New tensor network tools for and beyond Rydberg systems*

Tensor network methods offer potential features to support and improve the development and benchmarking of quantum processing units (QPUs). Their flexibility to simulate circuits directly or as Schrödinger and Lindblad equation enables a digital twin for a Rydberg atom QPU; both approaches are supported by the Quantum TEA library. Herein, we start from the pulse level, continue via compilation and optimization, and reach up to the full simulation of an 8x8 grid of strontium-88 atoms. We encode the two fine-structure states of the qubit and an additional Rydberg state; the latter is used for the entangling operation. The digital twin simulation of the QPU performs a parallel application of gates resulting in a Greenberger-Horne-Zeilinger state. The procedure is under the influence of crosstalk due to the long-range Rydberg interaction of CZ gates executing in parallel. We apply the new approaches for measurements, optimizations for higher-dimensional systems with and without long-range interactions, and parallelization for high-performance computing clusters to other systems in condensed matter and quantum information.