ElectronicDensity#
- class ElectronicDensity(alpha=None, beta=None, beta_alpha=None, *, validate=True)[source]#
Bases:
ElectronicIntegrals
The ElectronicDensity property.
This property adds operators to evaluate the 1- and 2-reduced density matrices (RDMs). It is implemented as a subclass of the
ElectronicIntegrals
which means that it supports mathematical operations and generally stores unrestricted spin data. However, you can trace out the spin usingtrace_spin()
.Any
None
-valued argument will internally be replaced by an emptyPolynomialTensor
(see alsoqiskit_nature.second_q.operators.PolynomialTensor.empty()
).- Parameters:
alpha (PolynomialTensor | None) – the up-spin electronic integrals
beta (PolynomialTensor | None) – the down-spin electronic integrals
beta_alpha (PolynomialTensor | None) – the beta-alpha-spin two-body electronic integrals. This may only contain the
++--
key.validate (bool) – when set to False, no validation will be performed. Disable this setting with care!
- Raises:
KeyError – if the
alpha
tensor contains keys other than""
,"+-"
, and"++--"
.KeyError – if the
beta
tensor contains keys other than""
,"+-"
, and"++--"
.KeyError – if the
beta_alpha
tensor contains keys other than"++--"
.ValueError – if the reported
register_length
attributes of the alpha-, beta-, and beta-alpha-spin tensors do not all match.
Attributes
- alpha#
The up-spin electronic integrals.
- alpha_beta#
The alpha-beta-spin two-body electronic integrals.
These get reconstructed from
beta_alpha
by transposing in the physicist’ ordering convention.
- beta#
The down-spin electronic integrals.
- beta_alpha#
The beta-alpha-spin two-body electronic integrals.
- one_body#
Returns only the one-body integrals.
- register_length#
The size of the operator that can be generated from these ElectronicIntegrals.
- two_body#
Returns only the two-body integrals.
Methods
- classmethod apply(function, *operands, multi=False, validate=True)#
Exposes the
qiskit_nature.second_q.operators.PolynomialTensor.apply()
method.This behaves identical to the
apply
implementation of thePolynomialTensor
, applied to thealpha
,beta
, andbeta_alpha
attributes of the providedElectronicIntegrals
operands.This method is special, because it handles the scenario in which any operand has a non-empty
beta
attribute, in which case the empty-beta attributes of any other operands will be filled withalpha
attributes of those operands. Thebeta_alpha
attributes will only be handled if they are non-empty in all supplied operands.- Parameters:
function (Callable[..., np.ndarray | SparseArray | complex]) – the function to apply to the internal arrays of the provided operands. This function must take numpy (or sparse) arrays as its positional arguments. The number of arguments must match the number of provided operands.
operands (ElectronicIntegrals) – a sequence of
ElectronicIntegrals
instances on which to operate.multi (bool) – when set to True this indicates that the provided numpy function will return multiple new numpy arrays which will each be wrapped into an
ElectronicIntegrals
instance separately.validate (bool) – when set to False, no validation will be performed. Disable this setting with care!
- Returns:
A new
ElectronicIntegrals
.- Return type:
- classmethod einsum(einsum_map, *operands, validate=True)#
Exposes the
qiskit_nature.second_q.operators.PolynomialTensor.einsum()
method.This behaves identical to the
einsum
implementation of thePolynomialTensor
, applied to thealpha
,beta
, andbeta_alpha
attributes of the providedElectronicIntegrals
operands.This method is special, because it handles the scenario in which any operand has a non-empty
beta
attribute, in which case the empty-beta attributes of any other operands will be filled withalpha
attributes of those operands. Thebeta_alpha
attributes will only be handled if they are non-empty in all supplied operands.- Parameters:
einsum_map (dict[str, tuple[str, ...]]) – a dictionary, mapping from
numpy.einsum()
subscripts to a tuple of strings. These strings correspond to the keys of matrices to be extracted from the providedElectronicIntegrals
operands. The last string in this tuple indicates the key under which to store the result in the returnedElectronicIntegrals
.operands (ElectronicIntegrals) – a sequence of
ElectronicIntegrals
instances on which to operate.validate (bool) – when set to False, no validation will be performed. Disable this setting with care!
- Returns:
A new
ElectronicIntegrals
.- Return type:
- classmethod empty(num_spatial_orbitals, *, include_rdm2=True)[source]#
Initializes an empty (all-zero)
ElectronicDensity
.- Parameters:
- Returns:
The resulting
ElectronicDensity
.- Return type:
- equiv(other)#
Check equivalence of first ElectronicIntegrals with other
- classmethod from_orbital_occupation(alpha_occupation, beta_occupation, *, include_rdm2=True)[source]#
Initializes an
ElectronicDensity
from the provided orbital occupations.This method assumes an orthonormal basis, and will initialize the 1-RDMs simply as diagonal matrices of the provided orbital occupations. The 2-RDMs are computed based on these 1-RDMs.
- classmethod from_particle_number(num_spatial_orbitals, num_particles, *, include_rdm2=True)[source]#
Initializes an
ElectronicDensity
from the provided number of particles.- Parameters:
num_spatial_orbitals (int) – the number of spatial orbitals.
num_particles (int | tuple[int, int]) – the number of particles. If this is an integer it is interpreted as the total number of particles. If it is a tuple of two integers, these are treated as the number of alpha- and beta-spin particles, respectively.
include_rdm2 (bool) – whether to include the 2-body RDMs.
