Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum algorithm and circuit design solving the Poisson equation" a quantum algorithm is shown running in polylog time to produce a quantum state representing the solution of the Poisson equation. In this paper a quantum simulation of an extended circuit design based on this algorithm is made on a classical computer. Our purpose is to test an efficient circuit design which can break the curse of dimensionality on a quantum computer. Due to the exponential rise of the Hilbert space this design is optimized on a small number of qubits. We use Microsoft's Quantum Development Kit and its simulator of an ideal quantum computer to validate the correctness of this algorithm.

中文翻译：

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求解多维泊松方程的量子仿真和电路设计

许多方法通过使用在每个维度上离散问题的网格技术来求解泊松方程。这些算法中的大多数都受到维数诅咒的影响，因此它们需要指数运行时间。在论文“求解泊松方程的量子算法和电路设计”中，量子算法在多对数时间内运行以产生表示泊松方程解的量子态。在本文中，在经典计算机上对基于该算法的扩展电路设计进行了量子模拟。我们的目的是测试一种有效的电路设计，它可以打破量子计算机上的维数诅咒。由于希尔伯特空间的指数增长，该设计在少量量子位上进行了优化。我们使用微软的