Generalized Deutsch-Jozsa Algorithm for Applications in Data Classification, Logistic Regression, and Quantum Key Distribution

TL;DR

This paper introduces a generalized Deutsch-Jozsa quantum algorithm that efficiently characterizes Boolean functions and retrieves their output values, enabling practical applications in data classification, logistic regression, and quantum cryptography.

Contribution

It extends the original Deutsch-Jozsa algorithm to determine explicit function outputs alongside global type with a single query, using Bell states as ancilla.

Findings

Enables richer function characterization with minimal queries

Applicable to data classification, logistic regression, and quantum cryptography

Achieves practical quantum advantages in these applications

Abstract

We present a generalized Deutsch-Jozsa (DJ) quantum algorithm that not only determines both the global type of an unknown Boolean function (constant or balanced) but also determines explicit output values of the function in a single oracle query. Unlike the original DJ algorithm, which identifies only whether a function is constant or balanced, our generalization retrieves actual function output values at the same time with using a Bell state as ancilla. This makes a richer function characterization with minimal queries to have practical quantum advantages, e.g. data classification, logistic regression, and quantum cryptography.