一些计算积和的算法的物理学推导
Physics-inspired derivations of some algorithms for computing the permanent
摘要：
我们提供了物理启发推导出的一些算法计算永久的矩阵。特别是，我们制定的计算永久格拉斯曼积分，可被视为一个相互作用的多费米子问题。应用离散的Hubbard Stratonovich解耦，然后给出近似方案，相当于熟悉的行列式蒙特卡洛算法。这导致了著名的估计的Godsil-Gutman和Karmarkar等人的初等推导。另一个straightfoward操纵的格拉斯曼积分，利用规范不变性，给出了有效的精确公式格林。除了这些已知的结果，我们还给出了一些额外的估计和公式，在我们的制定是自然的。
英文摘要：
We provide physics-inspired derivations of a number of algorithms for computing the permanent of a matrix. In particular we formulate the computation of the permanent as a Grassmann integral that may be viewed as an interacting many-fermion problem. Applying a discrete Hubbard-Stratonovich decoupling then gives approximation schemes that are equivalent to the familiar determinant Monte Carlo algorithm. This leads to elementary derivations of the well-known estimators of Godsil-Gutman and Karmarkar et al. Another straightfoward manipulation of the Grassmann integral, making use of gauge invariance, gives the efficient exact formula of Glynn. In addition to these known results we also give some additional estimators and formulas that are natural in our formulation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
