Example codes for using QTT to solve a PDE

DMRG and Numerical Methods
1

Hello,

I am a complete novice to ITensors and I am trying to learn to use MPS/MPO to solve PDEs (not necessarily of quantum mechanics origin).

I was wondering if there are simple but hopefully complete example codes one might be willing to share where one uses QTT to solve a PDE. It can perhaps be as simple as a 1D transient heat diffusion equation. Thanks in advance!

2

We have two different repositories, one (a 3rd party) for using QTTs on arbitrary topology ([2410.03572] Compressing multivariate functions with tree tensor networks) and another for using the well developed 1D (MPS) QTT

Here is an example of solving the 2D Laplace equation on an arbitrary tree tensor network: ITensorNumericalAnalysis.jl/examples/2d_laplace_solver.jl at main · JoeyT1994/ITensorNumericalAnalysis.jl · GitHub

and in 1D, solving an Airy equation: ITensorQTT.jl/examples/airy_equation at main · ITensor/ITensorQTT.jl · GitHub

3

Thanks so much!