- Returns:
The resulting
ElectronicDensity
.- Return type:
- classmethod from_raw_integrals(h1_a, h2_aa=None, h1_b=None, h2_bb=None, h2_ba=None, *, validate=True, auto_index_order=True)#
Loads the provided integral matrices into an
ElectronicIntegrals
instance.When
auto_index_order
is enabled,qiskit_nature.second_q.operators.tensor_ordering.find_index_order()
will be used to determine the index ordering of theh2_aa
matrix, based on which the two-body matrices will automatically be transformed to the physicist’ order, which is required by theqiskit_nature.second_q.operators.PolynomialTensor
.- Parameters:
h1_a (np.ndarray | SparseArray) – the alpha-spin one-body integrals.
h2_aa (np.ndarray | SparseArray | None) – the alpha-alpha-spin two-body integrals.
h1_b (np.ndarray | SparseArray | None) – the beta-spin one-body integrals.
h2_bb (np.ndarray | SparseArray | None) – the beta-beta-spin two-body integrals.
h2_ba (np.ndarray | SparseArray | None) – the beta-alpha-spin two-body integrals.
validate (bool) – whether or not to validate the integral matrices. Disable this setting with care!
auto_index_order (bool) – whether or not to automatically convert the matrices to physicists’ order.
- Raises:
QiskitNatureError – if auto_index_order=True, upon encountering an invalid
qiskit_nature.second_q.operators.tensor_ordering.IndexType
.- Returns:
The resulting
ElectronicIntegrals
.- Return type:
- classmethod identity(num_spatial_orbitals, *, include_rdm2=True)[source]#
Initializes an identity
ElectronicDensity
.- Parameters:
- Returns:
The resulting
ElectronicDensity
.- Return type:
- interpret(result)[source]#
Interprets an
qiskit_nature.second_q.problems.EigenstateResult
.In particular, this method gathers the evaluated auxiliary operator values and constructs the resulting
ElectronicDensity
and stores it in the result object.- Parameters:
result (qiskit_nature.second_q.problems.EigenstateResult) – the result to add meaning to.
- second_q_coeffs()#
Constructs the total
PolynomialTensor
contained the second-quantized coefficients.This function constructs the spin-orbital basis tensor as a
qiskit_nature.second_q.operators.PolynomialTensor
, by arranging thealpha
andbeta
attributes in a block-ordered fashion (up-spin integrals cover the first part, down-spin integrals the second part of the resulting register space).If the
beta
and/orbeta_alpha
attributes are empty, thealpha
data will be used in their place.- Returns:
The
PolynomialTensor
representing the entire system.- Return type:
- second_q_ops()[source]#
Returns the density evaluation operators.
- Returns:
A mapping of strings to FermionicOp objects.
- Return type:
- split(function, indices_or_sections, *, validate=True)#
Exposes the
qiskit_nature.second_q.operators.PolynomialTensor.split()
method.This behaves identical to the
split
implementation of thePolynomialTensor
, applied to thealpha
,beta
, andbeta_alpha
attributes of the providedElectronicIntegrals
operands.Note
When splitting arrays this will likely lead to array shapes which would fail the shape validation check. This is considered an advanced use case which is why the user is left to disable this check themselves, to ensure they know what they are doing.
- Parameters:
function (Callable[..., np.ndarray | SparseArray | Number]) – the splitting function to use. This function must take a single numpy (or sparse) array as its first input followed by a sequence of indices to split on. You should use
functools.partial
if you need to provide keyword arguments (e.g.partial(np.split, axis=-1)
). Common methods to use here arenumpy.hsplit()
andnumpy.vsplit()
.indices_or_sections (int | Sequence[int]) – a single index or sequence of indices to split on.
validate (bool) – when set to False, no validation will be performed. Disable this setting with care!
- Returns:
The new
ElectronicIntegrals
instances.- Return type:
- classmethod stack(function, operands, *, validate=True)#
Exposes the
qiskit_nature.second_q.operators.PolynomialTensor.stack()
method.This behaves identical to the
stack
implementation of thePolynomialTensor
, applied to thealpha
,beta
, andbeta_alpha
attributes of the providedElectronicIntegrals
operands.This method is special, because it handles the scenario in which any operand has a non-empty
beta
attribute, in which case the empty-beta attributes of any other operands will be filled withalpha
attributes of those operands. Thebeta_alpha
attributes will only be handled if they are non-empty in all supplied operands.Note
When stacking arrays this will likely lead to array shapes which would fail the shape validation check. This is considered an advanced use case which is why the user is left to disable this check themselves, to ensure they know what they are doing.
- Parameters:
function (Callable[..., np.ndarray | SparseArray | Number]) – the stacking function to apply to the internal arrays of the provided operands. This function must take a sequence of numpy (or sparse) arrays as its first argument. You should use
functools.partial
if you need to provide keyword arguments (e.g.partial(np.stack, axis=-1)
). Common methods to use here arenumpy.hstack()
andnumpy.vstack()
.operands (Sequence[ElectronicIntegrals]) – a sequence of
ElectronicIntegrals
instances on which to operate.validate (bool) – when set to False, no validation will be performed. Disable this setting with care!
- Returns:
A new
ElectronicIntegrals
.- Return type:
- trace_spin()#
Returns a
PolynomialTensor
where the spin components have been traced out.This will sum the
alpha
andbeta
components, tracing out the spin.- Returns:
A
PolynomialTensor
with the spin traced out.- Return type: