hqs_spin_mapper.transformables
Module containing the provided transformable objects for the HQS Spin Mapper.
Classes
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Data object for use in a spin determination calculation. |
Base Transformable class to avoid code duplication between the transformables. |
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Transformable system from a LatticeBuilder input. |
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Transformable system from input matrices for the Hamiltonian. |
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Transformable system from an electronic structure calculation input. |
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Transformable system from a LatticeBuilder input. |
- class hqs_spin_mapper.transformables.Transformable[source]
Base Transformable class to avoid code duplication between the transformables.
Construct empty base class (variables specified for linting purposes only!).
- __init__() None[source]
Construct empty base class (variables specified for linting purposes only!).
- property hamiltonians: Hamiltonian_Matrices
Return the matrix descriptions of the terms in the system Hamiltonian.
- Returns:
The stored Hamiltonian matrices
- Return type:
- property rotation_matrix: ndarray
Return the rotation matrix that transforms the system to the spin-optimized basis.
- Returns:
The stored rotation matrix \(U_{iq}\)
- Return type:
np.ndarray
- property spin_indices: Set[int]
Return the set of indices of the spin-like orbitals.
- Returns:
The indices of the spin-like orbitals
- Return type:
Set[int]
- property system_size: int
Return the system size i.e. the number of orbitals.
- Returns:
The combined size of the system
- Return type:
int
- property site_type: str
Return the type of orbitals (e.g.
spinful_fermionsorspinless_fermions).- Returns:
The type of the system sites
- Return type:
str
- property prefactor_cutoff: float
Return the cutoff for the prefactors of terms to be considered in the transformation.
- Returns:
The cutoff below which terms are dropped for the transformation
- Return type:
float
- property generator: ExpressionSpinful | ExpressionSpinful_complex
Return the generator \(S\) of the Schrieffer-Wolff transformation.
- Returns:
The generator of the Schrieffer-Wolff transformation
- Return type:
Union[ExpressionSpinful, ExpressionSpinfulComplex]
- property transformed_hamiltonian: ExpressionSpinful | ExpressionSpinful_complex
Return the Schrieffer-Wolff transformed Hamiltonian \(\tilde{H}\).
- Returns:
The transformed Hamiltonian
- Return type:
Union[ExpressionSpinful, ExpressionSpinful_complex]
- _abc_impl = <_abc._abc_data object>
- _is_protocol = False
- _is_runtime_protocol = True
- class hqs_spin_mapper.transformables.Transformable_Matrices(hamiltonians: Hamiltonian_Matrices, system_size: int | None = None, rotation_matrix: ndarray | None = None, prefactor_cutoff: float = 1e-06, site_type: str = 'spinful_fermions', spin_indices: Set[int] | None = None)[source]
Transformable system from input matrices for the Hamiltonian.
Construct the transformable system obtained from a matrix collection input.
- Parameters:
hamiltonians (Hamiltonian_Matrices) – Collection of matrix descriptions of the system
Hamiltonian
system_size (int) – Number of orbitals in the system
rotation_matrix (np.ndarray) – Transformation matrix \(U_{iq}\) to the spin-optimized
basis
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
site_type (str) – Type of excitations in the orbitals.
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- __init__(hamiltonians: Hamiltonian_Matrices, system_size: int | None = None, rotation_matrix: ndarray | None = None, prefactor_cutoff: float = 1e-06, site_type: str = 'spinful_fermions', spin_indices: Set[int] | None = None) None[source]
Construct the transformable system obtained from a matrix collection input.
- Parameters:
hamiltonians (Hamiltonian_Matrices) – Collection of matrix descriptions of the system
Hamiltonian
system_size (int) – Number of orbitals in the system
rotation_matrix (np.ndarray) – Transformation matrix \(U_{iq}\) to the spin-optimized
basis
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
site_type (str) – Type of excitations in the orbitals.
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- _spin_indices: Set[int]
- _abc_impl = <_abc._abc_data object>
- _is_protocol = False
- _is_runtime_protocol = True
- property generator: ExpressionSpinful | ExpressionSpinful_complex
Return the generator \(S\) of the Schrieffer-Wolff transformation.
