Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
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The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit a very rich structure including states with critical and topological properties. We prove, in particular, that coherent versions of thermal states of any local 2D classical spin model correspond to such PEPS, which are in turn ground states of local 2D quantum Hamiltonians. This correspondence maps thermal onto quantum fluctuations, and it allows us to analytically construct critical quantum models exhibiting a strict area law scaling of the entanglement entropy in the face of power law decaying correlations. Moreover, it enables us to show that there exist PEPS which can serve as computational resources for the solution of NP-hard problems.
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PEPS can provide a memory-efficient representation relative to MPS for some states with geometrically constrained patterns of entanglement and correlation, in particular a subset of area-law entangled states, when virtual indices are chosen to match the target topology.
“For some states subject to geometrically constrained patterns of entanglement and correlation, in particular a subset of those exhibiting area-law entanglement, PEPS can provide a memory-efficient representation relative to MPS when virtual indices (bonds) are chosen to match the target topology 49,93 .”
From Beyond-classical computation in quantum simulation (2025) · cites this paper as [49]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe underlying structure of the constructive approach to universal resources for MQC can be described mathematically using matrix-product states or projected-entangled-pairs.
“The underlying structure of this approach can be described mathematically using the language of matrix-product-states or projected-entangled-pairs 18,86,87 .”
From Measurement-based quantum computation (2009) · cites this paper as [87]
These connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting.
“For one, these connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting 87,92,95,96,99-102 .”
From Measurement-based quantum computation (2009) · cites this paper as [87]
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Self-citation
- Authors
- Verstraete, F., Wolf, M. M., Perez-Garcia, D., & Cirac, J. I.
- Affiliations
- California Institute of Technology (US)
- Max Planck Institute of Quantum Optics (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-06-06
- Volume
- 96
- Issue
- 22
- Pages
- 220601-220601
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2035298342
- Cited by
- 580
- References
- 31
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- 2026: 15 · 2025: 34 · 2024: 33 · 2023: 37 · 2022: 27 · 2021: 40 · 2020: 68 · 2019: 31 · 2018: 30 · 2017: 31 · 2016: 20 · 2015: 25 · 2014: 31 · 2013: 30 · 2012: 22
- FWCI
- 13.33
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (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 › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- projected entangled pair states, area law, entanglement entropy, quantum criticality, topological phases, classical spin systems, thermal states, NP-hard problems, quantum computing, two-dimensional lattice
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