skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Potential and limits to cluster-state quantum computing using probabilistic gates

Abstract

We establish bounds to the necessary resource consumption when building up cluster states for one-way computing using probabilistic gates. Emphasis is put on state preparation with linear optical gates, as the probabilistic character is unavoidable here. We identify rigorous general bounds to the necessary consumption of initially available maximally entangled pairs when building up one-dimensional cluster states with individually acting linear optical quantum gates, entangled pairs, and vacuum modes. As the known linear optics gates have a limited maximum success probability, as we show, this amounts to finding the optimal classical strategy of fusing pieces of linear cluster states. A formal notion of classical configurations and strategies is introduced for probabilistic nonfaulty gates. We study the asymptotic performance of strategies that can be simply described, and prove ultimate bounds to the performance of the globally optimal strategy. The arguments employ methods of random walks and convex optimization. This optimal strategy is also the one that requires the shortest storage time, and necessitates the fewest invocations of probabilistic gates. For two-dimensional cluster states, we find, for any elementary success probability, an essentially deterministic preparation of a cluster state with quadratic, hence optimal, asymptotic scaling in the use of entangled pairs. Wemore » also identify a percolation effect in state preparation, in that from a threshold probability on, almost all preparations will be either successful or fail. We outline the implications on linear optical architectures and fault-tolerant computations.« less

Authors:
; ;  [1]
  1. QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom) and Institute for Mathematical Sciences, Imperial College London, Prince's Gate, London SW7 2PG (United Kingdom)
Publication Date:
OSTI Identifier:
20857861
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 74; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.74.042343; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ENERGY LEVELS; GATING CIRCUITS; ONE-DIMENSIONAL CALCULATIONS; OPTICS; OPTIMIZATION; PERFORMANCE; POTENTIALS; PROBABILISTIC ESTIMATION; PROBABILITY; QUANTUM COMPUTERS; QUANTUM MECHANICS; QUANTUM NUMBERS; RANDOMNESS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Gross, D, Kieling, K, and Eisert, J. Potential and limits to cluster-state quantum computing using probabilistic gates. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.74.042343.
Gross, D, Kieling, K, & Eisert, J. Potential and limits to cluster-state quantum computing using probabilistic gates. United States. https://doi.org/10.1103/PHYSREVA.74.042343
Gross, D, Kieling, K, and Eisert, J. 2006. "Potential and limits to cluster-state quantum computing using probabilistic gates". United States. https://doi.org/10.1103/PHYSREVA.74.042343.
@article{osti_20857861,
title = {Potential and limits to cluster-state quantum computing using probabilistic gates},
author = {Gross, D and Kieling, K and Eisert, J},
abstractNote = {We establish bounds to the necessary resource consumption when building up cluster states for one-way computing using probabilistic gates. Emphasis is put on state preparation with linear optical gates, as the probabilistic character is unavoidable here. We identify rigorous general bounds to the necessary consumption of initially available maximally entangled pairs when building up one-dimensional cluster states with individually acting linear optical quantum gates, entangled pairs, and vacuum modes. As the known linear optics gates have a limited maximum success probability, as we show, this amounts to finding the optimal classical strategy of fusing pieces of linear cluster states. A formal notion of classical configurations and strategies is introduced for probabilistic nonfaulty gates. We study the asymptotic performance of strategies that can be simply described, and prove ultimate bounds to the performance of the globally optimal strategy. The arguments employ methods of random walks and convex optimization. This optimal strategy is also the one that requires the shortest storage time, and necessitates the fewest invocations of probabilistic gates. For two-dimensional cluster states, we find, for any elementary success probability, an essentially deterministic preparation of a cluster state with quadratic, hence optimal, asymptotic scaling in the use of entangled pairs. We also identify a percolation effect in state preparation, in that from a threshold probability on, almost all preparations will be either successful or fail. We outline the implications on linear optical architectures and fault-tolerant computations.},
doi = {10.1103/PHYSREVA.74.042343},
url = {https://www.osti.gov/biblio/20857861}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 74,
place = {United States},
year = {Sun Oct 15 00:00:00 EDT 2006},
month = {Sun Oct 15 00:00:00 EDT 2006}
}