- Returns:
The generator of the Schrieffer-Wolff transformation
- Return type:
Union[ExpressionSpinful, ExpressionSpinfulComplex]
- property hamiltonians: Hamiltonian_Matrices
Return the matrix descriptions of the terms in the system Hamiltonian.
- Returns:
The stored Hamiltonian matrices
- Return type:
- property prefactor_cutoff: float
Return the cutoff for the prefactors of terms to be considered in the transformation.
- Returns:
The cutoff below which terms are dropped for the transformation
- Return type:
float
- property rotation_matrix: ndarray
Return the rotation matrix that transforms the system to the spin-optimized basis.
- Returns:
The stored rotation matrix \(U_{iq}\)
- Return type:
np.ndarray
- property site_type: str
Return the type of orbitals (e.g.
spinful_fermionsorspinless_fermions).- Returns:
The type of the system sites
- Return type:
str
- property spin_indices: Set[int]
Return the set of indices of the spin-like orbitals.
- Returns:
The indices of the spin-like orbitals
- Return type:
Set[int]
- property system_size: int
Return the system size i.e. the number of orbitals.
- Returns:
The combined size of the system
- Return type:
int
- property transformed_hamiltonian: ExpressionSpinful | ExpressionSpinful_complex
Return the Schrieffer-Wolff transformed Hamiltonian \(\tilde{H}\).
- Returns:
The transformed Hamiltonian
- Return type:
Union[ExpressionSpinful, ExpressionSpinful_complex]
- class hqs_spin_mapper.transformables.Transformable_Struqture(system: FermionHamiltonianSystem, prefactor_cutoff: float = 1e-06, spin_indices: Set[int] | None = None)[source]
Transformable system from a LatticeBuilder input.
Construct the transformable system obtained from a Struqture input.
- Parameters:
system (FermionHamiltonianSystem) – Input Hamiltonian as struqture
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- Raises:
ValueError – Struqture incompatible with HQS Spin Mapper
- __init__(system: FermionHamiltonianSystem, prefactor_cutoff: float = 1e-06, spin_indices: Set[int] | None = None) None[source]
Construct the transformable system obtained from a Struqture input.
- Parameters:
system (FermionHamiltonianSystem) – Input Hamiltonian as struqture
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- Raises:
ValueError – Struqture incompatible with HQS Spin Mapper
- _spin_indices: Set[int]
- _abc_impl = <_abc._abc_data object>
- _is_protocol = False
- _is_runtime_protocol = True
- property generator: ExpressionSpinful | ExpressionSpinful_complex
Return the generator \(S\) of the Schrieffer-Wolff transformation.
- Returns:
The generator of the Schrieffer-Wolff transformation
- Return type:
Union[ExpressionSpinful, ExpressionSpinfulComplex]
- property hamiltonians: Hamiltonian_Matrices
Return the matrix descriptions of the terms in the system Hamiltonian.
- Returns:
The stored Hamiltonian matrices
- Return type:
- property prefactor_cutoff: float
Return the cutoff for the prefactors of terms to be considered in the transformation.
- Returns:
The cutoff below which terms are dropped for the transformation
- Return type:
float
- property rotation_matrix: ndarray
Return the rotation matrix that transforms the system to the spin-optimized basis.
- Returns:
The stored rotation matrix \(U_{iq}\)
- Return type:
np.ndarray
- property site_type: str
Return the type of orbitals (e.g.
spinful_fermionsorspinless_fermions).- Returns:
The type of the system sites
- Return type:
str
- property spin_indices: Set[int]
Return the set of indices of the spin-like orbitals.
- Returns:
The indices of the spin-like orbitals
- Return type:
Set[int]
- property system_size: int
Return the system size i.e. the number of orbitals.
- Returns:
The combined size of the system
- Return type:
int
- property transformed_hamiltonian: ExpressionSpinful | ExpressionSpinful_complex
Return the Schrieffer-Wolff transformed Hamiltonian \(\tilde{H}\).
- Returns:
The transformed Hamiltonian
- Return type:
Union[ExpressionSpinful, ExpressionSpinful_complex]
- class hqs_spin_mapper.transformables.Transformable_LatticeBuilder(builder: Builder | str, rotation_matrix: ndarray | None = None, prefactor_cutoff: float = 1e-06, spin_indices: Set[int] | None = None)[source]
Transformable system from a LatticeBuilder input.
