The computational expense of solving non-equilibrium chemistry equations in astrophysical simulations poses a significant challenge, particularly in high-resolution, large-scale cosmological models. In this work, we explore the potential of machine learning, specifically Neural Operators, to emulate the Grackle chemistry solver, which is widely used in cosmological hydrodynamical simulations. Neural Operators offer a mesh-free, data-driven approach to approximate solutions to coupled ordinary differential equations governing chemical evolution, gas cooling, and heating. We construct and train multiple Neural Operator architectures (DeepONet variants) using a dataset derived from cosmological simulations to optimize accuracy and efficiency. Our results demonstrate that the trained models accurately reproduce Grackle's outputs with an average error of less than 0.6 dex in most cases, though deviations increase in highly dynamic chemical environments. Compared to Grackle, the machine learning models provide computational speedups of up to a factor of six in large-scale simulations, highlighting their potential for reducing computational bottlenecks in astrophysical modeling. However, challenges remain, particularly in iterative applications where accumulated errors can lead to numerical instability. Additionally, the performance of these machine learning models is constrained by their need for well-represented training datasets and the limited extrapolation capabilities of deep learning methods. While promising, further development is required for Neural Operator-based emulators to be fully integrated into astrophysical simulations. Future work should focus on improving stability over iterative timesteps and optimizing implementations for hardware acceleration. This study provides an initial step toward the broader adoption of machine learning approaches in astrophysical chemistry solvers.

QXTools is a framework for simulating quantum circuits using tensor network methods. Weak simulation is the primary use case where given a quantum circuit and input state QXTools will efficiently calculate the probability amplitude of a given output configuration or set of configurations. Given this ability one can sample from the output distribution using random sampling approaches. QXTools is intended to be used by researchers interested in simulating circuits larger than those possible with full wave-function simulators or those interested in research and development of tensor network circuit simulation methods. See Brennan et al. (2021) for more complete background and scaling results and Brayford et al. (2021) for details about deploying in containerised environments. QXTools is written in Julia (Bezanson et al., 2017) and is designed to run on large distributed compute clusters and to support GPU accelerators. The simulation workflow is broken down into a number of stages, each of which is managed by a special purpose package which can be used independently or as part of the QXTools framework. To find efficient contraction orders for tensor networks, an algorithm called FlowCutter (Hamann & Strasser, 2018) is used to construct tree decompositions with optimal treewidth of the network’s line graph by iteratively partitioning it using maximal flows on the graph. A domain specific language (DSL) is used to express the simulation as a set of tensor network operations. This separates the high level index accounting and contraction planning from the

The simulation of quantum circuits using the tensor network method is very computationally demanding and requires significant High Performance Computing (HPC) resources to find an efficient contraction order and to perform the contraction of the large tensor networks. In addition, the researchers want a workflow that is easy to customize, reproduce and migrate to different HPC systems. In this paper, we discuss the issues associated with the deployment of the QuantEX quantum computing simulation software within containers on different HPC systems. Also, we compare the performance of the containerized software with the software running on bare metal.

Tensor network methods are incredibly effective for simulating quantum circuits. This is due to their ability to efficiently represent and manipulate the wave-functions of large interacting quantum systems. We describe the challenges faced when scaling tensor network simulation approaches to Exascale compute platforms and introduce QuantEx, a framework for tensor network circuit simulation at Exascale.