Towards efficient data compression and simulation of CFD with tensor networks and related methods

Tensor networks are a powerful classical tool for studying quantum many-body systems as they can capture the local correlation structures efficiently to provide both a memory compression and speedup of quantum simulation. Recently, tensor networks have been applied to small-scale computation fluid dynamics (CFD) simulations, with the most recent examples being a cylinder in a flow. Here, we look to extend these methods to large scale CFD problems commonly tackled using HPC facilities. We demonstrate mappings between data sets and tensor networks for optimal lossless compression. We then investigate if such mappings are consistent with end-to-end tensor network-based algorithms for CFD problems. Such tensor network approaches can also be translated to fully quantum algorithms for future fault-tolerant quantum computers, which we will discuss briefly.