dorsal/arxiv
View SchemaPotential and limits to cluster state quantum computing using probabilistic gates
| Authors | D. Gross, K. Kieling, J. Eisert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605014 |
| URL | https://arxiv.org/abs/quant-ph/0605014 |
| DOI | 10.1103/PhysRevA.74.042343 |
| Journal | Phys. Rev. A 74, 042343 (2006) |
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 non-faulty 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.
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"abstract": "We establish bounds to the necessary resource consumption when building up\ncluster states for one-way computing using probabilistic gates. Emphasis is put\non state preparation with linear optical gates, as the probabilistic character\nis unavoidable here. We identify rigorous general bounds to the necessary\nconsumption of initially available maximally entangled pairs when building up\none-dimensional cluster states with individually acting linear optical quantum\ngates, entangled pairs and vacuum modes. As the known linear optics gates have\na limited maximum success probability, as we show, this amounts to finding the\noptimal classical strategy of fusing pieces of linear cluster states. A formal\nnotion of classical configurations and strategies is introduced for\nprobabilistic non-faulty gates. We study the asymptotic performance of\nstrategies that can be simply described, and prove ultimate bounds to the\nperformance of the globally optimal strategy. The arguments employ methods of\nrandom walks and convex optimization. This optimal strategy is also the one\nthat requires the shortest storage time, and necessitates the fewest\ninvocations of probabilistic gates. For two-dimensional cluster states, we\nfind, for any elementary success probability, an essentially deterministic\npreparation of a cluster state with quadratic, hence optimal, asymptotic\nscaling in the use of entangled pairs. We also identify a percolation effect in\nstate preparation, in that from a threshold probability on, almost all\npreparations will be either successful or fail. We outline the implications on\nlinear optical architectures and fault-tolerant computations.",
"arxiv_id": "quant-ph/0605014",
"authors": [
"D. Gross",
"K. Kieling",
"J. Eisert"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.042343",
"journal_ref": "Phys. Rev. A 74, 042343 (2006)",
"title": "Potential and limits to cluster state quantum computing using probabilistic gates",
"url": "https://arxiv.org/abs/quant-ph/0605014"
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