English

Quantum computation and the evaluation of tensor networks

Quantum Physics 2010-02-09 v3

Abstract

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of looking at quantum computation in which unitary gates are replaced by tensors and time is replaced by the order in which the tensor-network is "swallowed". We use this result to derive new quantum algorithms that approximate the partition function of a variety of classical statistical mechanics models, including the Potts model.

Keywords

Cite

@article{arxiv.0805.0040,
  title  = {Quantum computation and the evaluation of tensor networks},
  author = {Itai Arad and Zeph Landau},
  journal= {arXiv preprint arXiv:0805.0040},
  year   = {2010}
}

Comments

35 pages, 11 figures, 3rd version includes: the section presenting statistical mechanical algorithms has been changed to clarify the relationship to other recent work. To appear in SICOMP

R2 v1 2026-06-21T10:36:24.634Z