品的一般稀疏哈密尔顿。
英文摘要：
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d^2(d+log* N)||Ht||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||Ht||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
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