Construct the transformable system obtained from a LatticeBuilder input.
- Parameters:
builder (Union[Builder, str]) – LatticeBuilder input describing the system
rotation_matrix (np.ndarray) – Transformation matrix \(U_{iq}\) to the spin-optimized
basis
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- Raises:
AssertionError – Input is not conforming to lattice validator requirements.
TypeError – The type of the input is incorrect.
- __init__(builder: Builder | str, rotation_matrix: ndarray | None = None, prefactor_cutoff: float = 1e-06, spin_indices: Set[int] | None = None) None[source]
Construct the transformable system obtained from a LatticeBuilder input.
- Parameters:
builder (Union[Builder, str]) – LatticeBuilder input describing the system
rotation_matrix (np.ndarray) – Transformation matrix \(U_{iq}\) to the spin-optimized
basis
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- Raises:
AssertionError – Input is not conforming to lattice validator requirements.
TypeError – The type of the input is incorrect.
- _spin_indices: Set[int]
- property particle_hole_symmetry_shift: float
Return the constant energy shift due to the particle-hole symetry of the interaction.
- Returns:
The the value of the constant energy shift
- Return type:
float
- _abc_impl = <_abc._abc_data object>
- _is_protocol = False
- _is_runtime_protocol = True
- property generator: ExpressionSpinful | ExpressionSpinful_complex
Return the generator \(S\) of the Schrieffer-Wolff transformation.
- Returns:
The generator of the Schrieffer-Wolff transformation
- Return type:
Union[ExpressionSpinful, ExpressionSpinfulComplex]
- property hamiltonians: Hamiltonian_Matrices
Return the matrix descriptions of the terms in the system Hamiltonian.
- Returns:
The stored Hamiltonian matrices
- Return type:
- property prefactor_cutoff: float
Return the cutoff for the prefactors of terms to be considered in the transformation.
- Returns:
The cutoff below which terms are dropped for the transformation
- Return type:
float
- property rotation_matrix: ndarray
Return the rotation matrix that transforms the system to the spin-optimized basis.
- Returns:
The stored rotation matrix \(U_{iq}\)
- Return type:
np.ndarray
- property site_type: str
Return the type of orbitals (e.g.
spinful_fermionsorspinless_fermions).- Returns:
The type of the system sites
- Return type:
str
- property spin_indices: Set[int]
Return the set of indices of the spin-like orbitals.
- Returns:
The indices of the spin-like orbitals
- Return type:
Set[int]
- property system_size: int
Return the system size i.e. the number of orbitals.
- Returns:
The combined size of the system
- Return type:
int
- property transformed_hamiltonian: ExpressionSpinful | ExpressionSpinful_complex
Return the Schrieffer-Wolff transformed Hamiltonian \(\tilde{H}\).
- Returns:
The transformed Hamiltonian
- Return type:
Union[ExpressionSpinful, ExpressionSpinful_complex]
- class hqs_spin_mapper.transformables.Transformable_QuantumChemistry(hamiltonians: Hamiltonian_Matrices, rdm1: ndarray | Tuple[ndarray, ...], rdm2: ndarray, system_size: int | None = None, rotation_matrix: ndarray | None = None, tolerance: float = 0.1, prefactor_cutoff: float = 1e-06, optimization_steps: int = 4, site_type: str = 'spinful_fermions', spin_indices: Set[int] | None = None)[source]
Transformable system from an electronic structure calculation input.
Construct the transformable system obtained from ab-initio calculation input.
- Parameters:
hamiltonians (Hamiltonian_Matrices) – Collection of matrix descriptions of the system
Hamiltonian
rdm1 (Union[np.ndarray, Tuple[np.ndarray, ...]]) – Matrix description of the 1-RDM
rdm2 (np.ndarray) – Tensor description of the 2-RDM
system_size (int) – Number of orbitals in the system
rotation_matrix (np.ndarray) – Transformation matrix \(U_{iq}\) to the spin-optimized
basis
tolerance (float) – Parity tolerance \(P_i=(-1 + \delta)\) for an orbital to be
spin-like
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
optimization_steps (int) – Number of optimization loops.
site_type (str) – Type of excitations in the orbitals.
