Chemistry

problems

Classes:

Name	Description
FermionHamiltonianProblem	Defines an electronic-structure problem using a Fermionic operator and electron count.

FermionHamiltonianProblem

FermionHamiltonianProblem(
    fermion_hamiltonian: FermionOperator,
    n_particles: tuple[int, int],
    n_orbitals: int | None = None,
)

Defines an electronic-structure problem using a Fermionic operator and electron count. Can also be constructed from a MolecularData object using the from_molecule method.

Attributes:

Name	Type	Description
fermion_hamiltonian	FermionOperator	The fermionic hamiltonian of the problem. Assumed to be in the block-spin labeling.
n_orbitals	int	Number of spatial orbitlas.
n_alpha	int	Number of alpha particles.
n_beta	int	Number of beta particles.
n_particles	tuple[int, int]	Number of alpha and beta particles.

Initializes a FermionHamiltonianProblem from the fermion hamiltonian, number of alpha and beta particles, and optionally the number of orbitals.

Parameters:

Name	Type	Description	Default
fermion_hamiltonian	FermionHamiltonianProblem	The fermionic hamiltonian of the problem. Assumed to be in the block-spin labeling.	required
n_particles	tuple[int, int]	Number of alpha and beta particles.	required
n_orbitals	int	Number of spatial orbitals. If not specified, the number is inferred from fermion_hamiltonian.	None

Methods:

Name	Description
from_molecule	Constructs a FermionHamiltonianProblem from a molecule data.

fermion_hamiltonian

fermion_hamiltonian = fermion_hamiltonian

n_orbitals

n_orbitals = min_n_orbitals

n_particles

n_particles = n_particles

occupied

occupied: list[int]

Indices list of occupied alpha and beta particles.

occupied_alpha

occupied_alpha: list[int]

Indices list of occupied alpha particles.

occupied_beta

occupied_beta: list[int]

Indices list of occupied beta particles.

virtual

virtual: list[int]

Indices list of virtual alpha and beta particles.

virtual_alpha

virtual_alpha: list[int]

Indices list of virtual alpha particles.

virtual_beta

virtual_beta: list[int]

Indices list of virtual beta particles.

from_molecule

from_molecule(
    molecule: MolecularData,
    first_active_index: int = 0,
    remove_orbitlas: Sequence[int] | None = None,
    op_compression_tol: float = 1e-13,
) -> FermionHamiltonianProblem

Constructs a FermionHamiltonianProblem from a molecule data.

Parameters:

Name	Type	Description	Default
molecule	MolecularData	The molecule data.	required
first_active_index	int	The first active index, indicates all prior indices are freezed.	0
remove_orbitlas	Sequence[int]	Active indices to be removed.	None
op_compression_tol	float	Tolerance for trimming the fermion operator.	1e-13

Returns:

Type	Description
FermionHamiltonianProblem	The fermion hamiltonian problem.

mapping

Classes:

Name	Description
FermionToQubitMapper	Mapper between fermionic operators to qubits operators, using one of the supported
MappingMethod	Mapping methods from fermionic operators to qubits operators.

FermionToQubitMapper

FermionToQubitMapper(method: MappingMethod = JORDAN_WIGNER)

Mapper between fermionic operators to qubits operators, using one of the supported mapping methods (see MappingMethod).

Attributes:

Name	Type	Description
method	MappingMethod	The mapping method.

Initializes a FermionToQubitMapper object using the specified method.

Parameters:

Name	Type	Description	Default
method	MappingMethod	The mapping method.	JORDAN_WIGNER

Methods:

Name	Description
get_num_qubits	Gets the number of qubits after mapping the given problem into qubits space.
map	Maps the given fermionic operator to a qubits operator using the mapper's

method

method = method

get_num_qubits

get_num_qubits(problem: FermionHamiltonianProblem) -> int

Gets the number of qubits after mapping the given problem into qubits space.

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem.	required

Returns:

Type	Description
int	The number of qubits.

map

map(
    fermion_op: FermionOperator, *args: Any, **kwargs: Any
) -> QubitOperator

Maps the given fermionic operator to a qubits operator using the mapper's configuration.

Parameters:

Name	Type	Description	Default
fermion_op	FermionOperator	A fermionic operator.	required
*args	Any	Extra parameters which are ignored, may be used in subclasses.	()
**kwargs	Any	Extra parameters which are ignored, may be used in subclasses.	{}

Returns:

Type	Description
QubitOperator	The mapped qubits operator.

MappingMethod

Bases: StrEnum

Mapping methods from fermionic operators to qubits operators.

Attributes:

Name	Type	Description
BRAVYI_KITAEV
JORDAN_WIGNER

BRAVYI_KITAEV

BRAVYI_KITAEV = 'bk'

JORDAN_WIGNER

JORDAN_WIGNER = 'jw'

z2_symmetries

Classes:

Name	Description
Z2SymTaperMapper	Mapper between fermionic operators to qubits operators, using one of the supported

Z2SymTaperMapper

Z2SymTaperMapper(
    generators: Sequence[QubitOperator],
    x_ops: Sequence[QubitOperator],
    method: MappingMethod = JORDAN_WIGNER,
    sector: Sequence[int] | None = None,
    tol: float = 1e-14,
)

Bases: FermionToQubitMapper

Mapper between fermionic operators to qubits operators, using one of the supported mapping methods (see MappingMethod), and taking advantage of Z2 symmetries in order to taper off qubits.

Attributes:

Name	Type	Description
method	MappingMethod	The mapping method.
generators	tuple[QubitOperator, ...]	Generators representing the Z2 symmetries.
x_ops	tuple[QubitOperator, ...]	Single-qubit X operations, such that each operation anti-commutes with its matching generator and commutes with all other generators.

