LAUSR

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s1x1 + s2x2 + ⋯ + sNxN is proposed. Here x = (x1, … , xN), xj ∈ R and the coefficients s = (s1, … , sN), sj ∈ N. Given the interpolation values (f(1),f(2),...,f(N))=y→$(f(1), f(2),...,f(N))=\vec {y}$, the unknown coefficients s=(s1(y→),…,sN(y→))$s = (s_{1}(\vec {y}),\dots , s_{N}(\vec {y}))$ of the linear function shall be determined, 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 to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.