dorsal/arxiv
View SchemaQuantum learning and universal quantum matching machine
| Authors | Masahide Sasaki, Alberto Carlini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202173 |
| URL | https://arxiv.org/abs/quant-ph/0202173 |
| DOI | 10.1103/PhysRevA.66.022303 |
| Journal | Phys. Rev. A66, 022303 (2002). |
Abstract
Suppose that three kinds of quantum systems are given in some unknown states $\ket f^{\otimes N}$, $\ket{g_1}^{\otimes K}$, and $\ket{g_2}^{\otimes K}$, and we want to decide which \textit{template} state $\ket{g_1}$ or $\ket{g_2}$, each representing the feature of the pattern class ${\cal C}_1$ or ${\cal C}_2$, respectively, is closest to the input \textit{feature} state $\ket f$. This is an extension of the pattern matching problem into the quantum domain. Assuming that these states are known a priori to belong to a certain parametric family of pure qubit systems, we derive two kinds of matching strategies. The first is a semiclassical strategy which is obtained by the natural extension of conventional matching strategies and consists of a two-stage procedure: identification (estimation) of the unknown template states to design the classifier (\textit{learning} process to train the classifier) and classification of the input system into the appropriate pattern class based on the estimated results. The other is a fully quantum strategy without any intermediate measurement which we might call as the {\it universal quantum matching machine}. We present the Bayes optimal solutions for both strategies in the case of K=1, showing that there certainly exists a fully quantum matching procedure which is strictly superior to the straightforward semiclassical extension of the conventional matching strategy based on the learning process.
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"abstract": "Suppose that three kinds of quantum systems are given in some unknown states\n$\\ket f^{\\otimes N}$, $\\ket{g_1}^{\\otimes K}$, and $\\ket{g_2}^{\\otimes K}$, and\nwe want to decide which \\textit{template} state $\\ket{g_1}$ or $\\ket{g_2}$,\neach representing the feature of the pattern class ${\\cal C}_1$ or ${\\cal\nC}_2$, respectively, is closest to the input \\textit{feature} state $\\ket f$.\nThis is an extension of the pattern matching problem into the quantum domain.\nAssuming that these states are known a priori to belong to a certain parametric\nfamily of pure qubit systems, we derive two kinds of matching strategies. The\nfirst is a semiclassical strategy which is obtained by the natural extension of\nconventional matching strategies and consists of a two-stage procedure:\nidentification (estimation) of the unknown template states to design the\nclassifier (\\textit{learning} process to train the classifier) and\nclassification of the input system into the appropriate pattern class based on\nthe estimated results. The other is a fully quantum strategy without any\nintermediate measurement which we might call as the {\\it universal quantum\nmatching machine}. We present the Bayes optimal solutions for both strategies\nin the case of K=1, showing that there certainly exists a fully quantum\nmatching procedure which is strictly superior to the straightforward\nsemiclassical extension of the conventional matching strategy based on the\nlearning process.",
"arxiv_id": "quant-ph/0202173",
"authors": [
"Masahide Sasaki",
"Alberto Carlini"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.022303",
"journal_ref": "Phys. Rev. A66, 022303 (2002).",
"title": "Quantum learning and universal quantum matching machine",
"url": "https://arxiv.org/abs/quant-ph/0202173"
},
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