双线性插值的T计数优化量子线路
T-count Optimized Quantum Circuits for Bilinear Interpolation
摘要：
在量子计算机上实现图像处理算法需要用于双线性插值等基本图像处理功能的量子线路。在这项工作中，我们提出了量子线路的NEQR编码图像的双线性插值的Clifford+T门的基础上。示出了用于按比例放大操作和按比例缩小操作的量子线路。所提出的量子线路基于量子Clifford+T门，并针对T计数进行了优化。基于Clifford+T门的量子线路可以容错，但是T门的实现成本非常高。因此，减少T计数是重要的优化目标。所提出的量子双线性插值电路基于（i）量子加法器，（ii）所提出的量子加法器，和（iii）量子乘法电路。此外，这两种设计进行了比较，并显示出优于现有的工作中的T计数。所提出的量子双线性插值电路的规模缩小操作和规模扩大操作的T-计数方面的$92.52\%$的改进相比，现有的工作。
英文摘要：
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.
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