The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebr...The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebra, thus making them able to relate with the control field and the Hamiltonian of the system to perform the gate. Finally the decomposition of the ternary SWAP gate is presented in detail.展开更多
In this paper, the synthesis and implementation of three-qubit SWAP gate is discussed. The three-qubit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Resear...In this paper, the synthesis and implementation of three-qubit SWAP gate is discussed. The three-qubit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.展开更多
电流型电路具有功耗低、速度快的特点,是当今集成电路研究的一个热点.文章基于阈算术代数系统,改进了非相交分解算法;设计了电流型互补金属氧化物半导体(complementary metal oxide semiconductor, CMOS)的异或门电路,并利用改进后的新...电流型电路具有功耗低、速度快的特点,是当今集成电路研究的一个热点.文章基于阈算术代数系统,改进了非相交分解算法;设计了电流型互补金属氧化物半导体(complementary metal oxide semiconductor, CMOS)的异或门电路,并利用改进后的新算法,将n变量函数分解成3变量函数,实现了任意n变量函数电路.模拟测试证明所设计的电路结构简单,且具有正确的逻辑功能.展开更多
Compared with complementary metal–oxide semiconductor(CMOS), the resonant tunneling device(RTD) has better performances; it is the most promising candidate for next-generation integrated circuit devices. The universa...Compared with complementary metal–oxide semiconductor(CMOS), the resonant tunneling device(RTD) has better performances; it is the most promising candidate for next-generation integrated circuit devices. The universal logic gate is an important unit circuit because of its powerful logic function, but there are few function synthesis algorithms that can implement an n-variable logical function by RTD-based universal logic gates. In this paper, we propose a new concept, i.e., the truth value matrix. With it a novel disjunctive decomposition algorithm can be used to decompose an arbitrary n-variable logical function into three-variable subset functions. On this basis, a novel function synthesis algorithm is proposed, which can implement arbitrary n-variable logical functions by RTD-based universal threshold logic gates(UTLGs), RTD-based three-variable XOR gates(XOR3s), and RTD-based three-variable universal logic gate(ULG3s). When this proposed function synthesis algorithm is used to implement an n-variable logical function, if the function is a directly disjunctive decomposition one, the circuit structure will be very simple, and if the function is a non-directly disjunctive decomposition one, the circuit structure will be simpler than when using only UTLGs or ULG3s. The proposed function synthesis algorithm is straightforward to program, and with this algorithm it is convenient to implement an arbitrary n-variable logical function by RTD-based universal logic gates.展开更多
基金the National Natural Science Foundation of China (Grant No. 60433050)the Key Project of the Science Foundation of Xuzhou Normal University, China (Grant No. 06XLA05)
文摘The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebra, thus making them able to relate with the control field and the Hamiltonian of the system to perform the gate. Finally the decomposition of the ternary SWAP gate is presented in detail.
基金Supported by the Natural Science Foundation of Jiangsu Education Bureau under Grant No.09KJB140010the Project Prepared for National Natural Science Foundation of Xuzhou Normal University under Grant No.08XLY03
文摘In this paper, the synthesis and implementation of three-qubit SWAP gate is discussed. The three-qubit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.
文摘电流型电路具有功耗低、速度快的特点,是当今集成电路研究的一个热点.文章基于阈算术代数系统,改进了非相交分解算法;设计了电流型互补金属氧化物半导体(complementary metal oxide semiconductor, CMOS)的异或门电路,并利用改进后的新算法,将n变量函数分解成3变量函数,实现了任意n变量函数电路.模拟测试证明所设计的电路结构简单,且具有正确的逻辑功能.
基金supported by the Zhejiang Provincial Natural Science Foundation,China(No.LY15F010011)the National Natural Science Foundation of China(Nos.61771179,61471314,and 61271124)
文摘Compared with complementary metal–oxide semiconductor(CMOS), the resonant tunneling device(RTD) has better performances; it is the most promising candidate for next-generation integrated circuit devices. The universal logic gate is an important unit circuit because of its powerful logic function, but there are few function synthesis algorithms that can implement an n-variable logical function by RTD-based universal logic gates. In this paper, we propose a new concept, i.e., the truth value matrix. With it a novel disjunctive decomposition algorithm can be used to decompose an arbitrary n-variable logical function into three-variable subset functions. On this basis, a novel function synthesis algorithm is proposed, which can implement arbitrary n-variable logical functions by RTD-based universal threshold logic gates(UTLGs), RTD-based three-variable XOR gates(XOR3s), and RTD-based three-variable universal logic gate(ULG3s). When this proposed function synthesis algorithm is used to implement an n-variable logical function, if the function is a directly disjunctive decomposition one, the circuit structure will be very simple, and if the function is a non-directly disjunctive decomposition one, the circuit structure will be simpler than when using only UTLGs or ULG3s. The proposed function synthesis algorithm is straightforward to program, and with this algorithm it is convenient to implement an arbitrary n-variable logical function by RTD-based universal logic gates.
