Efficient implementation of quantum arithmetic operation circuits

康博 高橋

Hai-Sheng Li, Ping Fan, Haiying Xia +2 more

Hai-Sheng Li, Yusi Xu, Yunbai Qin +2 more

The efficient quantum circuits of arithmetic operations are important to perform quantum algorithms. To implement efficient matrix operations, we first modify the generalized model of the novel enhanced quantum representation of digital images (GNEQR) to store unsigned and signed integer matrices. Next, we design the circuits of the circuits of quantum addition, quantum modulo addition, quantum subtraction, and quantum modulo subtraction, these operations all keeping two operands unchanged. Then, we propose the circuits of quantum matrix addition, quantum matrix modulo addition, quantum matrix subtraction, and quantum matrix modulo subtraction for the first time. Furthermore, we present a simulation method to verify the correctness of the proposed arithmetic operations of matrix. The results of simulation experiment show that the propose arithmetic operations of matrix are efficient and correct.

Hafiz Md. Hasan Babu

Yasuhiro Takahashi

Quantum circuits for elementary arithmetic operations are important not only for implementing Shor's factoring algorithm on a quantum computer but also for understanding the computational power of small quantum circuits, such as linear-size or logarithmic-depth quantum circuits. This paper surveys some recent approaches to constructing efficient quantum circuits for elementary arithmetic operations and their applications to Shor's factoring algorithm. It covers addition, comparison, and the quantum Fourier transform used for addition.

Thomas Häner, Mathias Soeken, Martin Roetteler +1 more