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

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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.