dorsal/arxiv
View SchemaA Scheme of Cartan Decomposition for su(N)
| Authors | Zheng-Yao Su |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603190 |
| URL | https://arxiv.org/abs/quant-ph/0603190 |
Abstract
A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The schme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated by a Cartan subalgebra and generally exist in su(N). In particular, the Lie algebras su(2^p) and every su(2^{p-1} < N < 2^p) share the isomorphic structure of the quotient algebra. This structure enables an efficient algorithm for the recursive and exhaustive construction of Cartan decompositions. Further with the scheme, a unitary transformation in SU(N) can be recursively decomposed into a product of certain designated operators, e.g., local and nonlocal gates. Such a recursive decomposition of a transformation implies an evolution path on the manifold of the group.
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"abstract": "A scheme to perform the Cartan decomposition for the Lie algebra su(N) of\narbitrary finite dimensions is introduced. The schme is based on two algebraic\nstructures, the conjugate partition and the quotient algebra, that are easily\ngenerated by a Cartan subalgebra and generally exist in su(N). In particular,\nthe Lie algebras su(2^p) and every su(2^{p-1} \u003c N \u003c 2^p) share the isomorphic\nstructure of the quotient algebra. This structure enables an efficient\nalgorithm for the recursive and exhaustive construction of Cartan\ndecompositions. Further with the scheme, a unitary transformation in SU(N) can\nbe recursively decomposed into a product of certain designated operators, e.g.,\nlocal and nonlocal gates. Such a recursive decomposition of a transformation\nimplies an evolution path on the manifold of the group.",
"arxiv_id": "quant-ph/0603190",
"authors": [
"Zheng-Yao Su"
],
"categories": [
"quant-ph"
],
"title": "A Scheme of Cartan Decomposition for su(N)",
"url": "https://arxiv.org/abs/quant-ph/0603190"
},
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