# 量子位元

## 维基百科，自由的百科全书

4个量子位元的IBM实验芯片，但最后并无实用价值。

## 定义

${\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle ;\quad \alpha ,\beta \in \mathbb {C} }$

${\displaystyle |\alpha |^{2}+|\beta |^{2}=1\,}$

${\displaystyle 1=\langle \psi |\psi \rangle =(\alpha |0\rangle +\beta |1\rangle )^{\dagger }(\alpha |0\rangle +\beta |1\rangle )=(\alpha ^{*}\langle 0|+\beta ^{*}\langle 1|)(\alpha |0\rangle +\beta |1\rangle )}$
${\displaystyle =\alpha ^{*}\alpha \langle 0|0\rangle +\beta ^{*}\beta \langle 1|1\rangle }$
${\displaystyle =|\alpha |^{2}+|\beta |^{2}\,}$，即要求总几率要是1。

## 按方向所采的诸多表示法

### z方向

${\displaystyle z_{-}=|1\rangle \langle 1|={\begin{pmatrix}0\\1\end{pmatrix))*{\begin{pmatrix}0&1\end{pmatrix))={\begin{pmatrix}0&0\\0&1\end{pmatrix))}$

### x方向

${\displaystyle x_{-}=|x_{-}\rangle \langle x_{-}|={\begin{pmatrix}{\frac {1}{\sqrt {2))}\\-{\frac {1}{\sqrt {2))}\end{pmatrix))*{\begin{pmatrix}{\frac {1}{\sqrt {2))}&-{\frac {1}{\sqrt {2))}\end{pmatrix))={\begin{pmatrix}{\frac {1}{2))&-{\frac {1}{2))\\-{\frac {1}{2))&{\frac {1}{2))\end{pmatrix))}$

### y方向

${\displaystyle y_{-}=|y_{-}\rangle \langle y_{-}|={\begin{pmatrix}{\frac {1}{\sqrt {2))}\\-{\frac {i}{\sqrt {2))}\end{pmatrix))*{\begin{pmatrix}{\frac {1}{\sqrt {2))}&{\frac {i}{\sqrt {2))}\end{pmatrix))={\begin{pmatrix}{\frac {1}{2))&{\frac {i}{2))\\-{\frac {i}{2))&{\frac {1}{2))\end{pmatrix))}$

## 注释

1. ^ MA Nielsen, IL Chuang. Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000).

## 参考文献

• Michael A. Nielsen, Isaac L. Chuang: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge 2000, ISBN 0-521-63503-9.
• Oliver Morsch: Quantum bits and quantum secrets - how quantum physics is revolutionizing codes and computers. Wiley-VCH, Weinheim 2008, ISBN 978-3-527-40710-1.
• Anthony J. Leggett: Quantum computing and quantum bits in mesoscopic systems. Kluwer Academic, New York 2004, ISBN 0-306-47904-4.

## 外部连接

• Qubit.org—cofounded by one of the pioneers in quantum computation, David Deutsch