## Quantum Algorithm Determining a Homogeneous Linear Function

**Authors:** Koji Nagata, Tadao Nakamura, Han Geurdes, Josep Batle, Soliman Abdalla, Ahmed Farouk, Do Ngoc Diep

We present
a method of fast determining a homogeneous linear function
$f(x):= s.x=s_1x_1+ s_2x_2+\dots+s_Nx_N$ from
$\{0,1,\dots,d-1\}^N$ with coefficients
$s=(s_1,\dots,s_N)$.
Here $x=(x_1,\dots,x_N)$ and $x_j\in{\bf R}$.
Given the interpolation values $(f(1), f(2),...,f(N))=\vec{y}$,
we shall determine the unknown coefficients
$s = (s_1(\vec{y}),\dots, s_N(\vec{y}))$
of the linear function, simultaneously.
The speed of determining the values is shown
to outperform
the classical case by a factor of $N$.
Our method is based on the generalized Bernstein-Vazirani
algorithm \cite{BVG} to qudit systems \cite{BVD}.

**Comments:** 6 Pages

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### Submission history

[v1] 2017-09-01 14:19:28

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