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

Journal Article · Sun Oct 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.042343· OSTI ID:20857861

Gross, D; Kieling, K; Eisert, J ^[1]

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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)

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.

• OSTI ID: 20857861
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 74; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

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