As a classic quantum computing implementation, the Deustch-Jozsa (DJ) algorithm is taught in many courses pertaining to quantum information science and technology (QIST). We exploit the DJ framework as an educational testbed, illustrating fundamental qubit concepts while identifying associated algorithmic challenges. In this work, we present a self-contained exploration which may be beneficial in educating the future quantum workforce. Quantum Key Distribution (QKD), an improvement over the classical Public Key Infrastructure (PKI), allows two parties, Alice and Bob, to share a secret key by using the quantum physical properties. For QKD the DJ-packets, consisting of the input qubits and the target qubit for the DJ algorithm, carry the secret information between Alice and Bob. Previous research from Nagata and Nakamura discovered in 2015 that the DJ algorithm for QKD allows an attacker to successfully intercept and remain undetected. Improving upon the past research we increased the entropy of DJ-packets through: (i) size hopping (H), where the number of qubits in consecutive DJ-packets keeps on changing and (ii) reordering (R) the qubits within the DJ-packets. These concepts together illustrate the multiple scales where entropy may increase in a DJ algorithm to make for a more robust QKD framework, and therefore significantly decrease Eve’s chance of success. The proof of concept of the new schemes is tested on Google’s Cirq quantum simulator, and detailed python simulations show that attacker’s interception success rate can be drastically reduced.As a classic quantum computing implementation, the Deustch-Jozsa (DJ) algorithm is taught in many courses pertaining to quantum information science and technology (QIST). We exploit the DJ framework as an educational testbed, illustrating fundamental qubit concepts while identifying associated algorithmic challenges. In this work, we present a self-contained exploration which may be beneficial in educating the future quantum workforce. Quantum Key Distribution (QKD), an improvement over the classical Public Key Infrastructure (PKI), allows two parties, Alice and Bob, to share a secret key by using the quantum physical properties. For QKD the DJ-packets, consisting of the input qubits and the target qubit for the DJ algorithm, carry the secret information between Alice and Bob. Previous research from Nagata and Nakamura discovered in 2015 that the DJ algorithm for QKD allows an attacker to successfully intercept and remain undetected. Improving upon the past research we increased the entropy of DJ-packets through: (i) size hopping (H), where the number of qubits in consecutive DJ-packets keeps on changing and (ii) reordering (R) the qubits within the DJ-packets. These concepts together illustrate the multiple scales where entropy may increase in a DJ algorithm to make for a more robust QKD framework, and therefore significantly decrease Eve’s chance of success. The proof of concept of the new schemes is tested on Google’s Cirq quantum simulator, and detailed python simulations show that attacker’s interception success rate can be drastically reduced.

IEEE International Conference on Quantum Computing and Engineering (QCE)Oct 1, 20218 citations

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

M. Ghadimi, V. Salari, S. Bakrani +4 more

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

Distributed exact quantum algorithms for Deutsch-Jozsa problem

Hao Li, Daowen Qiu, Le Luo

Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$ : $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can solve it exactly with one query. In this paper, we first discover the inherent structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between $f$ being constant (balanced) and some properties of $f$ 's subfunctions, and then we propose three distributed exact quantum algorithms for solving DJ problem. Our algorithms have essential acceleration over distributed classical deterministic algorithm, and can be extended to the case of multiple computing nodes. Compared with DJ algorithm, our algorithms can reduce the number of qubits and the depth of circuit implementing a single query operator. Therefore, we find that the structure of problem should be clarified for designing distributed quantum algorithm to solve it.Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can solve it exactly with one query. In this paper, we first discover the inherent structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between $f$ being constant (balanced) and some properties of $f$'s subfunctions, and then we propose three distributed exact quantum algorithms for solving DJ problem. Our algorithms have essential acceleration over distributed classical deterministic algorithm, and can be extended to the case of multiple computing nodes. Compared with DJ algorithm, our algorithms can reduce the number of qubits and the depth of circuit implementing a single query operator. Therefore, we find that the structure of problem should be clarified for designing distributed quantum algorithm to solve it.

arXiv:2303.10663Mar 19, 20235 citations

Quantum Cryptography Based on the Deutsch-Jozsa Algorithm

Koji Nagata, Tadao Nakamura, Ahmed Farouk

International Journal of Theoretical PhysicsJun 21, 201763 citations

Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function

f

\{0,1\}^n\rightarrow \{0,1\}

with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can solve it exactly with one query. In this paper, we first discover the inherent structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between

f

being constant (balanced) and some properties of

f

's subfunctions, and then we propose three distributed exact quantum algorithms for solving DJ problem. Our algorithms have essential acceleration over distributed classical deterministic algorithm, and can be extended to the case of multiple computing nodes. Compared with DJ algorithm, our algorithms can reduce the number of qubits and the depth of circuit implementing a single query operator. Therefore, we find that the structure of problem should be clarified for designing distributed quantum algorithm to solve it.