Necessary and Sufficient Condition for Quantum Computing

Koji Nagata; Tadao Nakamura; Ahmed Farouk; Do Ngoc Diep

doi:10.1007/s10773-018-3917-x

Necessary and Sufficient Condition for Quantum Computing

Koji Nagata^*
, Tadao Nakamura
, Ahmed Farouk
, Do Ngoc Diep

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

A necessary and sufficient condition for quantum computing performed with, for example, the Deutsch-Jozsa algorithm or the Bernstein-Vazirani algorithm, has theoretically been investigated. Assume a 2N qubit-quantum computing which starts with the state | 0 , 0 ,.. , 0 , 1 ⏞ N〉 | 1 , 1 ,.. , 1 ⏞ N〉 as follows: U_f|0,0,..,0,1〉|1,1,..,1〉 = |0,0,..,0,1〉 | f(0 , 0 ,.. , 0 , 1) ¯ 〉. Surprisingly the relation f(x) = f(−x) is the necessary and sufficient condition of holding this fundamental relation if local unitary operations can be used.

Original language	English
Pages (from-to)	136-142
Number of pages	7
Journal	International Journal of Theoretical Physics
Volume	58
Issue number	1
DOIs	https://doi.org/10.1007/s10773-018-3917-x
Publication status	Published - 15 Jan 2019
Externally published	Yes

Keywords

Quantum algorithms
Quantum computation

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10.1007/s10773-018-3917-x

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title = "Necessary and Sufficient Condition for Quantum Computing",

abstract = "A necessary and sufficient condition for quantum computing performed with, for example, the Deutsch-Jozsa algorithm or the Bernstein-Vazirani algorithm, has theoretically been investigated. Assume a 2N qubit-quantum computing which starts with the state | 0 , 0 ,.. , 0 , 1 ⏞ N〉 | 1 , 1 ,.. , 1 ⏞ N〉 as follows: Uf|0,0,..,0,1〉|1,1,..,1〉 = |0,0,..,0,1〉 | f(0 , 0 ,.. , 0 , 1) ¯ 〉. Surprisingly the relation f(x) = f(−x) is the necessary and sufficient condition of holding this fundamental relation if local unitary operations can be used.",

keywords = "Quantum algorithms, Quantum computation",

author = "Koji Nagata and Tadao Nakamura and Ahmed Farouk and Diep, \{Do Ngoc\}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

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doi = "10.1007/s10773-018-3917-x",

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T1 - Necessary and Sufficient Condition for Quantum Computing

AU - Nagata, Koji

AU - Nakamura, Tadao

AU - Farouk, Ahmed

AU - Diep, Do Ngoc

PY - 2019/1/15

Y1 - 2019/1/15

N2 - A necessary and sufficient condition for quantum computing performed with, for example, the Deutsch-Jozsa algorithm or the Bernstein-Vazirani algorithm, has theoretically been investigated. Assume a 2N qubit-quantum computing which starts with the state | 0 , 0 ,.. , 0 , 1 ⏞ N〉 | 1 , 1 ,.. , 1 ⏞ N〉 as follows: Uf|0,0,..,0,1〉|1,1,..,1〉 = |0,0,..,0,1〉 | f(0 , 0 ,.. , 0 , 1) ¯ 〉. Surprisingly the relation f(x) = f(−x) is the necessary and sufficient condition of holding this fundamental relation if local unitary operations can be used.

AB - A necessary and sufficient condition for quantum computing performed with, for example, the Deutsch-Jozsa algorithm or the Bernstein-Vazirani algorithm, has theoretically been investigated. Assume a 2N qubit-quantum computing which starts with the state | 0 , 0 ,.. , 0 , 1 ⏞ N〉 | 1 , 1 ,.. , 1 ⏞ N〉 as follows: Uf|0,0,..,0,1〉|1,1,..,1〉 = |0,0,..,0,1〉 | f(0 , 0 ,.. , 0 , 1) ¯ 〉. Surprisingly the relation f(x) = f(−x) is the necessary and sufficient condition of holding this fundamental relation if local unitary operations can be used.

KW - Quantum algorithms

KW - Quantum computation

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M3 - Article

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EP - 142

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JF - International Journal of Theoretical Physics

IS - 1

ER -

Necessary and Sufficient Condition for Quantum Computing

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