寻找非阿贝尔格点规范理论哈密顿模拟的有效公式
Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
摘要：
格点规范理论（LGT）的哈密顿公式是量子模拟的最自然的框架，量子模拟是一个随着量子计算算法和硬件的进步而发展的研究领域。因此，它仍然是一个重要的任务，以确定最准确的，而计算经济，哈密顿公式（S）在这样的理论，考虑到必要的截断施加在希尔伯特空间的规范玻色子与任何有限的计算资源。本文是第一步解决这个问题的情况下，非阿贝尔的LGT，这进一步需要施加非阿贝尔高斯定律的希尔伯特空间，引入额外的计算复杂性。针对1+1维SU（2）LGT与物质耦合的情形，分析了Kogut-Susskind框架中物理希尔伯特空间维数对边界条件、系统大小和规范玻色子激发截止的依赖关系.这种依赖关系的频谱和动力学的准确性的影响进行检查，并研究了（经典的）计算资源的要求，这些考虑。除了著名的角动量公式的理论，纯费米子和纯玻色子公式（开边界条件）的情况下，和环弦强子公式进行了分析，随着一个简单的讨论量子链接模型相同的理论。在使用环弦强子框架工作时发现明显的优势，该框架使用一套完整的规范不变算子先验地实现非阿贝尔高斯定律。虽然小格子的数值分析研究这项工作，只考虑最简单的算法，一系列的结论将适用于更大的系统，并可能更高的维度。
英文摘要：
Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore, remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories, considering the necessary truncation imposed on the Hilbert space of gauge bosons with any finite computing resources. This paper is a first step toward addressing this question in the case of non-Abelian LGTs, which further require the imposition of non-Abelian Gauss's laws on the Hilbert space, introducing additional computational complexity. Focusing on the case of SU(2) LGT in 1+1 D coupled to matter, a number of different formulations of the original Kogut-Susskind framework are analyzed with regard to the dependence of the dimension of the physical Hilbert space on boundary conditions, system's size, and the cutoff on the excitations of gauge bosons. The impact of such dependencies on the accuracy of the spectrum and dynamics is examined, and the (classical) computational-resource requirements given these considerations are studied. Besides the well-known angular-momentum formulation of the theory, the cases of purely fermionic and purely bosonic formulations (with open boundary conditions), and the Loop-String-Hadron formulation are analyzed, along with a brief discussion of a Quantum Link Model of the same theory. Clear advantages are found in working with the Loop-String-Hadron framework which implements non-Abelian Gauss's laws a priori using a complete set of gauge-invariant operators. Although small lattices are studied in the numerical analysis of this work, and only the simplest algorithms are considered, a range of conclusions will be applicable to larger systems and potentially to higher dimensions.
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