Quantum Physics


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}.

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

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