Year: 2017
Type: article
Abstract: Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the computational hardness of contracting projected entangled pair states in two- and higher-dimensional systems is often seen as a significant obstacle when devising higher-dimensional variants of the density-matrix renormalization group method. In this work, we show that for those projected entangled pair states that are expected to provide good approximations of such ground states of local Hamiltonians, one can compute local expectation values in quasipolynomial time. We therefore provide a complexity-theoretic justification of why state-of-the-art numerical tools work so well in practice. We finally turn to the computation of local expectation values on quantum computers, providing a meaningful application for a small-scale quantum computer.
Source: Physical Review A
Authors: M. Schwarz, O. Buerschaper, J. Eisert
Institution: Freie Universität Berlin
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Awards: G1688234926, G506998728, G6821242515
OpenAlex ID: W2463781544