Quantum Logic under Semiclassical Limit: Information Loss

Abstract

We consider the quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semiclassical limit. We show that this reduction is caused by the fact that any elementary quantum logic operation (gate) suffers the information loss during the transition to its classical analog. Amount of the information lost is estimated for any gate from the complete set. We demonstrate that the largest loss is obtained for non-commuting gates. This allows us to consider the non-commutativity as the quantum computational speed-up resource. Our method allows us to quantify advantages of a quantum computation as compared to the classical one by the direct analysis of the involved basic logic. The obtained results are illustrated by the application to a quantum discrete Fourier transform and Grover search algorithms.