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IEEE International Conference on Quantum Computing and Engineering (QCE)

Multi-Qubit Size-Hopping Deutsch-Jozsa Algorithm with Qubit Reordering for Secure Quantum Key Distribution

Rohit De, Raymond Moberly, Colton Beery, Jeremy Juybari, K. M. Sundqvist

Published Oct 1, 2021• 8 citations

Abstract

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.

DOI: 10.1109/qce52317.2021.00084

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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.

A scheme to execute an \\eta-bit Deutsch-Jozsa (DJ) algorithm using \\eta qubits has been implemented for up to three qubits on an NMR quantum computer. For the one- and the two-bit Deutsch problem, the qubits do not get entangled, and the NMR implementation is achieved without using spin-spin interactions. It is for the three-bit case, that the manipulation of entangled states becomes essential. The interactions through scalar J-couplings in NMR spin systems have been exploited to implement entangling transformations required for the three bit DJ algorithm.

The accelerating development of quantum computing capabilities poses an unprecedented challenge to conventional encryption methodologies that currently underpin global digital security infrastructure. Classical cryptographic systems, including widely adopted standards such as RSA and AES, derive their security from the computational intractability of specific mathematical problems, a foundation that quantum algorithms threaten to fundamentally undermine. This research presents a comprehensive investigation into the practical implementation of Quantum Key Distribution as a transformative approach to establishing unconditionally secure communication channels. Through experimental deployment of the BB84 protocol augmented with advanced quantum error correction and privacy amplification techniques, we systematically evaluate the performance characteristics and security guarantees of QKD in realistic network environments. Our experimental framework achieves a secure key generation rate of 2.5 megabits per second while maintaining an average quantum bit error rate of 3.2 percent, demonstrating the practical viability of quantum-secured communication. The implementation exhibits exceptional eavesdropping detection capabilities with a 98.5 percent success rate in identifying unauthorized interception attempts. Comparative security analysis reveals that QKD-based encryption reduces vulnerability to brute-force attacks by 65 percent when contrasted with classical encryption standards. The integration of lattice-based post-quantum cryptographic algorithms provides an additional security layer against store-now-decrypt-later attack strategies. These findings substantiate the position of Quantum Key Distribution as a cornerstone technology for next-generation cybersecurity frameworks, offering robust protection against both current threats and the anticipated capabilities of large-scale quantum computers.

Recently, quantum key distribution (QKD) with classical Bob has been suggested and proven completely robust by Boyer et al. [Phys. Rev. Lett.99 (2007) 140501] in which quantum Alice has a fully-fledged quantum power, while classical Bob is restricted to preparing and measuring a particle in the computational basis, reflecting or reordering the particles. In this paper, we describe two related but simpler semi-quantum key distribution protocol that exempts classical Bob from measurement (hereafter called limited classical Bob for convenience) and, prove them completely robust. As limited classical Bob can deterministically prepare the qubits, we exploit this feature to construct a semi-quantum secure direct communication protocol, which is the direct communication of secret messages without first producing a shared secret key.

We propose a way to implement a three-qubit refined Deutsh-Jozsa (DJ) algorithm. The present proposal is based on the construction of the 35

f

-controlled phase gates, which uses single-qubit

σ_z

gates and two-qubit {\it standard} controlled-phase (CP) gates only. This proposal is implementable because a single-qubit

σ_z

gate can be easily realized by applying a single classical pulse and a two-qubit CP gate has been experimentally demonstrated in various physical systems. Finally, it is noted that this proposal is quite general, and can be applied to implement a three-qubit refined DJ algorithm in a cavity-based or noncavity-based physical system.

The wide range of supported services in modern telecommunication networks has increased the demand for highly secure means of communication. Common security frameworks based on the computational security model are expected to become insecure due to significant advances in quantum computing. Quantum key distribution (QKD), a new secret key agreement primitive, enables long-anticipated practical information-theoretical security (ITS). Over the past two decades, academic and industrial communities have devoted their time and resources to developing QKD-based networks that can distribute and serve ITS keys to remote parties. However, because the availability of QKD network testbeds to the larger research community is limited and the deployment of such systems is costly and difficult, progress in this area is noticeably slow. To address this problem and spur future development and education, we provide a valuable, unique tool for simulating a QKD network. The tool is essential to testing novel network management methodologies applied to large-scale QKD networks. The simulator model contained in the tool was validated by simulating a network with six nodes and three pairs of users. The results indicate that the designed functional elements operate correctly.

The rapid advancement of quantum computing poses a significant threat to classical cryptographic systems that form the backbone of modern digital security.Algorithms such as RSA and ECC, which rely on the computational difficulty of integer factorization and discrete logarithm problems, become vulnerable to quantum attacks, particularly Shor's algorithm.This project presents a comprehensive Quantum Key Distribution (QKD) Simulator that implements the BB84 and E91 protocols using IBM's Qiskit quantum computing framework, providing an interactive platform for understanding, simulating, and analyzing quantum-safe key exchange mechanisms.The simulator features a full-stack architecture with a FastAPI backend powered by Python and Qiskit for quantum circuit execution, and a React 19 frontend with TypeScript for interactive visualization.The BB84 protocol implementation supports configurable qubit counts, multiple measurement bases (Z, X, and Diagonal), Eve's intercept-resend attack simulation with adjustable interception rates, and Quantum Bit Error Rate (QBER) calculation with a security threshold of 8.5%.The E91 protocol implementation uses entangled Bell state pairs with configurable measurement angles, CHSH inequality violation testing for quantum security verification, and reverse gate anti-eavesdropping mechanisms.Additionally, the system includes an AES encryption module that uses quantum-generated keys from BB84 and E91 simulations to perform AES-128, AES-192, and AES-256 encryption, with privacy amplification for keys shorter than the required length.A simulation history system with SQLite and PostgreSQL support enables experiment tracking, comparison, and analysis.The project demonstrates the practical application of quantum mechanics principles to cryptographic security and serves as an educational tool for understanding the transition from classical to quantum-safe cryptography.