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

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.