Quantum dynamics, entanglement, and computation: theory and simulation algorithms

量子动力学、纠缠和计算：理论和模拟算法

• 批准号: RGPIN-2020-05607
• 负责人: Kourtis, Stefanos
• 金额: $ 2.4万
• 依托单位: Université de Sherbrooke
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=763423
• 关键词: Quantum; dynamics; entanglement; computation; theory

The anticipated "second quantum revolution" aims to exploit dynamics and entanglement in quantum systems to accelerate information processing and to access novel electronic properties in materials. Near-term quantum devices, which promise exponential speedups over classical computers, as well as quantum states of matter with extraordinary properties are becoming increasingly available in ultracold-atom and solid-state setups. Recognizing the early advances in quantum technologies and anticipating those yet to come, this research project will address the challenge of simulating quantum dynamics on classical computers. To this end, we will develop new theoretical and numerical approaches based on the physics of entanglement in strongly correlated quantum systems. Furthermore, we will apply the same tools to quantum-mechanical reformulations of computational problems, to develop efficient quantum-inspired algorithms for classical computational challenges, such as those encountered in artificial intelligence. The main tool that we will use is that of tensor networks. Our studies of dynamics in quantum systems will elucidate the mechanisms that generate entanglement, both in quantum matter and in quantum computations. Detailed knowledge of the entanglement landscape in a particular problem will allow us to efficiently simulate quantum computations as well as dynamical properties of advanced quantum materials, and also to obtain efficient methods of solution for some challenging computational problems. Specifically, this research will advance the simulation of evolution and measurement in quantum systems in the context of the simulation of quantum computation. The algorithms we will develop will be useful in modeling computations carried out by quantum devices, including the ones currently developed by companies like IBM and Google. We will use the same methods to model the dynamical responses of quantum matter to experimental probes, as well as the dynamics of nontrivial excited states in novel quantum systems. Finally, we have found that tensor network methods are also useful for solving some hard and pervasive classical computational problems, and hence the techniques we will develop will also be applicable to classes of combinatorial optimization, sampling, and counting. Our techniques are therefore of great relevance to the fields of machine learning and data science.

预期的“第二量子革命”旨在利用量子系统中的动态和纠缠，以加速信息处理并访问材料中的新型电子性能。近期的量子设备，该设备有望在经典计算机上指数加速，以及具有非凡特性的物质状态，在超低原子和固态设置中越来越多地获得。认识到量子技术的早期进展并预期尚未来的研究项目，该研究项目将解决模拟古典计算机上量子动态的挑战。为此，我们将根据强相关的量子系统中的纠缠物理学开发新的理论和数值方法。此外，我们将将相同的工具应用于计算问题的量子力学重新汇总，以开发有效的量子启发算法，以应对经典的计算挑战，例如人工智能中遇到的算法。我们将使用的主要工具是张量网络。我们对量子系统动力学的研究将阐明在量子物质和量子计算中产生纠缠的机制。特定问题中纠缠格局的详细知识将使我们能够有效地模拟量子计算以及高级量子材料的动态特性，并获得有效的解决方案方法，以解决一些具有挑战性的计算问题。具体而言，这项研究将在量子计算模拟的背景下推动量子系统中进化和测量的模拟。我们将开发的算法对于建模量子设备进行的计算将非常有用，包括IBM和Google等公司当前开发的计算。我们将使用相同的方法来建模量子物质对实验探针的动态响应，以及新型量子系统中非平凡激发态的动力学。最后，我们发现张量网络方法也可用于解决一些硬性和普遍的经典计算问题，因此我们将开发的技术也适用于组合优化，采样和计数类别。因此，我们的技术与机器学习和数据科学领域非常相关。