Information-Theoretic Meaning of Quantum Information Flow and Its Applications to Amplitude Amplification Algorithms

TL;DR

This paper introduces an information-theoretic framework to analyze quantum information flow and applies it to understand amplitude amplification algorithms across various quantum computational models.

Contribution

It establishes a novel formalism linking quantum information flow to amplitude amplification, providing new insights into quantum algorithm dynamics.

Findings

Information flow corresponds to the rate of uncertainty change about the system.

The formalism applies to quantum circuits, analog, and adiabatic computations.

Insights into amplitude amplification through information leakage are obtained.

Abstract

The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of analyzing and quantifying loss or gain of information on a quantum system when the system interacts with its environment. We show that the information flow, the theoretical method of characterizing (non-)Markovianity of quantum dynamics, corresponds to the rate of the minimum uncertainty about the system given quantum side information. Thereafter, we analyze the information exchange among subsystems that are under the performance of quantum algorithms, in particular, the amplitude amplification algorithms where the computational process relies fully on quantum evolution. Different realizations of the algorithm are considered, such as i)quantum circuits, ii) analog computation, and iii) adiabatic computation. It is shown that, in all the cases, our formalism provides insights about the process of amplifying the amplitude from the information flow or leakage on the subsystems.