The computational complexity of PEPS

Author(s): N. Schuch, M. M. Wolf, F. Verstraete, J. I. Cirac

Journal: Physical Review Letters

Volume: 98

Page(s): 140506

Year: 2007

DOI Number: 10.1103/PhysRevLett.98.140506

Link: Link to publication

Abstract:

We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to solve PP problems, the latter two tasks are both proven to be #P-complete. We further show how PEPS can be used to approximate ground states of gapped Hamiltonians, and that creating them is easier than creating arbitrary PEPS. The main tool for our proofs is a duality between PEPS and postselection which allows to use existing results from quantum compexity.

Note: http://arxiv.org/abs/quant-ph/0611050

File: Link to PDF

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