QElephant/docs/Matrix.md

Matrix

Matrix(l: list[list[complexe]])

• l: representation of the matrix in a list

Attributes

• __m: list[list[complexe]]

  the values contained in the matrix.

• __size: tuple[int, int]

  the size of the matrix

Methode

• __init__(l: list[list[complex]]=[]) -> None

  initiates the matrix

• __mul__(__value: "Matrix") -> Matrix

  defines the natural multiplication as the Koeneger product for matrices

• __apply(x: list[complex]) -> list[complex]

  takes a list to represent a vector in a colonne, and return the proctuct of the matrix by this vector

• __str__() -> str

  returns a string representation of the matrix

Staticmethods

• to_list(matrix: Matrix) -> list[list[complex]]

  returns the a list representing the given Matrix.

• 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}

• SQRTX() -> Matrix

  returns the matrix

\begin{pmatrix}
\frac {1+i} {2} & \frac {1-i} {2}\\
\frac {1-i} {2} & \frac {1+i} {2}
\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}

• CX() -> Matrix

  returns the matrix

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

• CY() -> Matrix

  returns the matrix

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

• CZ() -> Matrix

  returns the matrix

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