论文标题
克服晶格量表理论的量子模拟中的指数级缩放
Overcoming exponential volume scaling in quantum simulations of lattice gauge theories
论文作者
论文摘要
使用经典计算机对量子场理论的实时演变需要以晶格位点数量呈指数缩放的资源。由于基本不同的计算策略，量子计算机原则上可用于对第一原理的这些动态进行详细研究。在执行此类计算之前，重要的是要确保所使用的量子算法没有与体积成倍扩展的成本。在这些程序中，我们提出了一个有趣的测试案例：在2+1个维度中，不含规格冗余的紧凑型u（1）仪表理论的表述。对量子电路的幼稚实现的栅极计数与音量呈指数缩放。我们讨论了如何通过执行操作员重新定义来降低哈密顿量的非本地性来打破指数缩放。虽然我们仅将一种理论研究为测试案例，但指数式栅极缩放可能会持续使用其他规格理论的表述，包括较高维度的非亚伯理论。
Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in principle be used to perform detailed studies of these dynamics from first principles. Before performing such calculations, it is important to ensure that the quantum algorithms used do not have a cost that scales exponentially with the volume. In these proceedings, we present an interesting test case: a formulation of a compact U(1) gauge theory in 2+1 dimensions free of gauge redundancies. A naive implementation onto a quantum circuit has a gate count that scales exponentially with the volume. We discuss how to break this exponential scaling by performing an operator redefinition that reduces the non-locality of the Hamiltonian. While we study only one theory as a test case, it is possible that the exponential gate scaling will persist for formulations of other gauge theories, including non-Abelian theories in higher dimensions.
