论文标题
为任意线性操作员生成Pauli坐标的有效算法
Efficient algorithm for generating Pauli coordinates for an arbitrary linear operator
论文作者
论文摘要
Several linear algebra routines for quantum computing use a basis of tensor products of identity and Pauli operators to describe linear operators, and obtaining the coordinates for any given linear operator from its matrix representation requires a basis transformation, which for an $\mathrm N\times\mathrm N$ matrix generally involves $\mathcal O(\mathrm N^4)$ arithmetic operations.本文中，我们提出了一种有效的算法，对于我们的特定基础转换，仅涉及$ \ mathcal o（\ mathrm n^2 \ log_2 \ log_2 \ mathrm n）$操作。由于该算法需要少于$ \ MATHCAL O（\ MATHRM n^3）$操作，因此对于大型$ \ Mathrm n $，它可以用作用于某些应用程序的量子计算算法的预处理步骤。作为演示，我们将算法应用于哈密顿量，该算法描述了相对论相互作用的自旋零玻色子系统，并使用量子计算机上的变异量子量化算法来计算地面能量。
Several linear algebra routines for quantum computing use a basis of tensor products of identity and Pauli operators to describe linear operators, and obtaining the coordinates for any given linear operator from its matrix representation requires a basis transformation, which for an $\mathrm N\times\mathrm N$ matrix generally involves $\mathcal O(\mathrm N^4)$ arithmetic operations. Herein, we present an efficient algorithm that for our particular basis transformation only involves $\mathcal O(\mathrm N^2\log_2\mathrm N)$ operations. Because this algorithm requires fewer than $\mathcal O(\mathrm N^3)$ operations, for large $\mathrm N$, it could be used as a preprocessing step for quantum computing algorithms for certain applications. As a demonstration, we apply our algorithm to a Hamiltonian describing a system of relativistic interacting spin-zero bosons and calculate the ground-state energy using the variational quantum eigensolver algorithm on a quantum computer.
