TY - JOUR
T1 - Necessary and Sufficient Condition for Quantum Computing
AU - Nagata, Koji
AU - Nakamura, Tadao
AU - Farouk, Ahmed
AU - Diep, Do Ngoc
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
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
UR - https://www.scopus.com/pages/publications/85055314937
U2 - 10.1007/s10773-018-3917-x
DO - 10.1007/s10773-018-3917-x
M3 - Article
AN - SCOPUS:85055314937
SN - 0020-7748
VL - 58
SP - 136
EP - 142
JO - International Journal of Theoretical Physics
JF - International Journal of Theoretical Physics
IS - 1
ER -