Parallel time-dependent variational principle algorithm for matrix product states
Open accessAbstract
Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum lattice systems with long-range interactions. We benchmark the accuracy and performance of the algorithm by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes, with parallel efficiencies as high as $86%$. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX spin chain with $1/{r}^{2}$ interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.
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Beyond-classical computation in quantum simulation
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Fast time evolution of matrix product states using the QR decomposition
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- Authors
- Secular, P., Gourianov, N., Lubasch, M., Dolgov, S., Clark, S. R., & Jaksch, D.
- Affiliations
- University of Bath (GB)
- University of Oxford (GB)
- University of Bristol (GB)
- Centre for Quantum Technologies (SG)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2020-06-05
- Volume
- 101
- Issue
- 23
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W3033248898
- Cited by
- 40
- References
- 148
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 12 · 2023: 5 · 2022: 6 · 2021: 6 · 2020: 4
- FWCI
- 2.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- Bristol Research (University of Bristol) (publishedVersion, other-oa)
- arXiv (Cornell University) (acceptedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Explore Bristol Research (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/M013243/1, EP/K038311/1, EP/P01058X/1, EP/P025110/2)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- time-dependent variational principle, matrix product states, parallel algorithms, long-range interactions, quantum lattice models, quench dynamics, long-range Ising model, dynamical correlation functions, tensor networks, parallel efficiency
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