论文标题
张量晶格场理论，应用于重新归一化组和量子计算
Tensor lattice field theory with applications to the renormalization group and quantum computing
论文作者
论文摘要
我们讨论了在晶格QCD背景下研究的一系列模型序列的统计抽样的成功和局限性，并强调需要新方法来处理有限密度和实时演变。我们表明，这些晶格模型可以使用张力方法进行重新重新制定，在该方法中，路径综合形式主义中的现场积分被离散的总和代替。这些配方涉及各种类型的二元性，并提供了确切的粗粒剂公式，可以将其与截断结合使用以获得Wilson Rentoralization Group计划的实际实现。张量重新构造是自然离散的，并提供可管理的转移矩阵。将截断与时间连续限制相结合，我们得出了适合执行量子模拟实验的汉密尔顿人，例如使用冷原子，或在现有的量子计算机上进行编程。我们回顾了有关非紧缩标量模型，超对称模型，经济的四维算法，高斯法律的噪声强制执行，对称性保留截断和拓扑考虑的进展的最新进展。我们讨论与其他张量网络方法的联系。
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group program. Tensor reformulations are naturally discrete and provide manageable transfer matrices. Combining truncations with the time continuum limit, we derive Hamiltonians suitable to perform quantum simulation experiments, for instance using cold atoms, or to be programmed on existing quantum computers. We review recent progress concerning the tensor field theory treatment of non-compact scalar models, supersymmetric models, economical four-dimensional algorithms, noise-robust enforcement of Gauss's law, symmetry preserving truncations and topological considerations. We discuss connections with other tensor network approaches.
