论文标题
使用dyson系列的时间相关微分方程的量子算法
Quantum algorithm for time-dependent differential equations using Dyson series
论文作者
论文摘要
时间依赖性线性微分方程是需要在古典物理学中解决的常见问题类型。在这里，我们提供了一种量子算法，用于求解时间依赖的线性微分方程，并具有对误差和衍生物的对数依赖性的对数依赖性。与往常一样，对与维度的复杂性缩放的经典方法有指数级的改进，并提醒解决方案在量子状态的振幅中编码。我们的方法是在线性方程系统中编码Dyson系列，然后通过最佳量子线性方程求解器求解。我们的方法在与时间无关的微分方程的情况下还提供了一种简化的方法。
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence of the complexity on the error and derivative. As usual, there is an exponential improvement over classical approaches in the scaling of the complexity with the dimension, with the caveat that the solution is encoded in the amplitudes of a quantum state. Our method is to encode the Dyson series in a system of linear equations, then solve via the optimal quantum linear equation solver. Our method also provides a simplified approach in the case of time-independent differential equations.
