TY - JOUR
T1 - New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm
AU - Nagata, Koji
AU - Nakamura, Tadao
AU - Geurdes, Han
AU - Batle, Josep
AU - Abdalla, Soliman
AU - Farouk, Ahmed
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values { a1, a2, a3, … , aN} and a function g: R→ { 0 , 1 } , we shall determine the following values { g(a1) , g(a2) , g(a3) , … , g(aN) } simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Next, we consider it as a number in binary representation; M1 = (g(a1),g(a2),g(a3),…,g(aN)). By using M parallel quantum systems, we have M numbers in binary representation, simultaneously. The speed of obtaining the M numbers is shown to outperform the classical case by a factor of M. Finally, we calculate the product; M1× M2× ⋯ × MM. The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.
AB - We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values { a1, a2, a3, … , aN} and a function g: R→ { 0 , 1 } , we shall determine the following values { g(a1) , g(a2) , g(a3) , … , g(aN) } simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Next, we consider it as a number in binary representation; M1 = (g(a1),g(a2),g(a3),…,g(aN)). By using M parallel quantum systems, we have M numbers in binary representation, simultaneously. The speed of obtaining the M numbers is shown to outperform the classical case by a factor of M. Finally, we calculate the product; M1× M2× ⋯ × MM. The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.
KW - Quantum algorithms
KW - Quantum computation
UR - http://www.scopus.com/inward/record.url?scp=85041906687&partnerID=8YFLogxK
U2 - 10.1007/s10773-018-3687-5
DO - 10.1007/s10773-018-3687-5
M3 - Article
AN - SCOPUS:85041906687
SN - 0020-7748
VL - 57
SP - 1605
EP - 1611
JO - International Journal of Theoretical Physics
JF - International Journal of Theoretical Physics
IS - 6
ER -