T-count Optimized Quantum Circuits for Bilinear Interpolation

Abstract: Quantum circuits for basic image processing functions such as bilinear interpolation are required to implement image processing algorithms on quantum computers. In this work, we propose quantum circuits for the bilinear interpolation of NEQR encoded images based on Clifford+T gates. Quantum circuits for the scale up operation and scale down operation are illustrated. The proposed quantum circuits are based on quantum Clifford+T gates and are optimized for T-count. Quantum circuits based on Clifford+T gates can be made fault tolerant but the T gate is very costly to implement. As a result, reducing T-count is an important optimization goal. The proposed quantum bilinear interpolation circuits are based on (i) a quantum adder, (ii) a proposed quantum subtractor, and (iii) a quantum multiplication circuit. Further, both designs are compared and shown to be superior to existing work in terms of T-count. The proposed quantum bilinear interpolation circuits for the scale down operation and for the scale up operation each have a $92.52\%$ improvement in terms of T-count compared to the existing work.