量子计算中旋转算子的相关性质
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摘要
讨论了一些特殊量子门和旋转算子的关系。研究了T门和Hadamard门与Bloch球上的关于坐标轴的旋转算子之间的关系;得到了Hadamard门和相位门与一般旋转算子的关系;给出了任意单量子比特上酉算子关于旋转算子的一个分解形式,并给出了Hadamard门的一个漂亮的分解形式。
The relations between some special quantum gates and rotation operators are discussed in detail. First of all,the relationship between the rotation operator on the coordinate axis and T gate and Hadamard gate on the Bloch sphere is studied. Secondly,the relationship between Hadamard gate and Phase gate and general rotation operator is got. Finally,a decomposition form of unitary operator on any single qubit in relation to rotation operators is obtained,and a beautiful decomposition form about Hadamard gate is given.
The relations between some special quantum gates and rotation operators are discussed in detail. First of all,the relationship between the rotation operator on the coordinate axis and T gate and Hadamard gate on the Bloch sphere is studied. Secondly,the relationship between Hadamard gate and Phase gate and general rotation operator is got. Finally,a decomposition form of unitary operator on any single qubit in relation to rotation operators is obtained,and a beautiful decomposition form about Hadamard gate is given.
引文
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[9]SIEMENS Mark,HANCOCK Jason,SIMINOVITCH David. Beyond Euler angles:exploiting the angle—axis parametrizationin a multipole expansion of the rotation operator[J]. Solid State Nuclear M agnetic Resonance,2006,31(1):35-54.
[10]PAVICIC Mladen. Quantum computation[M]. Boston:Springer Science+Business Media,2006.
[11]CASTAGNOLI Giuseppe. The mechanism of quantum computation[J]. International Journal of Theoretical Physics,2008,47(8):2181-2194.
[12]DHOOGHE Bart,PYKACZ Jaroslaw. Quantum mechanics and computation[J]. Foundations of Science,2005,9(4):511-522.
[2]RALESCU A,MAYFIELD L. Generalization of common gates for quantum computation[C]//Annual Meeting of the NorthAmerican. Detroit:IEEE,2005.
[3]ATEUAFACK M E,DIFFO J T,FAI L C. Rotation operator approach for the dynamics of non-dissipative multi-state Landau-Zener problems:exact solutions.[J]. Physica E:Low-dimensional Systems and Nanostructures,2017,85(1):74-81.
[4]SCHRER Wolffram. Application of the rotation operator in the design of light-scattering experiments[J]. Journal of MolecularLiquids,2002,98(5):227-242.
[5]FENG Guanru,RAHIMI Robabeh,LAFLAMME Raymond,et al. Randomized benchmarking of quantum gates implementedby electron spin resonance[J]. Journal of M agnetic Resonance,2016,267(6):68-78.
[6]CASTRO DE L A,NAPOLITANO R D J. Error correction in short time steps during the application of quantum gates[J]. An-nals of Physics,2016,367(4):199-211.
[7] SHENDE V V,MARKOV I L,BULLOCK S S. Smaller two-qubit circuits for quantum communication and computation[C]//Proceedings Design,Automation and Test in Europe Conference and Exhibition. Paris:IEEE,2004.
[8]GEORGEOT B.Quantum computing for physics research[J]. Nuclear Inst and Methods in Physics Research A,2005,559(1):6-12.
[9]SIEMENS Mark,HANCOCK Jason,SIMINOVITCH David. Beyond Euler angles:exploiting the angle—axis parametrizationin a multipole expansion of the rotation operator[J]. Solid State Nuclear M agnetic Resonance,2006,31(1):35-54.
[10]PAVICIC Mladen. Quantum computation[M]. Boston:Springer Science+Business Media,2006.
[11]CASTAGNOLI Giuseppe. The mechanism of quantum computation[J]. International Journal of Theoretical Physics,2008,47(8):2181-2194.
[12]DHOOGHE Bart,PYKACZ Jaroslaw. Quantum mechanics and computation[J]. Foundations of Science,2005,9(4):511-522.