Examples and Bibliography

In the directory examples of the library, we have created various Jupyter notebooks that solve canonical problems using the SeeMPS library tools, from computing ground states of many-body problems, to solving static and time-dependent partial differential equations.

• Computation of a spin-1/2 model ground state using DMRG.

• Solution of a Hamiltonian PDE.

• Function interpolation.

• Function differentiation.

• Function integration.

• Function optimization.

• Function loading with Chebyshev expansions.

• Function loading with TT-Cross.

Further examples of use appear in the datasets and associated codes to the following publications:

[GMRMGR22]

Paula García-Molina, Javier Rodríguez-Mediavilla, and Juan José García-Ripoll. Quantum fourier analysis for multivariate functions and applications to a class of schrödinger-type partial differential equations. Phys. Rev. A, 105:012433, Jan 2022. URL: https://link.aps.org/doi/10.1103/PhysRevA.105.012433, doi:10.1103/PhysRevA.105.012433.

[GMTGR24]

Paula García-Molina, Luca Tagliacozzo, and Juan José García-Ripoll. Global optimization of mps in quantum-inspired numerical analysis. 2024. arXiv:2303.09430.

[GR21]

Juan José García-Ripoll. Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations. Quantum, 5:431, April 2021. URL: https://doi.org/10.22331/q-2021-04-15-431, doi:10.22331/q-2021-04-15-431.