QTT-Based Compression of Merger Tree Trajectories for Assembly Bias Studies: A Proof-of-Concept with Dummy Implementation

Abstract: Assembly bias, the dependence of halo properties on their formation history, motivates the exploration of efficient methods for representing and analyzing merger tree trajectories. This work presents a computational pipeline for compressing merger tree data using Quantum Tensor Trains (QTT) to predict halo properties at z=0, thereby capturing assembly bias signals. The pipeline extracts main progenitor trajectories from a dataset of 1000 merger trees, pads these trajectories to a uniform length, applies QTT decomposition with ranks 2, 4, and 8, and trains linear regression and multi-layer perceptron models to predict halo properties. A key limitation is the use of a dummy implementation of the `qttpy` library, rendering the QTT compression and related analyses as placeholders; therefore, presented results, including reconstruction errors, compression ratios, and predictive performance of QTT-derived features, are artifacts of this dummy behavior and do not reflect the capabilities of actual QTT algorithms. Baseline models, using only the final state features of halos, demonstrate a moderate level of predictability (R² ≈ 0.41-0.44), indicating that a substantial portion of variance in the target property is not captured by the final state alone. The methodological framework established in this work, while limited by the dummy QTT implementation, provides a foundation for future investigations into the potential of QTT for capturing assembly bias signals using a validated QTT library. \

Subjects:	gr-qc; hep-th; astro-ph.CO
Cite as:	PX:2508.00077