This work presents an adjoint-based optimization framework for the inverse design of optical gate structures targeting quantum computing applications. The objective is to determine a physical photonic structure that implements a prescribed unitary transformation corresponding to a quantum gate, with emphasis on the Pauli-X (quantum NOT) operation. The problem is formulated as a large-scale electromagnetic inverse design task governed by Maxwell’s equations.

Material distribution is parametrized through a sigmoid mapping to constrain the relative permittivity within physically admissible bounds. A continuation strategy is employed by progressively increasing the sigmoid sharpness parameter, allowing smooth exploration of the design space before enforcing fabrication constraints such as minimum line width and spacing.

The proposed approach provides a systematic and computationally efficient method for synthesizing photonic structures that realize quantum logic operations, demonstrating its applicability through the optimized implementation of a Pauli-X optical gate.