🧩 BP works well on tree-like lattices—but on 2D square lattices, loops introduce errors.
To go beyond this BP limit, we developed a cluster expansion for IF-BP that systematically captures loop-induced correlations.

🧠 A key idea: we shift the computational bottleneck from spatial to temporal entanglement.

While spatial entanglement grows linearly with time, we find that temporal entanglement entropy grows only logarithmically—enabling simulations with polynomial cost.

🔄 Instead of representing the wavefunction as a tensor network state,
we reformulate the dynamics as a path integral over the subsystem—captured by an influence functional MPS (IF-MPS).
We adapt BP to efficiently construct the IF-MPS for 2D lattices.

🚀 New paper out on arXiv!
We developed a tensor network algorithm to simulate quantum dynamics in 2D lattices, combining the concept of tensor network influence functional (TN-IF) and belief propagation (BP).

arxiv.org/abs/2504.07344

I am volunteering at the DCP table at APS 2025.
The table is in front of the room 204B Annaheim convention center.
Say hi to me if you are nearby!