Limitations of quantum computing with Gaussian cluster states
Abstract
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information is not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable (CV) systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states, and points towards the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.
Cite
@article{arxiv.1004.0081,
title = {Limitations of quantum computing with Gaussian cluster states},
author = {M. Ohliger and K. Kieling and J. Eisert},
journal= {arXiv preprint arXiv:1004.0081},
year = {2017}
}
Comments
13 pages, 7 figures, details of main argument extended