Initializes a Z2SymTaperMapper object from the given configuration.

Parameters:

Name	Type	Description	Default
generators	Sequence[QubitOperator]	Generators representing the Z2 symmetries.	required
x_ops	Sequence[QubitOperator]	Single-qubit X operations, such that each operation anti-commutes with its matching generator and commutes with all other generators.	required
method	MappingMethod	The mapping method.	JORDAN_WIGNER
sector	Sequence[int] | None	(Sequence[int]): Symmetry sector coefficients, each is 1 or -1. If not specified, all coefficients defaults to 1.	None
tol	float	Tolerance for trimming off terms.	1e-14

Methods:

Name	Description
from_problem	Initializes a Z2SymTaperMapper object from a fermion problem (i.e. computing
get_num_qubits	Gets the number of qubits after mapping the given problem into qubits space.
map	Maps the given fermionic operator to qubits operator by using the
set_sector	Sets the symmetry sector coefficients.

generators

generators: tuple[QubitOperator, ...]

Generators representing the Z2 symmetries.

x_ops

x_ops: tuple[QubitOperator, ...]

Single-qubit X operations, such that each operation anti-commutes with its matching generator and commutes with all other generators.

from_problem

from_problem(
    problem: FermionHamiltonianProblem,
    method: MappingMethod = JORDAN_WIGNER,
    sector_from_hartree_fock: bool = True,
    tol: float = 1e-14,
) -> Z2SymTaperMapper

Initializes a Z2SymTaperMapper object from a fermion problem (i.e. computing the Z2 symmetries from the problem definition).

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem.	required
method	MappingMethod	The mapping method.	JORDAN_WIGNER
sector_from_hartree_fock	bool	Whether to compute the symmetry sector coefficients according to the Hartree-Fock state.	True
tol	float	Tolerance for trimming off terms.	1e-14

Returns:

Type	Description
Z2SymTaperMapper	The Z2 symmetries taper mapper.

get_num_qubits

get_num_qubits(problem: FermionHamiltonianProblem) -> int

Gets the number of qubits after mapping the given problem into qubits space.

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem.	required

Returns:

Type	Description
int	The number of qubits.

map

map(
    fermion_op: FermionOperator,
    *args: Any,
    is_invariant: bool = False,
    **kwargs: Any
) -> QubitOperator

Maps the given fermionic operator to qubits operator by using the mapper's method, and subsequently by tapering off qubits according to Z2 symmetries.

Parameters:

Name	Type	Description	Default
fermion_op	FermionOperator	A fermionic operator.	required
is_invariant	bool	If False, the operator is not necessarily in the symmetry subspace, and thus gets projected onto it before tapering.	False

Returns:

Type	Description
QubitOperator	The mapped qubits operator.

set_sector

set_sector(sector: Sequence[int]) -> None

Sets the symmetry sector coefficients.

Parameters:

Name	Type	Description	Default
sector	Sequence[int]	(Sequence[int]): Symmetry sector coefficients, each is 1 or -1.	required

hartree_fock

Functions:

Name	Description
get_hf_fermion_op	Constructs a fermion operator that creates the Hartree-Fock reference state in
get_hf_state	Computes the qubits state after applying the Hartree-Fock operator defined by the

get_hf_fermion_op

get_hf_fermion_op(
    problem: FermionHamiltonianProblem,
) -> FermionOperator

Constructs a fermion operator that creates the Hartree-Fock reference state in block-spin ordering.

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem. The Hartree-Fock fermion operator depends only on the number of spatial orbitals and the number of alpha and beta particles.	required

Returns:

Type	Description
FermionOperator	The Hartree-Fock fermion operator.

get_hf_state

get_hf_state(
    problem: FermionHamiltonianProblem,
    mapper: FermionToQubitMapper,
) -> list[bool]

Computes the qubits state after applying the Hartree-Fock operator defined by the given problem and mapper.

The Qmod function prepare_basis_state can be used on the returned value to allocate and initialize the qubits array.

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem.	required
mapper	FermionToQubitMapper	The mapper from fermion operator to qubits operator.	required

Returns:

Type	Description
list[bool]	The qubits state, given as a list of boolean values for each qubit.

ucc

Functions:

Name	Description
get_excitations	Gets all the possible excitations of the given problem according to the
get_ucc_hamiltonians	Computes the UCC hamiltonians of the given problem in the desired excitations,

get_excitations

get_excitations(
    problem: FermionHamiltonianProblem, num_excitations: int
) -> set[tuple[tuple[int, ...], tuple[int, ...]]]

Gets all the possible excitations of the given problem according to the given number of excitations, preserving the particles spin.

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem.	required
num_excitations	int	Number of excitations.	required

Returns:

Type	Description
set[tuple[tuple[int, ...], tuple[int, ...]]]	A set of all possible excitations, specified as a pair of source and target indices.

get_ucc_hamiltonians

get_ucc_hamiltonians(
    problem: FermionHamiltonianProblem,
    mapper: FermionToQubitMapper,
    excitations: int | Sequence[int],
) -> list[SparsePauliOp]

Computes the UCC hamiltonians of the given problem in the desired excitations, using the given mapper.

Parameters:

Name	Type	Description	Default
problem	FermionHamiltonianProblem	The fermion problem.	required
mapper	FermionToQubitMapper	The mapper from fermion to qubits operators.	required
excitations	(int, Sequence[int])	A single desired excitation or an excitations list.	required

Returns:

Type	Description
list[SparsePauliOp]	The UCC hamiltonians.