Van den Nest M, Dür W, Briegel H J
Institut für Quantenoptik und Quanteninformation der Osterreichischen Akademie der Wissenschaften, Innsbruck, Austria.
Phys Rev Lett. 2007 Mar 16;98(11):117207. doi: 10.1103/PhysRevLett.98.117207.
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum-stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum-information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and high-low temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded tree-width.
我们将一大类经典自旋模型，包括任意图上q态自旋的非均匀伊辛模型、波茨模型和时钟模型，与量子物理中的问题联系起来。更确切地说，我们展示了如何将配分函数表示为某些量子稳定器态与乘积态之间的内积。这种联系使我们能够使用量子信息理论中发展起来的强大技术，如稳定器形式主义和经典模拟技术，以统一的方式对这些模型获得一般性的见解。我们恢复并推广了几种对称性和高低温对偶性，并且为所有具有有界树宽的相互作用图提供了配分函数的有效经典评估。
