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A LinearOperator implied from a QubitOperator.
openfermion.linalg.LinearQubitOperator(
qubit_operator, n_qubits=None
)
The idea is that a single i_th qubit operator, O_i, is a 2-by-2 matrix, to
be applied on a vector of length n_hilbert / 2^i, performs permutations and/
or adds an extra factor for its first half and the second half, e.g. a Z
operator keeps the first half unchanged, while adds a factor of -1 to the
second half, while an I keeps it both components unchanged.
Note that the vector length is n_hilbert / 2^i, therefore when one works on i monotonically (in increasing order), one keeps splitting the vector to the right size and then apply O_i on them independently.
Also note that operator O_i, is an envelop operator for all operators after it, i.e. {O_j | j > i}, which implies that starting with i = 0, one can split the vector, apply O_i, split the resulting vector (cached) again for the next operator.
Methods
adjoint
adjoint()
Hermitian adjoint.
Returns the Hermitian adjoint of self, aka the Hermitian conjugate or Hermitian transpose. For a complex matrix, the Hermitian adjoint is equal to the conjugate transpose.
Can be abbreviated self.H instead of self.adjoint().
Returns
A_H : LinearOperator Hermitian adjoint of self.
dot
dot(
x
)
Matrix-matrix or matrix-vector multiplication.
Parameters
x : array_like 1-d or 2-d array, representing a vector or matrix.
Returns
Ax : array 1-d or 2-d array (depending on the shape of x) that represents the result of applying this linear operator on x.
matmat
matmat(
X
)
Matrix-matrix multiplication.
Performs the operation y=AX where A is an MxN linear operator and X dense NK matrix or ndarray.
Parameters
X : {matrix, ndarray} An array with shape (N,K).
Returns
Y : {matrix, ndarray} A matrix or ndarray with shape (M,K) depending on the type of the X argument.
Notes
This matmat wraps any user-specified matmat routine or overridden _matmat method to ensure that y has the correct type.
matvec
matvec(
x
)
Matrix-vector multiplication.
Performs the operation y=A*x where A is an MxN linear operator and x is a column vector or 1-d array.
Parameters
x : {matrix, ndarray} An array with shape (N,) or (N,1).
Returns
y : {matrix, ndarray} A matrix or ndarray with shape (M,) or (M,1) depending on the type and shape of the x argument.
Notes
This matvec wraps the user-specified matvec routine or overridden _matvec method to ensure that y has the correct shape and type.
rmatmat
rmatmat(
X
)
Adjoint matrix-matrix multiplication.
Performs the operation y = A^H * x where A is an MxN linear operator and x is a column vector or 1-d array, or 2-d array. The default implementation defers to the adjoint.
Parameters
X : {matrix, ndarray} A matrix or 2D array.
Returns
Y : {matrix, ndarray} A matrix or 2D array depending on the type of the input.
Notes
This rmatmat wraps the user-specified rmatmat routine.
rmatvec
rmatvec(
x
)
Adjoint matrix-vector multiplication.
Performs the operation y = A^H * x where A is an MxN linear operator and x is a column vector or 1-d array.
Parameters
x : {matrix, ndarray} An array with shape (M,) or (M,1).
Returns
y : {matrix, ndarray} A matrix or ndarray with shape (N,) or (N,1) depending on the type and shape of the x argument.
Notes
This rmatvec wraps the user-specified rmatvec routine or overridden _rmatvec method to ensure that y has the correct shape and type.
transpose
transpose()
Transpose this linear operator.
Returns a LinearOperator that represents the transpose of this one. Can be abbreviated self.T instead of self.transpose().
__add__
__add__(
x
)
__call__
__call__(
x
)
Call self as a function.
__matmul__
__matmul__(
other
)
__mul__
__mul__(
x
)
__neg__
__neg__()
__pow__
__pow__(
p
)
__rmatmul__
__rmatmul__(
other
)
__rmul__
__rmul__(
x
)
__sub__
__sub__(
x
)
__truediv__
__truediv__(
other
)
Class Variables | |
|---|---|
| ndim |
2
|