论文标题
哈密顿范式以外的量子模拟：分类量子模拟
Quantum simulation beyond Hamiltonian paradigm: categorical quantum simulation
论文作者
论文摘要
随着拓扑领域理论的发展，张量类别的数学工具也被引入物理学中。传统小组理论对应于特殊类别，小组类别。张量类别可以描述高阶相互作用和对称关系，而小组理论只能描述一阶相互作用。实际上，量子电路本身构成类别。但是，目前，量子计算领域主要使用组理论作为数学工具。如果将类别理论引入量子模拟领域，则可以大大扩展量子计算机的应用范围。本文提出了一种新的动态仿真方法，分类量子模拟。在我们的范式中，量子模拟不再基于组理论的结构，而是基于张量类别的结构。这可以使许多无法有效地模拟量子模拟的系统。在本文中，我们给出了$ su（3）$ yang-mills理论的分类模拟的具体示例。它表明，分类量子模拟提供了一种新的编码方法，即紧急编码，它节省了更多的资源，而不是简化主义量子编码。此外，许多域可以在类别理论的语言中描述，该语言允许量子电路直接编码和模拟这些域。
With the development of topological field theory, the mathematical tool of the tensor category was also introduced into physics. Traditional group theory corresponds to a special category,group category. Tensor categories can describe higher-order interactions and symmetric relations, while group theory can only describe first-order interactions. In fact, the quantum circuit itself constitutes a category. However, at present, the field of quantum computing mainly uses group theory as a mathematical tool. If category theory is introduced into the field of quantum simulation, the application scope of quantum computers can be greatly expanded. This paper propose a new dynamic simulation method,categorical quantum simulation. In our paradigm quantum simulation is no longer based on the structure of the group theory, but based on the structure of the tensor category. This could enable many systems that could not be efficiently quantum simulated before.In this article we give an concrete example of the categorical simulation of $SU(3)$ Yang-Mills theory. It shows that categorical quantum simulation provides a new encoding method,emergenism encoding, which saves more qubits resources than reductionism quantum encoding. In addition, many domains can be described in the language of category theory, which allows quantum circuits to directly encode and simulate these domains.
