New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

Koji Nagata; Tadao Nakamura; Han Geurdes; Josep Batle; Soliman Abdalla; Ahmed Farouk

doi:10.1007/s10773-018-3687-5

New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

Koji Nagata^*
, Tadao Nakamura
, Han Geurdes
, Josep Batle
, Soliman Abdalla
, Ahmed Farouk

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

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, … , a_N} and a function g: R→ { 0 , 1 } , we shall determine the following values { g(a₁) , g(a₂) , g(a₃) , … , g(a_N) } 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(a_N)). 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× ⋯ × M_M. The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.

Original language	English
Pages (from-to)	1605-1611
Number of pages	7
Journal	International Journal of Theoretical Physics
Volume	57
Issue number	6
DOIs	https://doi.org/10.1007/s10773-018-3687-5
Publication status	Published - 1 Jun 2018
Externally published	Yes

Keywords

Quantum algorithms
Quantum computation

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10.1007/s10773-018-3687-5

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title = "New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm",

abstract = "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.",

keywords = "Quantum algorithms, Quantum computation",

author = "Koji Nagata and Tadao Nakamura and Han Geurdes and Josep Batle and Soliman Abdalla and Ahmed Farouk",

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

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doi = "10.1007/s10773-018-3687-5",

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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

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

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M3 - Article

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SP - 1605

EP - 1611

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

IS - 6

ER -

New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

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