dorsal/arxiv
View SchemaClassical simulation versus universality in measurement based quantum computation
| Authors | M. Van den Nest, W. Dür, G. Vidal, H. J. Briegel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608060 |
| URL | https://arxiv.org/abs/quant-ph/0608060 |
| DOI | 10.1103/PhysRevA.75.012337 |
| Journal | Phys. Rev. A 75, 012337 (2007) |
Abstract
We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt--rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidt--rank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement based quantum computation is possible for all states with logarithmically bounded Schmidt--rank width (with respect to the system size). For graph states where the Schmidt--rank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory.
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"abstract": "We investigate for which resource states an efficient classical simulation of\nmeasurement based quantum computation is possible. We show that the\nSchmidt--rank width, a measure recently introduced to assess universality of\nresource states, plays a crucial role in also this context. We relate\nSchmidt--rank width to the optimal description of states in terms of tree\ntensor networks and show that an efficient classical simulation of measurement\nbased quantum computation is possible for all states with logarithmically\nbounded Schmidt--rank width (with respect to the system size). For graph states\nwhere the Schmidt--rank width scales in this way, we efficiently construct the\noptimal tree tensor network descriptions, and provide several examples. We\nhighlight parallels in the efficient description of complex systems in quantum\ninformation theory and graph theory.",
"arxiv_id": "quant-ph/0608060",
"authors": [
"M. Van den Nest",
"W. D\u00fcr",
"G. Vidal",
"H. J. Briegel"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.012337",
"journal_ref": "Phys. Rev. A 75, 012337 (2007)",
"title": "Classical simulation versus universality in measurement based quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0608060"
},
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