In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both cla...In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself A quantum system considered here can be any quantum system： a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented： the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.展开更多
The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes ...The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes has developed rapidly and been extended to protect quantum information over asymmetric quantum channels, in which phase-shift and qubit-flip errors occur with different probabilities. In this paper, we generalize the construction of symmetric quantum codes via graphs (or matrices) to the asymmetric case, converting the construction of asymmetric quantum codes to finding matrices with some special properties. We also propose some asymmetric quantum Maximal Distance Separable (MDS) codes as examples constructed in this way.展开更多
We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to sev...We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to several other interesting properties in symmetric tensor spaces.We then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius norm function of a symmetric tensor.Furthermore,we characterize the symmetric positive semidefinite tensor(SDT)cone by employing the properties of linear operators,design some face structures of its dual cone,and analyze its relationship to many other tensor cones.In particular,we show that the cone is self-dual if and only if the polynomial is quadratic,give specific characterizations of tensors that are in the primal cone but not in the dual for higher order cases,and develop a complete relationship map among the tensor cones appeared in the literature.展开更多
In this paper,we propose a roll angle measurement method with a large range based on the photoelectronic autocollimator.According to the corresponding relationship between the rotation position of the measured shaft a...In this paper,we propose a roll angle measurement method with a large range based on the photoelectronic autocollimator.According to the corresponding relationship between the rotation position of the measured shaft and the spot position on the circular trajectory,the roll angle is calculated quickly and conveniently using a simple algorithm.Only a mirror,a coupler and a fine shaft are contained in the measurement system besides the photoelectronic autocollimator.Aiming at the terrible measurement error induced by the axis wobbly error,two measurement schemes are proposed,which are linking the fine precision shaft to the measured shaft for reducing the axis wobbly error and using the segment measurement to enlarge the radius of the circular trajectory.The experimental results show that the measurement error is decreased by ±0.38°.The roll angle error of the mechanism is ±0.14°,and the measurement precision is about ±2′.The proposed method can be widely used in the engineering fields.展开更多
基金The project supported by the National Fundamental Research Program under Grant No. 001CB309308, National Natural Science Foundation of China under Grant Nos. 10325521 and 60433050, and the SRFDP Program of the Ministry of Education of China
文摘In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself A quantum system considered here can be any quantum system： a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented： the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
基金supported by the National High Technology Research and Development Program of China under Grant No. 2011AA010803
文摘The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes has developed rapidly and been extended to protect quantum information over asymmetric quantum channels, in which phase-shift and qubit-flip errors occur with different probabilities. In this paper, we generalize the construction of symmetric quantum codes via graphs (or matrices) to the asymmetric case, converting the construction of asymmetric quantum codes to finding matrices with some special properties. We also propose some asymmetric quantum Maximal Distance Separable (MDS) codes as examples constructed in this way.
基金supported by National Natural Science Foundation of China(Grant No.11301022)the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University(Grant Nos.RCS2014ZT20 and RCS2014ZZ001)+1 种基金Beijing Natural Science Foundation(Grant No.9144031)the Hong Kong Research Grant Council(Grant Nos.Poly U 501909,502510,502111 and 501212)
文摘We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to several other interesting properties in symmetric tensor spaces.We then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius norm function of a symmetric tensor.Furthermore,we characterize the symmetric positive semidefinite tensor(SDT)cone by employing the properties of linear operators,design some face structures of its dual cone,and analyze its relationship to many other tensor cones.In particular,we show that the cone is self-dual if and only if the polynomial is quadratic,give specific characterizations of tensors that are in the primal cone but not in the dual for higher order cases,and develop a complete relationship map among the tensor cones appeared in the literature.
基金supported by the National Natural Science Foundation of China(Nos.111742741117427961205021 and 11204299)
文摘In this paper,we propose a roll angle measurement method with a large range based on the photoelectronic autocollimator.According to the corresponding relationship between the rotation position of the measured shaft and the spot position on the circular trajectory,the roll angle is calculated quickly and conveniently using a simple algorithm.Only a mirror,a coupler and a fine shaft are contained in the measurement system besides the photoelectronic autocollimator.Aiming at the terrible measurement error induced by the axis wobbly error,two measurement schemes are proposed,which are linking the fine precision shaft to the measured shaft for reducing the axis wobbly error and using the segment measurement to enlarge the radius of the circular trajectory.The experimental results show that the measurement error is decreased by ±0.38°.The roll angle error of the mechanism is ±0.14°,and the measurement precision is about ±2′.The proposed method can be widely used in the engineering fields.
