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 g...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61762012,and 61763014)the Science and Technology Project of Guangxi(Grant No.2018JJA170083)+3 种基金the National Key Research and Development Plan(Grant Nos.2018YFC1200200,and 2018YFC1200205)the Fund for Distinguished Young Scholars of Jiangxi Province(Grant No.2018ACB2101)the Natural Science Foundation of Jiangxi Province of China(Grant No.20192BAB207014)the Science and Technology Research Project of Jiangxi Provincial Education Department(Grant No.GJJ190297)。
文摘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.
