Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. In this work, we propose two quantum integer division circuits. The first proposed quantum integer division circuit is based on the restoring division algorithm and the second proposed design implements the non-restoring division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring division circuit achieves average T-count savings from 79.03% to 91.69% compared to the existing works. Our proposed non-restoring division circuit achieves average Tcount savings from 49.75% to 90.37% compared to the existing works. Further, both our proposed designs have linear T-depth. We also illustrated the application of the proposed quantum division circuits in quantum image processing with a case study of quantum bilinear interpolation.

中文翻译：

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整数除法优化T-count和T-depth的量子电路设计

要使用量子计算机进行科学计算，需要用于数学函数（例如除法）的量子电路。在这项工作中，我们提出了两个量子整数除法电路。第一个提出的量子整数除法电路基于恢复除法算法，第二个提出的设计实现了非恢复除法算法。两种提议的设计都在 T 计数、T 深度和量子位方面进行了优化。两种提出的量子电路设计均基于 (i) 量子减法器、(ii) 量子加减法器电路和 (iii) 新型量子条件加法电路。与现有工作相比，我们提出的恢复划分电路实现了平均 T 计数从 79.03% 到 91.69% 的节省。我们提出的非恢复除法电路实现了从 49.75% 到 90% 的平均 Tcount 节省。37% 与现有作品相比。此外，我们提出的两种设计都具有线性 T 深度。我们还通过量子双线性插值的案例研究说明了所提出的量子分割电路在量子图像处理中的应用。