论文标题
用于计算非线性偏微分方程可观察到的量子算法
Quantum algorithms for computing observables of nonlinear partial differential equations
论文作者
论文摘要
我们构建量子算法以使用M初始数据计算非线性PDE的物理可观察物。基于使用级别集方法在非线性和线性PDE之间进行精确映射，可以使用独立于M的计算成本来执行这些非线性Hamilton-Jacobi和标量双曲线PDE的新量子算法，以进行任意非线性。根据初始数据的详细信息，它还可以在PDE的维度和计算其可观察物的错误中显示到指数优势。对于一般的非线性PDE，在较大的M极限中可能相对于M的量子优势。
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear Hamilton-Jacobi and scalar hyperbolic PDEs can be performed with a computational cost that is independent of M, for arbitrary nonlinearity. Depending on the details of the initial data, it can also display up to exponential advantage in both the dimension of the PDE and the error in computing its observables. For general nonlinear PDEs, quantum advantage with respect to M is possible in the large M limit.
