Quantum Information Transport, Algebra Representations, Orthogonal Polynomials and (Super)Integrable Models

量子信息传输、代数表示、正交多项式和（超）可积模型

• 批准号: RGPIN-2017-06166
• 负责人: Vinet, Luc
• 金额: $ 4.08万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=690672
• 关键词: Quantum; Information; Transport; Algebra; Representations

Theoretical physics attempts to understand nature by offering mathematical models of various phenomena. The validation of those descriptions and the determination of the predictions they entail require a detailed understanding of the dynamics of those systems. This is what is meant by « solving a model » and the better if this can be done exactly. It is therefore important to develop the mathematics, the tools, that will make possible the exact solution of a growing number of relevant dynamical systems and will help in the design of rich and sophisticate physical models.******The research of Luc Vinet will do precisely that. He will design devices relevant for quantum computers. He will work with experimentalists to validate his theoretical predictions. He will develop new mathematics that will advance the exact solutions of various problems and he will find new models whose dynamics can be fully understood.******For quantum information to operate, qubits i.e. quantum states need to be transported efficiently between locations. A resource known as quantum entanglement, ebits, must also be available. Luc Vinet will explore how one can use physical systems known as quantum spin chains to achieve those tasks. ******The dynamics of spin chains can be reproduced in photonic lattices formed by arrays of coupled waveguides. Luc Vinet will work with experimentalists to implement the transport of qubits and the generation of ebits in arrays engineered according to the specifications of the spin chains he will have identified for that purpose.******A high level of symmetry is typically a feature of systems admitting an exact solution. An expert of those questions, Luc Vinet will advance the mathematics associated with that key word which are referred to as algebra and representation theory. He will find new structures apt to describe situations of invariance and will also identify new functions often called special that encode symmetries through their properties.******Luc Vinet also has strategies to construct new models with a lot of symmetries called superintegrable that are the hallmark of exactly solvable models. He will bring new mathematical results to bear on their study and will explore their phenomenology and applications

理论物理学试图通过提供各种现象的数学模型来理解自然，验证这些描述并确定它们所需要的预测需要详细了解这些系统的动力学，这就是“求解模型”的含义。因此，如果能够准确地做到这一点就更好了，因此开发数学工具非常重要，这将使越来越多的相关动力系统的精确解决成为可能，并有助于设计丰富而复杂的物理模型。 *****Luc Vinet 的研究他将准确地做到这一点。他将与实验学家合作来验证他的理论预测，他将开发新的数学，以推进各种问题的精确解决方案，并且他将找到其动力学可以完全实现的新模型。理解。*****为了运行量子信息，量子位（即量子态）需要在不同位置之间有效传输，一种称为量子纠缠（ebit）的资源也必须可用，Luc Vinet 将探索如何使用物理系统。称为量子自旋链来实现这些******自旋链的动力学可以在耦合波导阵列形成的光子晶格中重现，Luc Vinet 将与实验人员合作，在根据规范设计的阵列中实现量子位的传输和 ebit 的生成。他将为此目的确定的自旋链。*****高度对称性通常是承认精确解决方案的系统的一个特征，Luc Vinet 是这些问题的专家，他将推进与该关键词相关的数学。被称为他将找到适合描述不变情况的新结构，并将识别通常称为特殊的新函数，通过其属性编码对称性。******Luc Vinet 也有构建新模型的策略。称为超可积的对称性是精确可解模型的标志，他将为他们的研究带来新的数学结果，并将探索它们的现象学和应用。