Hamiltonian Simulation in the Interaction Picture
Hamiltonian Simulation in the Interaction Picture
复制标题
交互图中的哈密顿模拟
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
N. Wiebe
中科院分区：
文献类型：
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作者：
G. Low;N. Wiebe
我们提出了一种基于截断戴森级数的低空间开销模拟算法，用于依赖时间的量子动力学。该算法通过转换到交互图来模拟与时间无关的哈密顿量，其中某些部分是与时间相关的。这可以提供有利的复杂性权衡，因为与原始哈密顿量相比，算法随时间相关分量的导数呈指数级扩展。我们表明，这会导致模拟某些类别的对角主导哈密顿量的门复杂度呈指数级提高。此外，我们还表明，这可以减少模拟具有任意长程相互作用的时间$t$的$N$位哈伯德模型的门复杂度缩放，并将类似大小的平面波基础内的量子化学模拟成本从$widetilde{mathcal{O}}(N^{11/3}t)$降低到$widetilde{mathcal{O}}(N^2t)$。我们还展示了模拟稀疏时间相关哈密顿量的查询复杂性的二次改进，这可能是独立的兴趣。
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture, where some portions are made time-dependent. This can provide a favorable complexity trade-off as the algorithm scales exponentially better with derivatives of the time-dependent component than the original Hamiltonian. We show that this leads to an exponential improvement in gate complexity for simulating some classes of diagonally dominant Hamiltonian. Additionally we show that this can reduce the gate-complexity scaling for simulating $N$-site Hubbard models for time $t$ with arbitrary long-range interactions as well as reduce the cost of quantum chemistry simulations within a similar-sized plane-wave basis to $widetilde{mathcal{O}}(N^2t)$ from $widetilde{mathcal{O}}(N^{11/3}t)$. We also show a quadratic improvement in query complexity for simulating sparse time-dependent Hamiltonians, which may be of independent interest.