Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermi...Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermite matrix are studied further,and thismust be useful for matrix theory and applications（like optimization theory,symplecticgeometry and physics etc）.In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A,展开更多
Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offere...In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.展开更多
A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
The most general duality gates were introduced by Long,Liu and Wang and named allowable generalized quantum gates (AGQGs,for short).By definition,an allowable generalized quantum gate has the form of U=YfkjsckUK,where...The most general duality gates were introduced by Long,Liu and Wang and named allowable generalized quantum gates (AGQGs,for short).By definition,an allowable generalized quantum gate has the form of U=YfkjsckUK,where Uk’s are unitary operators on a Hilbert space H and the coefficients ck’s are complex numbers with |Yfijo ck\ ∧ 1 an d 1ck| 【1 for all k=0,1,...,d-1.In this paper,we prove that an AGQG U=YfkZo ck∧k is realizable,i.e.there are two d by d unitary matrices W and V such that ck=W0kVk0 (0【k【d-1) if and only if YfkJt 1c*|【m that case,the matrices W and V are constructed.展开更多
Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under t...Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.展开更多
基金Supported by the Natural Science Foundation of Chongqing
文摘Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermite matrix are studied further,and thismust be useful for matrix theory and applications（like optimization theory,symplecticgeometry and physics etc）.In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A,
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
基金This work was funded by the Natural Science Foundation of Jiangsu Province(Grant No:BK20171458)the Yangzhou University International Academic Exchange Fund.
文摘In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571113 and 10871224)the Natural Science Research Program of Shaanxi Province (Grant No. 2009JM1011)
文摘The most general duality gates were introduced by Long,Liu and Wang and named allowable generalized quantum gates (AGQGs,for short).By definition,an allowable generalized quantum gate has the form of U=YfkjsckUK,where Uk’s are unitary operators on a Hilbert space H and the coefficients ck’s are complex numbers with |Yfijo ck\ ∧ 1 an d 1ck| 【1 for all k=0,1,...,d-1.In this paper,we prove that an AGQG U=YfkZo ck∧k is realizable,i.e.there are two d by d unitary matrices W and V such that ck=W0kVk0 (0【k【d-1) if and only if YfkJt 1c*|【m that case,the matrices W and V are constructed.
基金Supported by the National Natural Science Foundation of China(No.10671176)
文摘Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.
