TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.222
TI  - Gauging tensor networks with belief propagation
PY  - 2023/12/01
UR  - https://scipost.org/SciPostPhys.15.6.222
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 222
A1  - Tindall, Joseph
AU  - Fishman, Matthew
AB  - Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.
ER  -

@Article{10.21468/SciPostPhys.15.6.222,
	title={{Gauging tensor networks with belief propagation}},
	author={Joseph Tindall and Matt Fishman},
	journal={SciPost Phys.},
	volume={15},
	pages={222},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.222},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.222},
}