论文标题
非线性动力学系统和有效量子算法的前景的线性嵌入
Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms
论文作者
论文摘要
大型非线性动力系统的仿真，包括通过双曲线偏微分方程离散化产生的系统，可以是计算要求的。这种系统在流体和动力学计算等离子体物理学中都很重要。这激发了探索未来错误校正的量子计算机是否比任何经典计算机都能更有效地执行这些模拟。我们描述了一种将任何有限的非线性动力学系统映射到无限线性动力学系统（嵌入）的方法，并详细介绍了该方法的三种特定情况，与以前研究的映射相对应。然后，我们探索一种使用有限线性系统（截断）近似产生的无限线性系统的方法。如果非线性计算机的变量数量足够弱，则使用仅在非线性系统变量数量中的对数量子位数，可以模拟截短的系统近似输出数量。还讨论了三种详细嵌入策略的计算效率的其他方面。
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously-studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.
