We report on the photonic Ti:LiNbO3 circuit design of single-qubit Hadamard, polarization and spatially encoded single-photon two-qubit CSIGN and CNOT quantum gates, using continuous-wave pump source and 812nm photon-pairs. The proposed circuits aim at optimizing the overall performance in terms of optical power dissipation management and accurately realizing the desired functionalities. By utilizing S-bend structures, through simulations we have obtained Electrical-field amplitudes with approximate values of ± (1/2)1/2 at the output branches of the Hadamard circuit. CSIGN modified circuit exhibits a reduction of 0.618 dB and 0.4288 dB in polarization-odd and -even modes dispersion, respectively. The modified CNOT circuit is 128.7 μm less wide than the initially designed circuit and the unwanted TM ⇄ TE polarization conversion at the applied voltage of V = 53 V is addressed.