In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot n...In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot necessarily unitary.The duality mode provides a natural link between classical computing and quantum computing.In addition,the duality mode provides a new tool for quantum algorithm design.展开更多
The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a com...The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex combiner.It is proved that the divider and the combiner of a CDQC are an isometry and a contraction,respectively.It is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states(matrix-states) are also dual.Lastly,the loss of an input state passing through a CDQC is measured.展开更多
In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulat...In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi 's are complex numbers with module less or equal to 1 and constrained by|∑iPi|≤1.展开更多
In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross- Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality cont...In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross- Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.展开更多
With significant appraisals to the Original Double-Slit experiment, an audit of nature of electron is drafted. Electron has been proven to demonstrate unpredictable nature. It should behave as a particle, but it shows...With significant appraisals to the Original Double-Slit experiment, an audit of nature of electron is drafted. Electron has been proven to demonstrate unpredictable nature. It should behave as a particle, but it shows variations in behaviour when it is passed through two slits. In the experiment, photons (high-intensity light) are utilized as a detector, due to which interference pattern effectuates after detection. The wave-function is collapsed. A contemporary model is proposed, in which magnetic field of low-intensity is applied to canvass ever-changing nature of electron.展开更多
In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The ex...In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.展开更多
introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality relate...introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.展开更多
基金the National Fundamental Research Program under Grant No.2006CB921106National Natural Science Foundation of China under Grant Nos.10325521 and 60433050
文摘In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot necessarily unitary.The duality mode provides a natural link between classical computing and quantum computing.In addition,the duality mode provides a new tool for quantum algorithm design.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571113 and 11171197)the Fundamental Research Funds for the Central Universities (Grant No. GK201002006)
文摘The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex combiner.It is proved that the divider and the combiner of a CDQC are an isometry and a contraction,respectively.It is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states(matrix-states) are also dual.Lastly,the loss of an input state passing through a CDQC is measured.
基金supported by the National Fundamental Research Program Grant Nos.2006CB921106, 2009CB929042National Natural Science Foundation of China under Grant Nos. 10874098, 10775076, and 60433050
文摘In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi 's are complex numbers with module less or equal to 1 and constrained by|∑iPi|≤1.
基金Supported by National Natural Science Foundation of China under Grant Nos.10775076 and 10874098the National Basic Research Program of China under Grant No.2009CB929402the Specialized Research Fund for the Doctoral Program of Education Ministry of China under Grant No.20060003048
文摘In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross- Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.
文摘With significant appraisals to the Original Double-Slit experiment, an audit of nature of electron is drafted. Electron has been proven to demonstrate unpredictable nature. It should behave as a particle, but it shows variations in behaviour when it is passed through two slits. In the experiment, photons (high-intensity light) are utilized as a detector, due to which interference pattern effectuates after detection. The wave-function is collapsed. A contemporary model is proposed, in which magnetic field of low-intensity is applied to canvass ever-changing nature of electron.
基金supported by the SRFPD Program of Education Ministry ofChina (Grant No. 20090002110064)the National Natural Science Foundation of China (Grant No. 10874098)the National Basic Research Program of China (Grant Nos. 2009CB929402 and 2011CB921602)
文摘In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.
基金supported by the National Natural Science Foundation of China(NSFC)Grant 12071136.
文摘introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.