一维Burgers方程的一种有效量子算法
An efficient quantum algorithm for the one-dimensional Burgers equation
摘要：
我们分析一维经典和量子微观晶格气体模型所管辖的晶格玻尔兹曼方程在介观尺度上，通过系综平均微观实现。该模型是由伯格斯方程在宏观尺度上，通过采取限制的网格大小和时间步长都接近零，并通过执行微扰查普曼-Enskog膨胀。利用叠加和纠缠的量子算法比经典算法更有效，因为量子算法需要更少的内存。此外，其粘度可以任意小。
英文摘要：
We analyze one-dimensional classical and quantum microscopic lattice-gas models governed by a lattice Boltzmann equation at the mesoscopic scale, achieved by ensemble averaging over microscopic realizations. The models are governed by the Burgers equation at the macroscopic scale, achieved by taking the limit where the grid size and time step both approach zero and by performing a perturbative Chapman-Enskog expansion. The quantum algorithm exploiting superposition and entanglement is more efficient than the classical one because the quantum algorithm requires less memory. Furthermore, its viscosity can be made arbitrarily small.
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