Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States

2006/06/06 by Frank Verstraete, M. M. Wolf, David Pérez-Garcı́a +1 · 1 voice · 8 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems

paper · pdf · doi:10.1103/physrevlett.96.220601

openalex publication_date 2006/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Fault-tolerant quantum computation by anyons

Cited by

• Tensor network states for the description of quantum many-body systems
• From gauging to duality in one-dimensional quantum lattice models
• Locally purified density operators for noisy quantum circuits
• Tensor Networks in a Nutshell
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• The Augmented Tree Tensor Network Cookbook
• Entanglement and its applications in systems with many degrees of freedom
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Discussions

• In the paper Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States , Verstraete et al give the following definition of the PEPS of a ground state of the toric code: [stackexchange, 2 points]

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