Tensor networks
Tensor networks are a computational method used to compute models in physics. Tensor network methods work best when they are used to compute models that how short-range interactions. This ensures that the entanglement will not grow too much in the wavefunction, and this is important because the core principle of these methods is to compute these systems with the density matrix. The concepts of renormalization are also key to understanding how algorithms work and what new algorithms need to be used. In this group, we often use them to compute quantum models.
Tutorials in tensor networks:
We have authored a bilingual paper on tensor network. We could recommend a lot of papers in the literature, but we noticed it was hard to jump right to coding on the library that we have, so we wrote our own tailored around our code.
T.E. Baker, S. Desrosiers, M. Tremblay, and M.P. Thompson, "Méthodes de calcul avec réseaux de tenseurs (Basic tensor network computations in physics)" Can. J. Phys. 99, 4 (2021) [online] [arxiv:1911.11566] [pdf] [bibtex]
S. Desrosiers, G.B. Evenbly, and T.E. Baker, The basics of tensor networks: An overview of tensors and renormalization [online] [pdf] [bibtex]
Code your own tensor network library (or understand ours to use it well):
We've also built our own coding library in the julia programming language. We spent a lot of time trying to make it easy to read and use, so hopefully you will find it easy to use too!
If you've read through the introduction above and you want to see how the code functions and how some advanced algorithms like the density matrix renormalization group (DMRG) work, then take a look at these:
T.E. Baker and M.P. Thompson, "Build your own tensor network library: DMRjulia I. Basic library for the density matrix renormalization group" [online] [arxiv: 2109.03120] [bibtex]
Tensor networks in various situations:
T.E. Baker, "Block Lanczos method for excited states on a quantum computer" [online] [arxiv: 2109.14114] [bibtex]
M.O. Flynn, T.E. Baker, S. Jindal, and R.R.P. Singh, "On two phases inside the Bose condensation dome of Yb2Si2O7" Phys. Rev. Lett. 126, 067201 (2021) [online] [arxiv:2001.08219] [pdf] [bibtex]
A. Di Paolo, T.E. Baker, A. Prémont-Foley, D. Sénéchal, and A. Blais, "Efficient modeling of superconducting quantum circuits with tensor networks" npj Quant. Info. 7, 11 (2021) [online] [arxiv:1912.01018] [pdf] [bibtex]
T.E. Baker, S. Desrosiers, M. Tremblay, and M.P. Thompson, "Méthodes de calcul avec réseaux de tenseurs (Basic tensor network computations in physics)" Can. J. Phys. 99, 4 (2021) [online] [arxiv:1911.11566] [pdf] [bibtex]
J. Hollingsworth, L. Li (李力), T.E. Baker, and K. Burke, "Can exact conditions improve machine-learned density functionals?" J. Chem. Phys. 148, 241743 (2018) [online] [pdf] [bibtex]
T.E. Baker, K. Burke, and S.R. White, "Accurate correlation energies in one-dimensional systems from small system-adapted basis functions" Phys. Rev. B 97, 085129 (2018) [online] [arxiv:1709.03460] [pdf] [bibtex]
A. Tkatchenko, M. Afzal, C, Anderson, T. Baker, R. Banisch, S. Chiama, C. Draxl, M. Haghighatlari, F. Heidar-Zadeh, M. Hirn, J. Hoja, O. Isayev, R. Kondor, L. Li, Y. Li, G. Martyna, M. Meila, K.S. Ruiz, M. Rupp, H. Sauceda, A. Shapeev, M. Stöhr, K.-R. Müller, S. Shankar, Recent Progress and Open Problems--Program on Machine Learning & Many-Particle Systems [online] [pdf] [bibtex]
L. Li (李力), T.E. Baker, S.R. White, and K. Burke, "Pure density functional for strong correlations and the thermodynamic limit from machine learning" Phys. Rev. B 94, 245129 (2016) [online] [arxiv:1609.03705] [pdf] [bibtex]
T.E. Baker, E.M. Stoudenmire, L.O. Wagner, K. Burke, and S.R. White, "One dimensional mimicking of electronic structure: the case for exponentials" Phys. Rev. B 91, 235141 (2015) [online] [arxiv:1506.05620] [pdf] [bibtex]
L.O. Wagner, T.E. Baker, E.M. Stoudenmire, K. Burke, and S.R. White, "Kohn-Sham calculations with the exact functional" Phys. Rev. B 90, 045109 (2014) [Editor's choice] [online] [arxiv:1405.0864] [pdf] [bibtex]