论文标题
基于测量的亚伯晶格理论的量子模拟
Measurement-based quantum simulation of Abelian lattice gauge theories
论文作者
论文摘要
晶格计理论的数值模拟是高能物理学中必不可少的工具，预计其量子模拟将来将成为量子计算机的主要应用。在这项工作中，对于$ d $时空维度中的Abelian晶格量规理论，我们定义了一个纠缠的资源状态（广义群集状态），它反映了量规理论的时空结构。我们表明，根据以前的测量结果对基础进行适应的基础测量，对边界上的量规理论进行了确定性的汉密尔顿量子模拟。我们的构造包括$（2+1）$ - 维数的Abelian晶格规程，以三维群集状态进行了模拟，并概括地模拟了Wegner的晶格模型$ M _ {（d，n）} $，涉及更高格式的Abelian Gauge场。我们证明，广义群集状态与与边界上模拟仪表理论的对称性相关的广义全局对称性具有对称性保护的拓扑顺序。我们的程序可以推广到在费米子资源状态下对基塔耶夫的Majorana链的模拟。我们还研究了具有两量量测量和选择后的假想时间量子模拟，以及经典的量词对应关系，其中模型$ M _ {（d，n）} $的统计分区函数写作是两Qubit测量碱基的乘积与一般群集状态的波浪函数之间的重叠。
Numerical simulation of lattice gauge theories is an indispensable tool in high energy physics, and their quantum simulation is expected to become a major application of quantum computers in the future. In this work, for an Abelian lattice gauge theory in $d$ spacetime dimensions, we define an entangled resource state (generalized cluster state) that reflects the spacetime structure of the gauge theory. We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. Our construction includes the $(2+1)$-dimensional Abelian lattice gauge theory simulated on three-dimensional cluster state as an example, and generalizes to the simulation of Wegner's lattice models $M_{(d,n)}$ that involve higher-form Abelian gauge fields. We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries that are related to the symmetries of the simulated gauge theories on the boundary. Our procedure can be generalized to the simulation of Kitaev's Majorana chain on a fermionic resource state. We also study the imaginary-time quantum simulation with two-qubit measurements and post-selections, and a classical-quantum correspondence, where the statistical partition function of the model $M_{(d,n)}$ is written as the overlap between the product of two-qubit measurement bases and the wave function of the generalized cluster state.
