Chapter 158 Implementation of Quantum Optical Phase Shift Gate Adopting Multi-passing Technique in Lithium Niobate Based Electro-Optic Crystal Minakshi Mandal and Sourangshu Mukhopadhyay Abstract Quantum phase shift gate operates ordinarily on a single qubit. Here the authors propose a new scheme of implementation of quantum optical phase shift gate adopting multi-passing technique in lithium niobate (LiNbO 3 ) based electro-optic crystal. By using the multi-passing technique the phase operation can be done by very low voltage. 158.1 Introduction Quantum logic gates are the basic quantum circuits which operate on qubits. Quantum logic systems are important for very fast and secured computation, communication and data processing due to its reversibility, large storage capacity and high degree of parallelism [1–3]. There are so many quantum logic gates which are implemented by various encoding approaches, such as polarization encoding, phase encoding etc. Here in this paper the authors propose a new method of implementation of quantum optical phase shift gate adopting the multi-passing technique in Lithium Niobate based electro-optic crystal. When a polarized light is passing through an electro-optic Pockels material, there is seen a change in refractive index (r.i) occurring in the material. In case of lithium niobate (LiNbO 3 ) the change in refractive index is expressed as, n x = n 0 - 1 2 n 3 0 r 13 E (158.1) where, n 0 and r 13 are the constant r.i term and elctro-optic co-efficient of the material respectively. E is the applied electric field to the material. M. Mandal (B ) · S. Mukhopadhyay Department of Physics, The University of Burdwan, Golapbag, Burdwan, West Bengal 713104, India e-mail: minakshi.bcc@gmail.com © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 K. Singh et al. (eds.), ICOL-2019, Springer Proceedings in Physics 258, https://doi.org/10.1007/978-981-15-9259-1_158 687