QElephant/docs/QuBit/QuBit.md

QuBit

QuBit(alpha: complexe, beta: complexe)

• alpha: complexe value for |0>
• beta: complexe value for |1>

Attributes

• __state: list[complexe]

  list of the values for the state |0> and |1>

• __intricated: bool

  tells if the qubit is intricated or not

Methode

• __init__(alpha: complexe=1, beta: complexe=0) -> None

  initiates the qubit

• is_intricated() -> bool

  returns the value of __intricated

• get_MuBit() -> None

  returns the MuBit in wich the QuBit is intricated. If not intricated, rerurns None

• __str__() -> str

  returns a string representation of the list of __state

• __apply(m: Matrix) -> None

  takes a Matrix and modifies the QuBit according the matrix

• observe() -> list[int]

  forces the QuBit in a state, where the probabilities are given throught __state. Returns the new __state obtained.

Staticmethods

• I() -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0\\
0 & 1
\end{pmatrix}

• H() -> Matrix

  returns the matrix

\begin{pmatrix}
\frac {1} {\sqrt 2} & \frac {1} {\sqrt 2}\\
\frac {1} {\sqrt 2} & -\frac{1} {\sqrt 2}
\end{pmatrix}

• X() -> Matrix

  returns the matrix

\begin{pmatrix}
0 & 1\\
1 & 0
\end{pmatrix}

• Y() -> Matrix

  returns the matrix

\begin{pmatrix}
0 & -i\\
i & 0
\end{pmatrix}

• Z() -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0\\
0 & -1
\end{pmatrix}

• S() -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0\\
0 & i
\end{pmatrix}

• T() -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0\\
0 & e^{i\frac {\pi} {4}}
\end{pmatrix}

• Rx(phi: float) -> Matrix

  returns the matrix

\begin{pmatrix}
\cos(\frac \phi 2) & -i\sin(\frac \phi 2)\\
-i\sin(\frac \phi 2) & \cos(\frac \phi 2)
\end{pmatrix}

• Ry(phi: float) -> Matrix

  returns the matrix

\begin{pmatrix}
\cos(\frac \phi 2) & -\sin(\frac \phi 2)\\
\sin(\frac \phi 2) & \cos(\frac \phi 2)
\end{pmatrix}

• Rz(phi: float) -> Matrix

  returns the matrix

\begin{pmatrix}
e^{-i\frac \phi 2} & 0\\
0 & e^{i\frac \phi 2}
\end{pmatrix}

• R1(phi: float) -> Matrix

  returns the matrix

\begin{pmatrix}
1 & p\\
0 & e^{i\phi}
\end{pmatrix}

• CNOT() -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 0 & 1\\
0 & 0 & 1 & 0
\end{pmatrix}

• SWAP() -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 0 & 1 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 0 & 0
\end{pmatrix}

• Cu(u: Matrix) -> Matrix

  returns the matrix

\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & u_{00} & u_{01}\\
0 & 0 & u_{10} & u_{11}
\end{pmatrix}