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- Raises:
ValueError – HU does not conform to the requirements needed for basis rotation
ValueError – The 2-RDM does not conform to the requirements needed for spin optimization
- __init__(hamiltonians: Hamiltonian_Matrices, rdm1: ndarray | Tuple[ndarray, ...], rdm2: ndarray, system_size: int | None = None, rotation_matrix: ndarray | None = None, tolerance: float = 0.1, prefactor_cutoff: float = 1e-06, optimization_steps: int = 4, site_type: str = 'spinful_fermions', spin_indices: Set[int] | None = None) None[source]
Construct the transformable system obtained from ab-initio calculation input.
- Parameters:
hamiltonians (Hamiltonian_Matrices) – Collection of matrix descriptions of the system
Hamiltonian
rdm1 (Union[np.ndarray, Tuple[np.ndarray, ...]]) – Matrix description of the 1-RDM
rdm2 (np.ndarray) – Tensor description of the 2-RDM
system_size (int) – Number of orbitals in the system
rotation_matrix (np.ndarray) – Transformation matrix \(U_{iq}\) to the spin-optimized
basis
tolerance (float) – Parity tolerance \(P_i=(-1 + \delta)\) for an orbital to be
spin-like
prefactor_cutoff (float) – Cutoff for the absolute value of the coupling strength of
transformation. (terms to be considered in the Schrieffer-Wolff)
optimization_steps (int) – Number of optimization loops.
site_type (str) – Type of excitations in the orbitals.
spin_indices (Set[int]) – Set of indices of the dedicated spin-like orbitals.
- Raises:
ValueError – HU does not conform to the requirements needed for basis rotation
ValueError – The 2-RDM does not conform to the requirements needed for spin optimization
- _spin_indices: Set[int]
- _abc_impl = <_abc._abc_data object>
- _is_protocol = False
- _is_runtime_protocol = True
- property generator: ExpressionSpinful | ExpressionSpinful_complex
Return the generator \(S\) of the Schrieffer-Wolff transformation.
- Returns:
The generator of the Schrieffer-Wolff transformation
- Return type:
Union[ExpressionSpinful, ExpressionSpinfulComplex]
- property hamiltonians: Hamiltonian_Matrices
Return the matrix descriptions of the terms in the system Hamiltonian.
- Returns:
The stored Hamiltonian matrices
- Return type:
- property prefactor_cutoff: float
Return the cutoff for the prefactors of terms to be considered in the transformation.
- Returns:
The cutoff below which terms are dropped for the transformation
- Return type:
float
- property rotation_matrix: ndarray
Return the rotation matrix that transforms the system to the spin-optimized basis.
- Returns:
The stored rotation matrix \(U_{iq}\)
- Return type:
np.ndarray
- property site_type: str
Return the type of orbitals (e.g.
spinful_fermionsorspinless_fermions).- Returns:
The type of the system sites
- Return type:
str
- property spin_indices: Set[int]
Return the set of indices of the spin-like orbitals.
- Returns:
The indices of the spin-like orbitals
- Return type:
Set[int]
- property system_size: int
Return the system size i.e. the number of orbitals.
- Returns:
The combined size of the system
- Return type:
int
- property transformed_hamiltonian: ExpressionSpinful | ExpressionSpinful_complex
Return the Schrieffer-Wolff transformed Hamiltonian \(\tilde{H}\).
- Returns:
The transformed Hamiltonian
- Return type:
Union[ExpressionSpinful, ExpressionSpinful_complex]
- property tolerance: float
Return the tolerated parity deviation \(\delta\) in \(P=(-1+\delta)\) to be considered a spin-orbital.
- Returns:
The stored value for the tolerance :maht:`delta` of the parity
- Return type:
float
- property optimization_steps: int
Return the number of optimization loops.
- Returns:
The number of optimization loops
- Return type:
int
- property immutable_indices: Set[int]
Return the orbital indices that should remained unaltered by the optimization.
