论文标题
用于求解多维泊松方程的量子模拟和电路设计
Quantum simulation and circuit design for solving multidimensional Poisson equations
论文作者
论文摘要
许多方法通过使用网格技术来求解泊松方程，从而在每个维度中离散问题。这些算法中的大多数受维度的诅咒，因此它们需要指数运行时。在论文“量子算法和电路设计求解泊松方程”中，显示了量子算法在多聚仪的时间内运行的量子算法，以产生代表泊松方程溶液的量子状态。在本文中，基于该算法的扩展电路设计的量子模拟是在经典计算机上进行的。我们的目的是测试有效的电路设计，该设计可以打破量子计算机上的维度诅咒。由于希尔伯特空间的指数升高，该设计在少数Qubits上进行了优化。我们使用Microsoft的量子开发套件及其对理想量子计算机的模拟器来验证该算法的正确性。
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.
