Simulating quantum dynamics in two-dimensional lattice with Tensor Network Influence Functional approach

Tensor Network Influence Functional approach has demonstrated success in simulating quantum dynamics of local observables in one-dimensional systems, which can reduce rapid entanglement growth. Here, we extend its applicability to two-dimensional lattices. This extension is achieved by approximating influence functional tensors as locally separable matrix product states (MPS). While the local separability condition is only exact in tree geometries, recent studies of the classical simulation of IBM's kicked Ising experiment with the projected entangled pair state (PEPS) wavefunction ansatz suggest that it often serves as a good approximation in locally tree-like geometries, including the IBM's heavy-hex lattice. Our study involves the computation of the expectation values for local observables in the kicked Ising model within the infinite heavy-hex lattice. We achieve this by formulating a self-consistency relationship for the influence functional tensors with the local separability condition. Additionally, we compute the entanglement entropy of the influence functional tensors along the temporal direction. Notably, we identify a regime in which entanglement growth is slower than that of PEPS, allowing for the simulation of longer-time dynamics.