Simulation of time evolution with multiscale entanglement renormalization ansatz
Open accessAbstract
We describe an algorithm to simulate time evolution using the multiscale entanglement renormalization ansatz and test it by studying a critical Ising chain with periodic boundary conditions and with up to $L\ensuremath{\approx}{10}^{6}$ quantum spins. The cost of a simulation, which scales as $L\text{ }{\text{log}}_{2}(L)$, is reduced to ${\text{log}}_{2}(L)$ when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the ground-state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The unfavorable computational scaling O(χ^9) of time-dependent MERA makes a generalization to finite, higher dimensional disordered models impractical.
“Although a time-dependent MERA algorithm has been proposed and successfully applied to translationally invariant 1D systems 90 , its unfavorable computational scaling O(χ 9 ) makes a generalization to our finite, higher dimensional disordered models impractical.”
From Beyond-classical computation in quantum simulation (2025) · cites this paper as [90]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745 · see citing works
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323 · see citing works
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 2
- [19]R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, U.K., 1990).
- York) 16, 407 (1961).
Cited by
Sorted by citations
<i>Colloquium</i> : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873 · see citing works
Entanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688 · see citing works
Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
Barthel, T., Pineda, C., & Eisert, J. (2009) · Physical Review A · doi:10.1103/physreva.80.042333 · Cited by 139 · see citing works
Beyond-classical computation in quantum simulation
King, A. D., Nocera, A., Rams, M. M., Dziarmaga, J., Wiersema, R., Bernoudy, W., Raymond, J., Kaushal, N., Heinsdorf, N., Harris, R., et al. (2025) · Science · doi:10.1126/science.ado6285 · Cited by 138 · see citing works
Holographic dynamics from multiscale entanglement renormalization ansatz
Chua, V., Passias, V., Tiwari, A., & Ryu, S. (2017) · Physical Review B · doi:10.1103/physrevb.95.195152 · Cited by 5 · see citing works
- Authors
- Rizzi, M., Montangero, S., & Vidal, G.
- Affiliations
- Scuola Normale Superiore (IT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2008-05-22
- Volume
- 77
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1538812421
- Cited by
- 56
- References
- 3
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 3 · 2022: 3 · 2021: 3 · 2020: 1 · 2019: 6 · 2017: 2 · 2016: 1 · 2015: 1 · 2014: 6 · 2013: 1 · 2012: 1
- FWCI
- 3.98
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Padua Research Archive (University of Padova) (submittedVersion)
- arXiv (Cornell University)
- 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 › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- multiscale entanglement renormalization ansatz, time evolution simulation, quantum many-body systems, periodic boundary conditions, ground state energy, imaginary time evolution, translation invariance, computational cost scaling, quantum spin chains
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
