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。这些描述的验证以及对它们所带来的预测的确定需要详细了解这些系统的动态。这就是“求解模型”的含义，如果可以准确地完成此操作，越好。因此，重要的是要开发数学，工具，这将使越来越多的相关动态系统的确切解决方案成为可能，并将有助于设计丰富而复杂的物理模型。**** Luc Vinet的研究将正是这样做的。他将设计与量子计算机相关的设备。他将与实验者合作以验证他的理论预测。他将开发新的数学，这些数学将推进各种问题的确切解决方案，并将找到可以充分理解动态的新模型。******对于量子信息运行，量子（即需要在位置之间有效地运输量子状态）。还必须可用一种称为量子纠缠的资源。 Luc Vinet将探索如何使用称为量子旋转链的物理系统来实现这些任务。 *****可以在由耦合波导阵列形成的光子晶格中复制自旋链的动力学。 Luc Vinet将与实验者合作实施数量的运输，并根据他将确定为此目的确定的旋转链的规格在阵列中生成EBIT。 Luc Vinet是这些问题的专家，将推进与该关键词相关的数学，这些数学被称为代数和代表理论。他将发现新的结构易于描述不变性的情况，还将确定通常称为特殊的新功能，该功能通过其属性编码对称性。**** luc Vinet还具有策略，策略具有具有许多共同体的新模型，称为可溶性模型的标志。他将带来新的数学结果，并将探索他们的现象学和应用