减法器
量子电路
量子位元
量子计算机
计算机科学
量子门
除法算法
师(数学)
量子
电子线路
量子算法
门计数
加法器
算法
算术
数学
量子纠错
量子力学
计算机硬件
物理
电信
延迟(音频)
作者
Himanshu Thapliyal,Edgard Muñoz‐Coreas,T. S. S. Varun,Travis S. Humble
出处
期刊:IEEE Transactions on Emerging Topics in Computing
[Institute of Electrical and Electronics Engineers]
日期:2021-04-01
卷期号:9 (2): 1045-1056
被引量:30
标识
DOI:10.1109/tetc.2019.2910870
摘要
Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for integer division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. 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 percent compared to the existing works. Our proposed non-restoring division circuit achieves average T-count savings from 49.22 to 90.03 percent compared to the existing works. Further, both our proposed designs have linear T-depth. We also illustrate the application of the proposed quantum division circuits in quantum image processing with a case study of quantum bilinear interpolation.
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