论文标题
迈向量子计算机上晶格量规理论的可扩展模拟
Toward scalable simulations of Lattice Gauge Theories on quantum computers
论文作者
论文摘要
由于所需资源的指数缩放,晶格计理论中实时动力学的模拟特别困难。另一方面,量子算法可以通过对自由度数的多项式依赖性执行相同的计算。然而,对于在任意维度中的晶格计理论的模拟模拟,量规范围是动态变量,除了粒子场之外,量规场是动态变量。此外,存在几种选择,用于在晶格上离散粒子和量规场,每个选择都以不同的价格在量子寄存器的大小和电路深度方面以不同的价格出现。在这里,我们为$ u(1)$量表理论的实时演变(例如量子电动力学)提供了一种资源计数,使用粒子的Wilson Fermion表示,以及量规场的量子链接模型方法。我们研究了使用量子电路的经典模拟,研究通量弦的现象,分解为真正的双维模型,并讨论了我们离散化选择的优势,以模拟更具挑战性的$ SU(N)$ GAUGE理论,例如量子染色体动力学。
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same calculation with a polynomial dependence on the number of degrees of freedom. A precise estimation is however particularly challenging for the simulation of lattice gauge theories in arbitrary dimensions, where, gauge fields are dynamical variables, in addition to the particle fields. Moreover, there exist several choices for discretizing particles and gauge fields on a lattice, each of them coming at different prices in terms of qubit register size and circuit depth. Here we provide a resource counting for real-time evolution of $U(1)$ gauge theories, such as Quantum Electrodynamics, on arbitrary dimension using the Wilson fermion representation for the particles, and the Quantum Link Model approach for the gauge fields. We study the phenomena of flux-string breaking up to a genuine bi-dimensional model using classical simulations of the quantum circuits, and discuss the advantages of our discretization choice in simulation of more challenging $SU(N)$ gauge theories such as Quantum Chromodynamics.