dorsal/arxiv
View SchemaClassical simulatability, entanglement breaking, and quantum computation thresholds
| Authors | S. Virmani, Susana F. Huelga, Martin B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408076 |
| URL | https://arxiv.org/abs/quant-ph/0408076 |
| DOI | 10.1103/PhysRevA.71.042328 |
| Journal | Phys. Rev. A. 71, 042328 (2005) |
Abstract
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding the nature of the quantum/classical computational transition. We refine some previously known upper bounds using two different strategies. The first one involves the introduction of bi-entangling operations, a class of classically simulatable machines that can generate at most bipartite entanglement. Using this class we show that it is possible to sharpen previously obtained upper bounds in certain cases. As an example, we show that under depolarizing noise on the controlled-not gate, the previously known upper bound of 74% can be sharpened to around 67%. Another interesting consequence is that measurement based schemes cannot work using only 2-qubit non-degenerate projections. In the second strand of the work we utilize the Gottesman-Knill theorem on the classically efficient simulation of Clifford group operations. The bounds attained for the pi/8 gate using this approach can be as low as 15% for general single gate noise, and 30% for dephasing noise.
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"abstract": "We investigate the amount of noise required to turn a universal quantum gate\nset into one that can be efficiently modelled classically. This question is\nuseful for providing upper bounds on fault tolerant thresholds, and for\nunderstanding the nature of the quantum/classical computational transition. We\nrefine some previously known upper bounds using two different strategies. The\nfirst one involves the introduction of bi-entangling operations, a class of\nclassically simulatable machines that can generate at most bipartite\nentanglement. Using this class we show that it is possible to sharpen\npreviously obtained upper bounds in certain cases. As an example, we show that\nunder depolarizing noise on the controlled-not gate, the previously known upper\nbound of 74% can be sharpened to around 67%. Another interesting consequence is\nthat measurement based schemes cannot work using only 2-qubit non-degenerate\nprojections. In the second strand of the work we utilize the Gottesman-Knill\ntheorem on the classically efficient simulation of Clifford group operations.\nThe bounds attained for the pi/8 gate using this approach can be as low as 15%\nfor general single gate noise, and 30% for dephasing noise.",
"arxiv_id": "quant-ph/0408076",
"authors": [
"S. Virmani",
"Susana F. Huelga",
"Martin B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.042328",
"journal_ref": "Phys. Rev. A. 71, 042328 (2005)",
"title": "Classical simulatability, entanglement breaking, and quantum computation thresholds",
"url": "https://arxiv.org/abs/quant-ph/0408076"
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