Computational Complexity of Projected Entangled Pair States

DOI10.1103/PhysRevLett.98.140506zbMath1228.81134arXivquant-ph/0611050OpenAlexW1964713133WikidataQ59458713 ScholiaQ59458713MaRDI QIDQ3107793

J. Ignacio Cirac, Norbert Schuch, Frank Verstraete, Michael M. Wolf

Publication date: 26 December 2011

Published in: Physical Review Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0611050

Mathematics Subject Classification ID

Quantum computation (81P68) Quantum measurement theory, state operations, state preparations (81P15) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)

Related Items (27)

A construction of combinatorial NLTS ⋮ Two-dimensional local Hamiltonian problem with area laws is \textsf{QMA}-complete ⋮ A practical introduction to tensor networks: Matrix product states and projected entangled pair states ⋮ Computations in quantum tensor networks ⋮ Representations of hypergraph states with neural networks* ⋮ Renormalization Group Circuits for Weakly Interacting Continuum Field Theories ⋮ Simulation of quantum many-body systems on Amazon cloud ⋮ Representations of graph states with neural networks ⋮ Probabilistic nonunitary gate in imaginary time evolution ⋮ Characterizing symmetries in a projected entangled pair state ⋮ Practical learning method for multi-scale entangled states ⋮ A Complete Characterization of Unitary Quantum Space ⋮ On efficiently solvable cases of quantum \(k\)-SAT ⋮ Entropic measure and hypergraph states ⋮ Unifying projected entangled pair state contractions ⋮ Entanglement Hamiltonian of the quantum Néel state ⋮ Physical consequences of P≠NP and the density matrix renormalization group annealing conjecture ⋮ Twisted injectivity in projected entangled pair states and the classification of quantum phases ⋮ Approximating the ground state of gapped quantum spin systems ⋮ PEPS as ground states: degeneracy and topology ⋮ Bipartite entanglement and hypergraph states ⋮ Colloquium: Area laws for the entanglement entropy ⋮ Unifying Variational Methods for Simulating Quantum Many-Body Systems ⋮ Mathematical open problems in projected entangled pair states ⋮ Disentanglement approach to quantum spin ground states: field theory and stochastic simulation ⋮ On traces of tensor representations of diagrams ⋮ Hand-waving and interpretive dance: an introductory course on tensor networks

Cites Work

• Limitations of Quantum Advice and One-Way Communication
• The density-matrix renormalization group
• Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
• Quantum computing, postselection, and probabilistic polynomial-time

This page was built for publication: Computational Complexity of Projected Entangled Pair States