The computational complexity of PEPS

Details The computational complexity of PEPS The computational complexity of PEPS

2006-11-06

arxiv.org/abs/quant-ph/0611050v2

Phys. Rev. Lett. 98, 140506 (2007)

Physics

Quantum Physics

5 pages, 1 figure. Published version, plus a few extras

Scientific paper

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.

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