qalgebra.core package

The fundamental object hiearchies that constitute QNET’s various algebras

Submodules:

• qalgebra.core.abstract_algebra module
• qalgebra.core.abstract_quantum_algebra module
• qalgebra.core.algebraic_properties module
• qalgebra.core.exceptions module
• qalgebra.core.hilbert_space_algebra module
• qalgebra.core.indexed_operations module
• qalgebra.core.matrix_algebra module
• qalgebra.core.operator_algebra module
• qalgebra.core.scalar_algebra module
• qalgebra.core.state_algebra module
• qalgebra.core.super_operator_algebra module

Summary

__all__ Exceptions:

AlgebraError	Base class for all algebraic errors.
AlgebraException	Base class for all algebraic exceptions.
BasisNotSetError	Raised if the basis or a Hilbert space dimension is unavailable.
CannotSimplify	Raised when a rule cannot further simplify an expression.
CannotSymbolicallyDiagonalize	Matrix cannot be diagonalized analytically.
InfiniteSumError	Raised when expanding a sum into an infinite number of terms.
NoConjugateMatrix	Raised when entries of Matrix have no defined conjugate.
NonSquareMatrix	Raised when a Matrix fails to be square.
OverlappingSpaces	Raised when objects fail to be in separate Hilbert spaces.
SpaceTooLargeError	Raised when objects fail to be have overlapping Hilbert spaces.
UnequalSpaces	Raised when objects fail to be in the same Hilbert space.

__all__ Classes:

Adjoint	Symbolic Adjoint of an operator
BasisKet	Local basis state, identified by index or label
Bra	The associated dual/adjoint state for any ket
BraKet	The symbolic inner product between two states
CoherentStateKet	Local coherent state, labeled by a complex amplitude \(\alpha\).
Commutator	Commutator of two operators
Expression	Base class for all QAlgebra Expressions.
HilbertSpace	Base class for Hilbert spaces
IndexedSum	Base class for indexed sums.
KetBra	Outer product of two states
KetIndexedSum	Indexed sum over Kets.
KetPlus	Sum of states.
KetSymbol	Symbolic state.
LocalKet	A state on a LocalSpace.
LocalOperator	Base class for “known” operators on a LocalSpace.
LocalSigma	Level flip operator between two levels of a LocalSpace.
LocalSpace	Hilbert space for a single degree of freedom.
Matrix	Matrix of Expressions.
NullSpaceProjector	Projection operator onto the nullspace of its operand.
Operation	Base class for “operations”
Operator	Base class for all quantum operators.
OperatorDerivative	Symbolic partial derivative of an operator
OperatorIndexedSum	Indexed sum over operators
OperatorPlus	Sum of Operators
OperatorPlusMinusCC	An operator plus or minus its complex conjugate.
OperatorSymbol	Symbolic operator
OperatorTimes	Product of operators
OperatorTimesKet	Product of an operator and a state.
OperatorTrace	(Partial) trace of an operator
ProductSpace	Tensor product of local Hilbert spaces.
PseudoInverse	Unevaluated pseudo-inverse \(\Op{X}^+\) of an operator \(\Op{X}\).
QuantumAdjoint	Base class for adjoints of quantum expressions
QuantumDerivative	Symbolic partial derivative.
QuantumExpression	Base class for expressions associated with a Hilbert space
QuantumIndexedSum	Base class for indexed sums of quantum expressions.
QuantumOperation	Base class for operations on quantum expression
QuantumPlus	General implementation of addition of quantum expressions
QuantumSymbol	Symbolic element of an algebra.
QuantumTimes	General implementation of product of quantum expressions
SPost	Linear post-multiplication operator.
SPre	Linear pre-multiplication operator
Scalar	Base class for Scalars
ScalarDerivative	Symbolic partial derivative of a scalar
ScalarExpression	Base class for scalars with non-scalar arguments
ScalarIndexedSum	Indexed sum over scalars.
ScalarPlus	Sum of scalars
ScalarPower	A scalar raised to a power.
ScalarTimes	Product of scalars
ScalarTimesKet	Product of a Scalar coefficient and a ket
ScalarTimesOperator	Product of a Scalar coefficient and an Operator.
ScalarTimesQuantumExpression	Product of a Scalar and a QuantumExpression
ScalarTimesSuperOperator	Product of a Scalar coefficient and a SuperOperator.
ScalarValue	Wrapper around a numeric or symbolic value
SingleQuantumOperation	Base class for operations on a single quantum expression
State	Base class for states in a Hilbert space
StateDerivative	Symbolic partial derivative of a state
SuperAdjoint	Adjoint of a super-operator.
SuperOperator	Base class for super-operators
SuperOperatorDerivative	Symbolic partial derivative of a super-operator
SuperOperatorPlus	A sum of super-operators
SuperOperatorSymbol	Symbolic super-operator
SuperOperatorTimes	Product of super-operators
SuperOperatorTimesOperator	Application of a super-operator to an operator.
TensorKet	A tensor product of kets.

__all__ Functions:

KroneckerDelta	Kronecker delta symbol.
LocalProjector	A projector onto a specific level of a LocalSpace
Sum	Instantiator for an arbitrary indexed sum.
adjoint	Return the adjoint of an obj.
anti_commutator	If B != None, return the anti-commutator \(\{A,B\}\), otherwise return the super-operator \(\{A,\cdot\}\).
block_matrix	Generate the operator matrix with quadrants
commutator	Commutator of A and B
decompose_space	Simplifies OperatorTrace expressions over tensor-product spaces by turning it into iterated partial traces.
diagm	Generalizes the diagonal matrix creation capabilities of numpy.diag to Matrix objects.
factor_coeff	Factor out coefficients of all factors.
factor_for_trace	Factor ls out of op for easy tracing.
get_coeffs	Create a dictionary with all Operator terms of the expression (understood as a sum) as keys and their coefficients as values.
hstackm	Generalizes numpy.hstack to Matrix objects.
identity_matrix	Generate the N-dimensional identity matrix.
lindblad	Return the super-operator Lindblad term of the Lindblad operator C
liouvillian	Return the Liouvillian super-operator associated with H and Ls
rewrite_with_operator_pm_cc	Try to rewrite expr using OperatorPlusMinusCC.
sqrt	Square root of a Scalar or scalar value.
substitute	Substitute symbols or (sub-)expressions with the given replacements.
tr	Instantiate while applying automatic simplifications.
vstackm	Generalizes numpy.vstack to Matrix objects.
zerosm	Generalizes numpy.zeros to Matrix objects.

__all__ Data:

FullSpace	The ‘full space’, i.e.
II	IdentityOperator constant (singleton) object.
IdentityOperator	IdentityOperator constant (singleton) object.
IdentitySuperOperator	Neutral element for product of super-operators
One	The neutral element with respect to scalar multiplication
TrivialKet	TrivialKet constant (singleton) object.
TrivialSpace	The ‘nullspace’, i.e.
Zero	The neutral element with respect to scalar addition
ZeroKet	ZeroKet constant (singleton) object for the null-state.
ZeroOperator	ZeroOperator constant (singleton) object.
ZeroSuperOperator	Neutral element for sum of super-operators