dorsal/arxiv
View SchemaFundamentals of universality in one-way quantum computation
| Authors | M. Van den Nest, W. Dür, A. Miyake, H. J. Briegel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702116 |
| URL | https://arxiv.org/abs/quant-ph/0702116 |
| DOI | 10.1088/1367-2630/9/6/204 |
| Journal | New J. Phys. 9 204 (2007) |
Abstract
We build a framework allowing for a systematic investigation of the issue: "Which quantum states are universal resources for one-way quantum computation?" We start by re-examining what is exactly meant by "universality" in quantum computation, and what the implications are for universal one-way quantum computation. Given the framework of a measurement-based quantum computer, where quantum information is processed by local operations only, the most general universal one-way quantum computer is one which is capable of accepting arbitrary classical inputs and producing arbitrary quantum outputs--we refer to this property as CQ-universality. We then show that a systematic study of CQ-universality in one-way quantum computation is possible by identifying entanglement features that must be present in every universal resource. These insights are used to identify several states as being not universal, such as 1D cluster states, W states, and ground states of non-critical 1D spin systems. Our criteria are strengthened by considering the efficiency of a quantum computation, and we find that entanglement measures must obey a certain scaling law with the system size for all efficient universal resources. This again leads to examples of non-universal resources, such as, e.g., ground states of critical 1D spin systems. We also provide several examples of efficient universal resources, namely graph states corresponding to hexagonal, triangular and Kagome lattices. Finally, we consider the more general notion of encoded CQ-universality, where quantum outputs are allowed to be produced in an encoded form. Again we provide entanglement-based criteria for encoded universality. Moreover, we present a general procedure to construct encoded universal resources.
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"abstract": "We build a framework allowing for a systematic investigation of the issue:\n\"Which quantum states are universal resources for one-way quantum computation?\"\nWe start by re-examining what is exactly meant by \"universality\" in quantum\ncomputation, and what the implications are for universal one-way quantum\ncomputation. Given the framework of a measurement-based quantum computer, where\nquantum information is processed by local operations only, the most general\nuniversal one-way quantum computer is one which is capable of accepting\narbitrary classical inputs and producing arbitrary quantum outputs--we refer to\nthis property as CQ-universality. We then show that a systematic study of\nCQ-universality in one-way quantum computation is possible by identifying\nentanglement features that must be present in every universal resource. These\ninsights are used to identify several states as being not universal, such as 1D\ncluster states, W states, and ground states of non-critical 1D spin systems.\nOur criteria are strengthened by considering the efficiency of a quantum\ncomputation, and we find that entanglement measures must obey a certain scaling\nlaw with the system size for all efficient universal resources. This again\nleads to examples of non-universal resources, such as, e.g., ground states of\ncritical 1D spin systems. We also provide several examples of efficient\nuniversal resources, namely graph states corresponding to hexagonal, triangular\nand Kagome lattices. Finally, we consider the more general notion of encoded\nCQ-universality, where quantum outputs are allowed to be produced in an encoded\nform. Again we provide entanglement-based criteria for encoded universality.\nMoreover, we present a general procedure to construct encoded universal\nresources.",
"arxiv_id": "quant-ph/0702116",
"authors": [
"M. Van den Nest",
"W. D\u00fcr",
"A. Miyake",
"H. J. Briegel"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/9/6/204",
"journal_ref": "New J. Phys. 9 204 (2007)",
"title": "Fundamentals of universality in one-way quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0702116"
},
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