论文标题
在量子计算机上实施了数字编码的多族算法
Implementation of a digitally encoded multigrid algorithm on a quantum computer
论文作者
论文摘要
Multigrid已成为解决一些最具挑战性的现实计算问题的流行方法，例如计算流体动力学（CFD）。其原因是相对于问题大小而言，Multigrid的非常好的缩放属性通常是线性或接近线性的。在本文中，提出了一种方法，该方法可用于实现跨国算法的量子版本。该方法依赖于在整个计算过程中保持平等叠加的量子状态，以及以类似于经典计算机更相似的方式将信息以数字方式编码。这不同于许多现有的量子算法，其中信息在叠加中的量子状态的振幅中编码。该方法的核心是一种用于在叠加中共享状态之间信息的算法。为解决方案向量有效压缩的问题提供了指数加速，并且量子编译器可以有效地减少量子电路深度。
Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is often linear, or close to linear, with respect to problem size. In this paper a method is presented, which can be used to implement a quantum version of the multigrid algorithm. The method relies upon a quantum state that is maintained in a equal superposition throughout the calculation, and where information is encoded digitally in the qubits in a way more similar to a classical computer. This differs from many existing quantum algorithms where information is encoded in the amplitudes of the quantum states in the superposition. At the core of the method is an algorithm for sharing information between the states in the superposition. An exponential speedup is provided for classes of problems where the solution vector can be compressed efficiently, and where a quantum compiler can reduce the quantum circuit depth efficiently.
