BIMSA >
YMSC-BIMSA量子信息讨论班
On the Algebra of Qubit Quantum States: Part I - String Diagrams, Non-Orthogonal Factorizations, and the Tropical Kernel Algebra of Parent Hamiltonians
On the Algebra of Qubit Quantum States: Part I - String Diagrams, Non-Orthogonal Factorizations, and the Tropical Kernel Algebra of Parent Hamiltonians
组织者
演讲者
雅各布·比亚蒙特
时间
2023年03月17日 09:30 至 10:30
地点
JCY-1
线上
Tencent 494 8360 9451
(2023)
摘要
We consider the algebraic properties of quantum states represented as polynomials that map binary tuples to complex numbers. Using string diagrams, we review the general factorization results previously established in joint work with Clark, and Jaksch, and explore ongoing developments related to non-orthogonal factorizations based on graded algebra expansions. By imposing a real-valued codomain restriction on these functions, penalty functions are generated that correspond to generalized Ising-type models. We recall the concept of a parent Hamiltonian, a non-negative operator that has a specific state in its zero energy sector, and explain the algebra necessary to control the kernel structure of non-negative pseudo-Boolean functions that represent parent Hamiltonians of quantum states. Our results contribute to the ongoing development of mathematical tools for analyzing and manipulating quantum states, with applications in quantum information science.
演讲者介绍
物理学家和计算机科学家，2010年从英国牛津大学博士毕业，之后同时在哈佛大学、牛津大学/新加坡国立大学联合项目任博士后。2012年加入意大利都灵ISI研究所并领导量子科学组。2017年起加入莫斯科Skoltech研究院，从2019年开始担任该机构量子信息实验室主任。长期致力于量子计算机科学和现代量子理论的研究，因奠定了量子机器学习的理论基础而闻名，并贡献了多个普适性证明。此外他在量子张量网络的数学理论发表了多项成果，提供了用图形化的语言重新理解量子物理中的过程的新观念。曾荣获郎格特希金斯奖等多个国际奖项。