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 orthogonal polynomial expansions.

• Function loading with TCI.

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

[CSW23]

Jielun Chen, E. Miles Stoudenmire, and Steven R. White. Quantum fourier transform has small entanglement. PRX Quantum, 4:040318, Nov 2023. URL: https://link.aps.org/doi/10.1103/PRXQuantum.4.040318, doi:10.1103/PRXQuantum.4.040318.

[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.

[HCO+11]

Jutho Haegeman, J. Ignacio Cirac, Tobias J. Osborne, Iztok Pizorn, Henri Verschelde, and Frank Verstraete. Time-dependent variational principle for quantum lattices. Phys. Rev. Lett., 107:070601, Aug 2011. URL: https://link.aps.org/doi/10.1103/PhysRevLett.107.070601, doi:10.1103/PhysRevLett.107.070601.

[HLO+16]

Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, and Frank Verstraete. Unifying time evolution and optimization with matrix product states. Phys. Rev. B, 94:165116, Oct 2016. URL: https://link.aps.org/doi/10.1103/PhysRevB.94.165116, doi:10.1103/PhysRevB.94.165116.

[HNSK91]

D. K. Hoffman, N. Nayar, O. A. Sharafeddin, and D. J. Kouri. Analytic banded approximation for the discretized free propagator. J. Phys. Chem., 95(21):8299–8305, 1991. doi:10.1021/j100174a052.

[KuhnerW99]

Thomas D. Kühner and Steven R. White. Dynamical correlation functions using the density matrix renormalization group. Phys. Rev. B, 60:335–343, Jul 1999. URL: https://link.aps.org/doi/10.1103/PhysRevB.60.335, doi:10.1103/PhysRevB.60.335.

[RSO22]

Maxim Rakhuba, Dmitry Savostyanov, and Ivan Oseledets. Robust alternating direction implicit solver in quantized tensor formats for a three-dimensional elliptic pde. 2022. arXiv:2209.14808.