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arXiv:2508.14659 · IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT)

Deutsch-Jozsa and Bernstein-Vazirani algorithm using single-particle discrete-time quantum walk

Ravi Sangwan, Vikas Ramaswamy, Henry Sukumar, Gudapati Naresh Raghava

Published Jul 10, 2025• 1 citation

Abstract

The paper introduces an efficient implementation of the Deutsch-Jozsa and Bernstein-Vazirani algorithm using the single-particle discrete-time quantum walk. We also provide a detailed optical framework with specific optical components to achieve these implementations in the photonic quantum walk scheme by simultaneously exploiting both polarization and path degrees of freedom. These implementations demonstrate improved resource efficiency while maintaining the exponential speedup characteristic of both algorithms. This work contributes to the growing field of universal quantum computing using singleparticle discrete-time quantum walk.

DOI: 10.1109/conecct65861.2025.11306771

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We show that fundamental versions of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms can be performed using a small entangled cluster state resource of only six qubits. We then investigate the minimal resource states needed to demonstrate general

n

-qubit versions and a scalable method to produce them. For this purpose, we propose a versatile photonic on-chip setup.