dorsal/arxiv
View SchemaAlgebras and universal quantum computations with higher dimensional systems
| Authors | Alexander Yu. Vlasov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210049 |
| URL | https://arxiv.org/abs/quant-ph/0210049 |
| DOI | 10.1117/12.517863 |
| Journal | Proc. SPIE 5128, 29 (2003) |
Abstract
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and discussed well known applications to product operator formalism in NMR, Jordan-Wigner construction in fermionic quantum computations. It is introduced universal set of quantum gates for higher dimensional system (``qudit''), as some generalization of these models. Finally it is briefly mentioned possible application of such algebraic methods to design of quantum processors (programmable gates arrays) and discussed generalization to quantum computation with continuous variables.
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"abstract": "Here is discussed application of the Weyl pair to construction of universal\nset of quantum gates for high-dimensional quantum system. An application of Lie\nalgebras (Hamiltonians) for construction of universal gates is revisited first.\nIt is shown next, how for quantum computation with qubits can be used\ntwo-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford\nalgebras, and discussed well known applications to product operator formalism\nin NMR, Jordan-Wigner construction in fermionic quantum computations. It is\nintroduced universal set of quantum gates for higher dimensional system\n(``qudit\u0027\u0027), as some generalization of these models. Finally it is briefly\nmentioned possible application of such algebraic methods to design of quantum\nprocessors (programmable gates arrays) and discussed generalization to quantum\ncomputation with continuous variables.",
"arxiv_id": "quant-ph/0210049",
"authors": [
"Alexander Yu. Vlasov"
],
"categories": [
"quant-ph"
],
"doi": "10.1117/12.517863",
"journal_ref": "Proc. SPIE 5128, 29 (2003)",
"title": "Algebras and universal quantum computations with higher dimensional systems",
"url": "https://arxiv.org/abs/quant-ph/0210049"
},
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