- Returns:
The set of immutable indices
- Return type:
Set[int]
- property rdm1: ndarray | Tuple[ndarray, ...]
Return the matrix descriptions of the 1-RDM (\(\langle c^{\dagger}_{i\sigma} c_{j\sigma'}\rangle\)).
- Returns:
The (spin-resolved) 1-RDM(s)
- Return type:
Union[np.ndarray, Tuple[np.ndarray, …]]
- property rdm2: ndarray
Return the tensor of the 2-RDM (\(\langle c^{\dagger}_{i\uparrow} c^{\dagger}_{j\downarrow} c_{k\downarrow} c_{l\uparrow}\rangle\)).
- Returns:
Tensor description of the 2-RDM
- Return type:
np.ndarray
- class hqs_spin_mapper.transformables.SpinFinder(rdm1: ndarray | Tuple[ndarray, ...], rdm2: ndarray, tolerance: float = 0.1, optimization_steps: int = 4, spin_indices: Set[int] | None = None)[source]
Data object for use in a spin determination calculation.
Construct the object ab-initio calculation input.
- Parameters:
rdm1 (Union[np.ndarray, Tuple[np.ndarray, ...]]) – Matrix descriptions of the 1-RDM
rdm2 (np.ndarray) – Tensor description of the 2-RDM
tolerance (float) – Parity tolerance \(delta\) in \(P=(-1 + \delta)\) for an
spin-like (orbital to be)
optimization_steps (int) – Number of optimization loops
spin_indices (Set[int]) – Set of indices of the dedicated spinful orbitals
- Raises:
ValueError – The 2-RDM does not conform to the requirements needed for spin optimization
- _abc_impl = <_abc._abc_data object>
- _is_protocol = False
- _is_runtime_protocol = True
- __init__(rdm1: ndarray | Tuple[ndarray, ...], rdm2: ndarray, tolerance: float = 0.1, optimization_steps: int = 4, spin_indices: Set[int] | None = None) None[source]
Construct the object ab-initio calculation input.
- Parameters:
rdm1 (Union[np.ndarray, Tuple[np.ndarray, ...]]) – Matrix descriptions of the 1-RDM
rdm2 (np.ndarray) – Tensor description of the 2-RDM
tolerance (float) – Parity tolerance \(delta\) in \(P=(-1 + \delta)\) for an
spin-like (orbital to be)
optimization_steps (int) – Number of optimization loops
spin_indices (Set[int]) – Set of indices of the dedicated spinful orbitals
- Raises:
ValueError – The 2-RDM does not conform to the requirements needed for spin optimization
- property rotation_matrix: ndarray
Return the rotation matrix that transforms the system to the spin-optimized basis.
- Returns:
The stored rotation matrix \(U_{iq}\)
- Return type:
np.ndarray
- property spin_indices: Set[int]
Return the set of indices of the spin-like orbitals.
- Returns:
The indices of the spin-like orbitals
- Return type:
Set[int]
- property system_size: int
Return the system size i.e. the number of orbitals.
- Returns:
The combined size of the system
- Return type:
int
- property tolerance: float
Return the tolerated parity deviation \(\delta\) in \(P=(-1+\delta)\) to be considered a spin-orbital.
- Returns:
The stored parity tolerance
- Return type:
float
- property optimization_steps: int
Return the number of optimization loops.
- Returns:
The number of optimization loops
- Return type:
int
- property immutable_indices: Set[int]
Return the orbital indices that should remained unaltered by the optimization.
- Returns:
The set of immutable indices
- Return type:
Set[int]
- property rdm1: ndarray | Tuple[ndarray, ...]
Return the matrix/ces of the 1-RDM (\(\langle c^{\dagger}_{i\sigma} c_{j\sigma'}\rangle\)).
- Returns:
The matrix descriptions of the 1-RDM
- Return type:
Union[np.ndarray, Tuple[np.ndarray, …]
- property rdm2: ndarray
Return the tensor description of the 2-RDM (\(\langle c^{\dagger}_{i\uparrow} c^{\dagger}_{j\downarrow} c_{k\downarrow} c_{l\uparrow}\rangle\)).
- Returns:
The tensor description of the 2-RDM
- Return type:
np.ndarray