Eigen-vector/value Statistics (quanguru.QuantumToolbox.eigenVecVal
)#
Contains functions to calculate eigen-vector/value statistics in various cases.
Functions#
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Calculates eigenvalues and eigenvectors of a given matrix (intended for internal use). |
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Calculates all the amplitudes \(|c_{i,k}|^{2}\) of entries \(|k\rangle := \begin{bmatrix} c_{1,k} \\ \vdots \\ c_{i,k} \\ \vdots \\c_{\mathcal{D},k} \end{bmatrix}_{\mathcal{D}\times 1}\) for all the eigenvectors \(\{|k\rangle\}\) of a given matrix. |
|
Calculates all the amplitudes \(|c_{i,k}|^{2}\) of entries \(|k\rangle := \begin{bmatrix} c_{1,k} \\ \vdots \\ c_{i,k} \\ \vdots \\c_{\mathcal{D},k} \end{bmatrix}_{\mathcal{D}\times 1}\) for a given list of eigenvectors \(\{|k\rangle\}\). |
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Intended for internal use, and used in eigenvector statistics calculation of symplectic class. |
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Intended for internal use, and used in eigenvector statistics calculation of symplectic class. |
|
Calculates component amplitudes \(|c_{i,k}|^{2}\) of a ket \(|k\rangle := \sum_{i}c_{i,k}|i\rangle\) in a basis \(\{|i\rangle\}\). |
Function Name |
Docstrings |
Examples |
Unit Tests |
Tutorials |
---|---|---|---|---|
_eigs |
✅ |
❌ |
❌ |
❌ |
_eigStat |
✅ |
❌ |
❌ |
❌ |
_eigStatSymp |
✅ |
❌ |
❌ |
❌ |
_eigStatEig |
✅ |
❌ |
❌ |
❌ |
_eigsStatEigSymp |
✅ |
❌ |
❌ |
❌ |
eigVecStatKet |
✅ |
✅ |
❌ |
❌ |
- _eigs(Mat: spmatrix | ndarray) tuple [source]#
Calculates eigenvalues and eigenvectors of a given matrix (intended for internal use).
- Parameters:
Mat (Matrix) – a matrix
- Returns:
tuple containing (eigenvalues, eigenvectors)
- Return type:
tuple
Examples
# TODO
- _eigStat(Mat: spmatrix | ndarray, symp: bool = False) List[float] [source]#
Calculates all the amplitudes \(|c_{i,k}|^{2}\) of entries \(|k\rangle := \begin{bmatrix} c_{1,k} \\ \vdots \\ c_{i,k} \\ \vdots \\c_{\mathcal{D},k} \end{bmatrix}_{\mathcal{D}\times 1}\) for all the eigenvectors \(\{|k\rangle\}\) of a given matrix.
symp is used to calculate eigenvector statistics of systems with degeneracies, corresponding to symplectic class by summing every odd entry amplitude with the following even entry amplitude.
- Parameters:
Mat (Matrix) – a matrix
symp (bool, optional) – If True (False) sum every odd entry amplitude with the following even entry amplitude.
- Returns:
list of entry amplitudes
- Return type:
floatList
Examples
# TODO
- _eigStatSymp(Mat: spmatrix | ndarray) List[float] [source]#
Intended for internal use, and used in eigenvector statistics calculation of symplectic class.
- Parameters:
Mat (Matrix) – a matrix
- Returns:
list of entry amplitudes
- Return type:
floatList
Examples
# TODO
- _eigStatEig(EigVecs: spmatrix | ndarray, symp=False) List[float] [source]#
Calculates all the amplitudes \(|c_{i,k}|^{2}\) of entries \(|k\rangle := \begin{bmatrix} c_{1,k} \\ \vdots \\ c_{i,k} \\ \vdots \\c_{\mathcal{D},k} \end{bmatrix}_{\mathcal{D}\times 1}\) for a given list of eigenvectors \(\{|k\rangle\}\).
symp is used to calculate eigenvectors statistics of systems with degeneracies, corresponding to symplectic class by summing every odd entry amplitude with the following even entry amplitude.
- Parameters:
EigVecs (Matrix) – a list of ket vectors
symp (bool, optional) – If True (False) sum every odd entry amplitude with the following even entry amplitude.
- Returns:
list of entry amplitudes
- Return type:
floatList
Examples
# TODO
- _eigsStatEigSymp(EigVecs: spmatrix | ndarray) List[float] [source]#
Intended for internal use, and used in eigenvector statistics calculation of symplectic class.
- Parameters:
EigVecs (Matrix) – a list of ket vectors
- Returns:
list of entry amplitudes
- Return type:
floatList
Examples
# TODO
- eigVecStatKet(basis: List[spmatrix | ndarray], ket: spmatrix | ndarray, symp=True) Tuple [source]#
Calculates component amplitudes \(|c_{i,k}|^{2}\) of a ket \(|k\rangle := \sum_{i}c_{i,k}|i\rangle\) in a basis \(\{|i\rangle\}\).
Main use is in eigenvector statistics.
- Parameters:
basis (matrixList) – a complete basis
ket (Matrix) – the ket state
- Returns:
list of component values in the basis
- Return type:
floatList
Examples
>>> ket = basis(2, 1) >>> completeBasis = completeBasis(dimension=2) >>> eigVecStatKet(basis=completeBasis, ket=ket) [0, 1]