In the long-time pursuit of the solution to calculate the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral approach that works at least four orders faster. In present work, the above two methods were applied to solid argon at temperatures up to $300$K, and the derived internal energy and pressure were compared with the molecular dynamics simulation as well as experimental measurements, showing that the calculation precision of our approach is about 10 times higher than that of the nested sampling method.
Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers
A quantum algorithm for additive approximation of Ising partition functions
研究了计算伊辛模型的配分函数的量子计算复杂性。我们构造了一个量子算法，用于平方格上Ising配分函数的加性近似。为此，我们利用Van den Nest、Dür和Briegel [Phys. Rev. Lett. 98，117207（2007）]及其通过基于测量的量子计算（MBQC）的解释。我们指定一个算法域，所提出的算法的工作原理，和近似规模，这决定了近似的精度。我们表明，所提出的算法做了一个非平凡的任务，这将是棘手的任何经典计算机，通过显示所提出的量子算法可解决的问题是BQP-完全的。在构造BQP完备问题时，耦合强度和磁场取复值。然而，统计物理学和计算机科学的核心兴趣伊辛模型由真实的耦合强度和磁场组成。因此，我们将所提出的算法的算法域扩展到这样一个真实的物理参数区域，并显式地计算近似尺度。我们发现，重叠映射及其MBQC解释提高了近似规模指数相比，一个简单的恒定深度量子算法。另一方面，该量子算法也为我们提供了一个部分的证据，证明即使在正方形格点上也不存在有效的经典算法来计算Ising配分函数的乘法近似.这一结果支持了所提出的量子算法在物理参数区域也做了非平凡的任务。
