Cosmological Parameter Inference from Merger Trees Using Hierarchical Quantum Tensor Networks

Abstract: Inferring cosmological parameters from the intricate, hierarchical structures of dark matter merger trees is crucial for understanding cosmic evolution but presents significant challenges for conventional statistical methods. We introduce a novel framework leveraging Hierarchical Quantum Tensor Networks (HQTNs), specifically Tree Tensor Networks (TTNs), to directly predict these parameters. Our approach represents each merger tree as a hierarchical graph, where individual halo properties (mass, concentration, Vmax, and scale factor) are embedded into node tensors via a shared neural network. Hierarchical relationships and varying tree topologies are captured by learnable basis tensors, selected according to a node's number of children, which are then contracted from the leaves to the root using the \texttt{quimb} library. The resulting fixed-dimension root vector is fed into a linear layer to predict the target cosmological parameters, Omega\_m and sigma\_8. The complete model, including feature embedding, basis tensors, and the prediction head, is trained end-to-end on a dataset of 1000 simulated merger trees using Mean Squared Error loss and optimized with \texttt{JAX} and \texttt{optax} for efficient automatic differentiation. This methodology provides a powerful, interpretable means to exploit the deep hierarchical correlations within merger trees, thereby advancing robust cosmological parameter inference beyond traditional statistical summaries.

Subjects:	gr-qc; hep-th; astro-ph.CO
Cite as:	PX:2508.00076