Efficient quantum arithmetic operation circuits for quantum image processing
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August 2020 Vol. 63 No. 8: 280311 https://doi.org/10.1007/s11433-020-1582-8
Efficient quantum arithmetic operation circuits for quantum image processing Hai-Sheng Li1* , Ping Fan2, Haiying Xia1, Huiling Peng1, and Gui-Lu Long3,4,5* 1 College 2 College
of Electronic Engineering, Guangxi Normal University, Guilin 541004, China; of Information Engineering, East China JiaoTong University, Nanchang 330013, China; 3 Department of Physics, Tsinghua University, Beijing 100084, China; 4 Beijing Academy of Quantum Information Sciences, Beijing 100193, China; 5 Frontier Science Center for Quantum Information, Beijing 100084, China
Received February 10, 2020; accepted May 20, 2020; published online June 4, 2020
Efficient quantum circuits for arithmetic operations are vital for quantum algorithms. A fault-tolerant circuit is required for a robust quantum computing in the presence of noise. Quantum circuits based on Clifford+T gates are easily rendered faulttolerant. Therefore, reducing the T-depth and T-Count without increasing the qubit number represents vital optimization goals for quantum circuits. In this study, we propose the fault-tolerant implementations for TR and Peres gates with optimized T-depth and T-Count. Next, we design fault-tolerant circuits for quantum arithmetic operations using the TR and Peres gates. Then, we implement cyclic and complete translations of quantum images using quantum arithmetic operations, and the scalar matrix multiplication. Comparative analysis and simulation results reveal that the proposed arithmetic and image operations are efficient. For instance, cyclic translations of a quantum image produce 50% T-depth reduction relative to the previous best-known cyclic translation. quantum arithmetic operation, quantum fault tolerant circuit, quantum computation, quantum image processing PACS number(s): Citation:
03.67.Lx, 42.30.Va, 03.67.Pp
H.-S. Li, P. Fan, H. Xia, H. Peng, and G.-L. Long, Efficient quantum arithmetic operation circuits for quantum image processing, Sci. China-Phys. Mech. Astron. 63, 280311 (2020), https://doi.org/10.1007/s11433-020-1582-8
1 Introduction Based on the principles of quantum mechanics, quantum computation utilizes quantum states [1, 2] to efficiently solve mathematical problems that are commonly insurmountable using classical computers [3, 4]. Also, quantum principles facilitate communication, thus providing an approach absolutely guarantees communication security [5, 6]. Quantum communication includes areas such as quantum secure direct communication [7-10], quantum key distribution [11], *Corresponding authors (Hai-Sheng Li, email: [email protected]; Gui-Lu Long, email: [email protected])
and quantum private query [12]. Several models exist for quantum computation, including blind quantum computation [13], Turing machine, and quantum circuit [14]. These models promote efficient implementation of quantum algorithms, such as the quantum search algorithm [4], discrete transform [15], wavelet transform [16, 17], Fourier transform [18], geometric transform
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