EAGER: Collaborative Research: Tensor Network Methods for Quantum Simulations

The University Of Central Florida Board Of Trustees, Orlando FL

Investigators

Abstract

Recent advances in quantum technologies have made small, high-quality quantum computers with tens of qubits finally available. While these machines are still too small to make an impact on areas such as cryptography, they are big enough to study physical and chemical systems of relevance to materials science and chemistry, thus helping us better understand the origins of certain materials properties and how certain important chemical reactions take place. This project aims at developing novel simulation techniques to help benchmark these quantum machines. These simulations will run on ordinary computers, but will make use of cloud computing services to scale up the system sizes as far as possible. The simulation techniques will also be used to investigate other quantum systems of relevance to physics and materials science that are not yet accessible to quantum hardware. Advancing knowledge in those areas is essential for developing better and stronger materials, as well as faster and smaller electronics. These projects will have the additional societal benefit of training graduate students in a very interdisciplinary area of research, at the interface between computer science and physics, thus helping bring highly-sought skills into the workforce. The project consists of developing and deploying a novel method to simulate quantum many-body systems using tensor networks. The method is based on the state history representation of the quantum dynamical evolution, as expressed in the Keldysh-Schwinger formalism. Thus, rather than using the tensor network to represent the evolution of the probability amplitude of a state vector over time, the method uses the tensor network to represent the evolution itself, such that the full contraction of the network directly calculates quantities such as the expectation value of an observable or a two-point correlation function. In this approach, entanglement is kept low, resulting in low bond dimensions on the network links, making contractions more amenable to exact computations. For the contraction, a two-step contraction-decimation scheme is used to collapse the network. More specifically, the scheme consists of the removal of local entanglement by compressing the information via singular value decomposition, followed by the decimation of the network by selectively removing rows or columns of the network. This contraction scheme will be coded to optimally utilize the resources available on the largest instances of commercial cloud computing services. The codes developed during the project will be made available through public repositories. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.