Qubit Rotations (quanguru.QuantumToolbox.spinRotations)#

Contains functions to create qubit rotation operators.

Functions#

qubRotation(xyz, angle[, sparse])

Creates the operator \(R_{i}(\theta) := e^{-i\sigma_{i}\theta/2}\) for qubit rotation around the i = x/y/z-axis by angle \(\theta\).

spinRotation(xyz, angle, j[, sparse, isDim])

Creates the operator \(R_{i}(\theta) := e^{-iJ_{i}\theta}\) for a spin value j rotation around i = x/y/z-axis by angle \(\theta\).

xRotation(angle[, sparse])

Creates the operator \(R_{x}(\theta)\) for qubit rotation around the x-axis by angle \(\theta\).

yRotation(angle[, sparse])

Creates the operator \(R_{y}(\theta)\) for qubit rotation around the y-axis by angle \(\theta\).

zRotation(angle[, sparse])

Creates the operator \(R_{z}(\theta)\) for qubit rotation around the z-axis by angle \(\theta\).

Function Name

Docstrings

Examples

Unit Tests

Tutorials

qubRotation

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spinRotation

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xRotation

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yRotation

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zRotation

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xRotation(angle: float, sparse: bool = True) → spmatrix | ndarray[source]#

Creates the operator \(R_{x}(\theta)\) for qubit rotation around the x-axis by angle \(\theta\).

Parameters:

  • angle (float) – angle of rotation around x

  • sparse (bool) – if True(False), the returned Matrix type will be sparse(array)

Returns:

Qubit X rotation operator \(R_{x}(\theta)\)

Return type:

Matrix

Examples

# TODO

yRotation(angle: float, sparse: bool = True) → spmatrix | ndarray[source]#

Creates the operator \(R_{y}(\theta)\) for qubit rotation around the y-axis by angle \(\theta\).

Parameters:

  • angle (float) – angle of rotation around y

  • sparse (bool) – if True(False), the returned Matrix type will be sparse(array)

Returns:

Qubit Y rotation operator \(R_{y}(\theta)\)

Return type:

Matrix

Examples

# TODO

zRotation(angle: float, sparse: bool = True) → spmatrix | ndarray[source]#

Creates the operator \(R_{z}(\theta)\) for qubit rotation around the z-axis by angle \(\theta\).

Parameters:

  • angle (float) – angle of rotation around z

  • sparse (bool) – if True(False), the returned Matrix type will be sparse(array)

Returns:

Qubit Z rotation operator \(R_{z}(\theta)\)

Return type:

Matrix

Examples

# TODO

qubRotation(xyz: str, angle: float, sparse: bool = True) → spmatrix | ndarray[source]#

Creates the operator \(R_{i}(\theta) := e^{-i\sigma_{i}\theta/2}\) for qubit rotation around the i = x/y/z-axis by angle \(\theta\).

Parameters:

  • xyz (str) – string for rotation direction x, y, or z

  • angle (float) – angle of rotation

  • sparse (bool) – if True(False), the returned Matrix type will be sparse(array)

Returns:

Qubit x/y/z rotation operator.

Return type:

Matrix

Examples

# TODO

spinRotation(xyz: str, angle: float, j: float, sparse: bool = True, isDim: bool = False) → spmatrix | ndarray[source]#

Creates the operator \(R_{i}(\theta) := e^{-iJ_{i}\theta}\) for a spin value j rotation around i = x/y/z-axis by angle \(\theta\).

Parameters:

  • xyz (str) – string for rotation direction x, y, or z

  • angle (float) – angle of rotation

  • j (int or float) – integer or half-integer spin quantum number, or the dimension (then spin quantum number = (d-1)/2)

  • sparse (bool) – if True(False), the returned Matrix type will be sparse(array)

  • isDim (bool) – boolean for whether j is spin quantum number of dimension

Returns:

Spin x/y/z rotation operator.

Return type:

Matrix

Examples

# TODO