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

预期中的“第二次量子革命”旨在利用量子系统中的动力学和纠缠来加速信息处理并获得材料中的新型电子特性。近期量子设备有望实现比经典计算机指数级的加速，而且具有非凡特性的物质的量子态在超冷原子和固态装置中越来越可用。认识到量子技术的早期进展，并预测那些尚未到来，本研究项目将解决在经典计算机上模拟量子动力学的挑战。为此，我们将基于强相关量子系统中的纠缠物理发展新的理论和数值方法。此外，我们将把同样的工具应用于计算问题的量子力学重新表述，为经典的计算挑战开发有效的量子启发算法，例如在人工智能中遇到的那些挑战。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。详细了解特定问题中的纠缠景观将使我们能够有效地模拟量子计算以及先进量子材料的动态特性，并为一些具有挑战性的计算问题获得有效的解决方法。具体而言，本研究将在量子计算模拟的背景下推进量子系统中进化和测量的模拟。我们将开发的算法将用于量子设备的建模计算，包括IBM和谷歌等公司目前开发的量子设备。我们将使用相同的方法来模拟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对于解决一些困难和普遍的经典计算问题也很有用，因此我们将开发的技术也将适用于组合优化，采样和计数类。因此，我们的技术与机器学习和数据科学领域密切相关。

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.