A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.
Cited by 3
Dunnett et al., Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states
Phys. Rev. B 104, 214302 (2021) [Crossref]
Montangero et al., Loop-free tensor networks for high-energy physics
Phil. Trans. R. Soc. A. 380, 20210065 (2022) [Crossref]
Vanderstraeten et al., Variational methods for contracting projected entangled-pair states
Phys. Rev. B 105, 195140 (2022) [Crossref]
Authors / Affiliation: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Bram Vanhecke,
- 1 Maarten Van Damme,
- 1 Jutho Haegeman,
- 1 Laurens Vanderstraeten,
- 1 Frank Verstraete
- European Research Council [ERC]
- Fonds Wetenschappelijk Onderzoek (FWO) (through Organization: Fonds voor Wetenschappelijk Onderzoek - Vlaanderen / Research Foundation - Flanders [FWO])