【讲座题目】More than perfect: ℏ-perfect graphs and their applications
【主 讲 人】许振朋（安徽大学）
【讲座时间】2026年01月08日周四上午09：00
【讲座地点】主楼C座636
【主讲人简介】许振朋教授现就职于安徽大学，毕业于南开大学陈省身数学研究所，毕业后在德国锡根大学从事博士后工作，期间获德国洪堡基金会支持。研究方向为量子力学基础问题和量子信息，专注于不同系统中的量子关联。迄今已在量子信息理论基础领域发表SCI论文四十余篇，含Physical Review Letters 8篇（第一／通讯作者4篇），Nature Communications、Science Advances、PRX Quantum 各1篇。基于以往工作，申请人荣获2021年度奥地利科学院颁发的埃伦费斯特量子基础最佳论文奖。
【讲座内容简介】A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in this work. We investigate all aspects of this interface for a special class of graphs that bears tight connections between the groundstate structures of a spin systems and topological structure of a graph. We call this class ℏ-perfect, as it extends the class of perfect and h-perfect graphs. Having an ℏ-perfect graph opens up several applications: we find efficient schemes for entanglement detection, a connection to the complexity of shadow tomography, tight uncertainty relations and a construction for computing good lower on bounds ground state energies. Conversely this also induces quantum algorithms for computing the independence number. Albeit those algorithms do not immediately promise an advantage in runtime, we show that an approximate Hamilton encoding of the independence number can be achieved with an amount of qubits that typically scales logarithmically in the number of vertices. We also we also determine the behavior of ℏ-perfectness under basic graph operations and evaluate their prevalence among all graphs.
参考文献：
[1] PRX Quantum 5, 020318, 2024
[2] arXiv: 2511.13531
