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.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.

quant-pharXiv:2512.00715Physical Review ADec 2, 20250 citations

Quantum Computing Concepts with Deutsch Jozsa Algorithm

Poornima Aradyamath, N. M. Naghabhushana, Rohitha Ujjinimatad

In this paper, we briefly review the basic concepts of quantum computation, entanglement, quantum cryptography and quantum fourier transform. Quantum algorithms like Deutsch Jozsa, Shor’s factorization and Grover’s data search are developed using fourier transform and quantum computation concepts to build quantum computers. Researchers are finding a way to build quantum computer that works more efficiently than classical computer. Among the standard well known algorithms in the field of quantum computation and communication we describe mathematically Deutsch Jozsa algorithm in detail for 2 and 3 qubits. Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.In this paper, we briefly review the basic concepts of quantum computation, entanglement, quantum cryptography and quantum fourier transform. Quantum algorithms like Deutsch Jozsa, Shor’s factorization and Grover’s data search are developed using fourier transform and quantum computation concepts to build quantum computers. Researchers are finding a way to build quantum computer that works more efficiently than classical computer. Among the standard well known algorithms in the field of quantum computation and communication we describe mathematically Deutsch Jozsa algorithm in detail for 2 and 3 qubits. Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.

JOIV International Journal on Informatics VisualizationJan 10, 20196 citations

Quantum Cryptography and Quantum Computation

John Rarity

European Quantum Electronics Conference (EQEC)Jan 1, 19962 citations

Quantum Cryptography

Toshio HASEGAWA, Tsuyoshi Nishioka, Hirokazu ISHIZUKA

Nihon Kikai Gakkaishi/Journal of the Japan Society of Mechanical EngineersJan 1, 20060 citations

Deutsch-Jozsa Algorithm Revisited in the Domain of Cryptographically Significant Boolean Functions

Subhamoy Maitra, Partha Mukhopadhyay

Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let $f$ be an $n$ -variable Boolean function and its Walsh spectra is denoted by $W_f(ω)$ at the point $ω\in \{0, 1\}^n$ . The Boolean function is available in the form of an oracle. We like to find an $ω$ such that $W_f(ω) \neq 0$ as this will provide one of the linear functions which are correlated to $f$ . We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in $n$ . We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let $f$ be an $n$-variable Boolean function and its Walsh spectra is denoted by $W_f(ω)$ at the point $ω\in \{0, 1\}^n$. The Boolean function is available in the form of an oracle. We like to find an $ω$ such that $W_f(ω) \neq 0$ as this will provide one of the linear functions which are correlated to $f$. We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in $n$. We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.

arXiv:quant-ph/0410042Oct 6, 20044 citations

f

be an

n

-variable Boolean function and its Walsh spectra is denoted by

W_f(ω)

at the point

ω\in \{0, 1\}^n

. The Boolean function is available in the form of an oracle. We like to find an

ω

such that

W_f(ω) \neq 0

as this will provide one of the linear functions which are correlated to

f

. We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in

n

. We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.