A fault-tolerant circuit is required for robust quantum computing in the presence of noise.Clifford+T circuits are widely used in fault-tolerant implementations.As a result,reducing T-depth,T-count,and circuit width h...A fault-tolerant circuit is required for robust quantum computing in the presence of noise.Clifford+T circuits are widely used in fault-tolerant implementations.As a result,reducing T-depth,T-count,and circuit width has emerged as important optimization goals.A measure-and-fixup approach yields the best T-count for arithmetic operations,but it requires quantum measurements.This paper proposes approximate Toffoli,TR,Peres,and Fredkin gates with optimized T-depth and T-count.Following that,we implement basic arithmetic operations such as quantum modular adder and subtractor using approximate gates that do not require quantum measurements.Then,taking into account the circuit width,T-depth,and T-count,we design and optimize the circuits of two multipliers and a divider.According to the comparative analysis,the proposed multiplier and divider circuits have lower circuit width,T-depth,and T-count than the current works that do not use the measure-and-fixup approach.Significantly,the proposed second multiplier produces approximately 77%T-depth,60%T-count,and 25%width reductions when compared to the existing multipliers without quantum measurements.展开更多
In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided pow...In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided power algebra Sq（n） of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq（sln＋1）. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.61762012,61763014,and 62062035)the Science and Technology Project of Guangxi(Grant No.2020GXNSFDA238023).
文摘A fault-tolerant circuit is required for robust quantum computing in the presence of noise.Clifford+T circuits are widely used in fault-tolerant implementations.As a result,reducing T-depth,T-count,and circuit width has emerged as important optimization goals.A measure-and-fixup approach yields the best T-count for arithmetic operations,but it requires quantum measurements.This paper proposes approximate Toffoli,TR,Peres,and Fredkin gates with optimized T-depth and T-count.Following that,we implement basic arithmetic operations such as quantum modular adder and subtractor using approximate gates that do not require quantum measurements.Then,taking into account the circuit width,T-depth,and T-count,we design and optimize the circuits of two multipliers and a divider.According to the comparative analysis,the proposed multiplier and divider circuits have lower circuit width,T-depth,and T-count than the current works that do not use the measure-and-fixup approach.Significantly,the proposed second multiplier produces approximately 77%T-depth,60%T-count,and 25%width reductions when compared to the existing multipliers without quantum measurements.
基金Supported by National Natural Science Foundation of China(Grant No.11271131)
文摘In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided power algebra Sq（n） of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq（sln＋1）. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.
