dorsal/arxiv
View SchemaComputational approach to quantum encoder design for purity optimization
| Authors | Naoki Yamamoto, Maryam Fazel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606106 |
| URL | https://arxiv.org/abs/quant-ph/0606106 |
| DOI | 10.1103/PhysRevA.76.012327 |
| Journal | Physical Review A 76, 012327 (2007) |
Abstract
In this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min optimization problem with a rank constraint on an appropriately defined matrix variable. The problem is computationally very hard because it is non-convex with respect to both the objective function (output purity) and the rank constraint. Despite this difficulty, we provide a tractable computational algorithm that produces the exact optimal solution for codespace of dimension two. Moreover, this algorithm is easily extended to cover the general class of codespaces, in which case the solution is suboptimal in the sense that the suboptimized output purity serves as a lower bound of the exact optimal purity. The algorithm consists of a sequence of semidefinite programmings and can be performed easily. Two typical quantum error channels are investigated to illustrate the effectiveness of our method.
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"abstract": "In this paper, we address the problem of designing a quantum encoder that\nmaximizes the minimum output purity of a given decohering channel, where the\nminimum is taken over all possible pure inputs. This problem is cast as a\nmax-min optimization problem with a rank constraint on an appropriately defined\nmatrix variable. The problem is computationally very hard because it is\nnon-convex with respect to both the objective function (output purity) and the\nrank constraint. Despite this difficulty, we provide a tractable computational\nalgorithm that produces the exact optimal solution for codespace of dimension\ntwo. Moreover, this algorithm is easily extended to cover the general class of\ncodespaces, in which case the solution is suboptimal in the sense that the\nsuboptimized output purity serves as a lower bound of the exact optimal purity.\nThe algorithm consists of a sequence of semidefinite programmings and can be\nperformed easily. Two typical quantum error channels are investigated to\nillustrate the effectiveness of our method.",
"arxiv_id": "quant-ph/0606106",
"authors": [
"Naoki Yamamoto",
"Maryam Fazel"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.76.012327",
"journal_ref": "Physical Review A 76, 012327 (2007)",
"title": "Computational approach to quantum encoder design for purity optimization",
"url": "https://arxiv.org/abs/quant-ph/0606106"
},
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