Quantum logic under semi-classical limit: information loss

TL;DR

This paper analyzes how quantum logic operations lose information when transitioning to classical logic under semi-classical limits, quantifying the loss and its impact on quantum computational advantages.

Contribution

It introduces a method to quantify information loss in quantum gates during semi-classical transition, linking it to quantum speed-up resources.

Findings

Non-commuting gates exhibit the largest information loss.

Quantum algorithms like Fourier transform and Grover search are analyzed for information loss.

The method quantifies quantum advantage by analyzing basic quantum logic operations.

Abstract

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