dorsal/arxiv
View SchemaTheoretical Analyses of Quantum Counting against Decoherence Errors
| Authors | Jun Hasegawa, Fumitaka Yura |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503202 |
| URL | https://arxiv.org/abs/quant-ph/0503202 |
Abstract
In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the quantum counting with the depolarizing channel. We also implement two circuits for the quantum counting -- the ascending-order circuit and the descending-order circuit -- by reversing ordering of application of controlled-Grover operations. By theoretical and numerical calculations for probability distributions, we reveal the difference of probability distributions on two circuits in the presence of decoherence and show that the ascending-order circuit is more robust against the decoherence than the descending-order circuit. This property of the robustness is applicable to the phase estimation such as the factoring.
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"abstract": "In this paper, we analyze the quantum counting under the decoherence, which\ncan find the number of solutions satisfying a given oracle. We investigate\nprobability distributions related to the first order term of the error rate on\nthe quantum counting with the depolarizing channel. We also implement two\ncircuits for the quantum counting -- the ascending-order circuit and the\ndescending-order circuit -- by reversing ordering of application of\ncontrolled-Grover operations. By theoretical and numerical calculations for\nprobability distributions, we reveal the difference of probability\ndistributions on two circuits in the presence of decoherence and show that the\nascending-order circuit is more robust against the decoherence than the\ndescending-order circuit. This property of the robustness is applicable to the\nphase estimation such as the factoring.",
"arxiv_id": "quant-ph/0503202",
"authors": [
"Jun Hasegawa",
"Fumitaka Yura"
],
"categories": [
"quant-ph"
],
"title": "Theoretical Analyses of Quantum Counting against Decoherence Errors",
"url": "https://arxiv.org/abs/quant-ph/0503202"
},
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