qml.operation.Tensor¶

class
Tensor
(*args)[source]¶ Bases:
pennylane.operation.Observable
Container class representing tensor products of observables.
To create a tensor, simply initiate it like so:
>>> T = Tensor(qml.PauliX(0), qml.Hermitian(A, [1, 2]))
You can also create a tensor from other Tensors:
>>> T = Tensor(T, qml.PauliZ(4))
The
@
symbol can be used as a tensor product operation:>>> T = qml.PauliX(0) @ qml.Hadamard(2)
Attributes
Arithmetic depth of the operator.
Batch size of the operator if it is used with broadcasted parameters.
Raw parameters of all constituent observables in the tensor product.
Integer hash that uniquely represents the operator.
Dictionary of nontrainable variables that this operation depends on.
Custom string to label a specific operator instance.
All observables must be hermitian
All constituent observable names making up the tensor product.
Number of dimensions per trainable parameter of the operator.
Returns the nonidentity observables contained in the tensor product.
Raw parameters of all constituent observables in the tensor product.
Number of wires the tensor product acts on.
Evaluated parameter values of all constituent observables in the tensor product.
Measurement type that this observable is called with.
All wires in the system the tensor product acts on.

arithmetic_depth
¶

batch_size
¶ Batch size of the operator if it is used with broadcasted parameters.
The
batch_size
is determined based onndim_params
and the provided parameters for the operator. If (some of) the latter have an additional dimension, and this dimension has the same size for all parameters, its size is the batch size of the operator. If no parameter has an additional dimension, the batch size isNone
. Returns
Size of the parameter broadcasting dimension if present, else
None
. Return type
int or None

data
¶ parameters of the operator
 Type
list[Any]

has_matrix
= False¶

hash
¶ Integer hash that uniquely represents the operator.
 Type
int

hyperparameters
¶ Dictionary of nontrainable variables that this operation depends on.
 Type
dict

id
¶ Custom string to label a specific operator instance.

is_hermitian
¶ All observables must be hermitian

name
¶ All constituent observable names making up the tensor product.
 Returns
list containing all observable names
 Return type
list[str]

ndim_params
¶ Number of dimensions per trainable parameter of the operator.
By default, this property returns the numbers of dimensions of the parameters used for the operator creation. If the parameter sizes for an operator subclass are fixed, this property can be overwritten to return the fixed value.
 Returns
Number of dimensions for each trainable parameter.
 Return type
tuple

non_identity_obs
¶ Returns the nonidentity observables contained in the tensor product.
 Returns
list containing the nonidentity observables in the tensor product
 Return type
list[
Observable
]

num_params
¶ Raw parameters of all constituent observables in the tensor product.
 Returns
flattened list containing all dependent parameters
 Return type
list[Any]

num_wires
¶ Number of wires the tensor product acts on.
 Returns
number of wires
 Return type
int

parameters
¶ Evaluated parameter values of all constituent observables in the tensor product.
 Returns
nested list containing the parameters per observable in the tensor product
 Return type
list[list[Any]]

return_type
= None¶ Measurement type that this observable is called with.
 Type
None or ObservableReturnTypes

tensor
= True¶
Methods
adjoint
()Create an operation that is the adjoint of this one.
Tests whether any two observables in the Tensor have partially overlapping wires and raise a warning if they do.
compare
(other)Compares with another
Hamiltonian
,Tensor
, orObservable
, to determine if they are equivalent.compute_decomposition
(*params[, wires])Representation of the operator as a product of other operators (static method).
compute_diagonalizing_gates
(*params, wires, …)Sequence of gates that diagonalize the operator in the computational basis (static method).
compute_eigvals
(*params, **hyperparams)Eigenvalues of the operator in the computational basis (static method).
compute_matrix
(*params, **hyperparams)Representation of the operator as a canonical matrix in the computational basis (static method).
compute_sparse_matrix
(*params, **hyperparams)Representation of the operator as a sparse matrix in the computational basis (static method).
compute_terms
(*params, **hyperparams)Representation of the operator as a linear combination of other operators (static method).
Representation of the operator as a product of other operators.
Return the gate set that diagonalizes a circuit according to the specified tensor observable.
eigvals
()Return the eigenvalues of the specified tensor product observable.
expand
()Returns a tape that has recorded the decomposition of the operator.
Generator of an operator that is in singleparameterform.
label
([decimals, base_label, cache])How the operator is represented in diagrams and drawings.
matrix
([wire_order])Matrix representation of the Tensor operator in the computational basis.
pow
(z)A list of new operators equal to this one raised to the given power.
prune
()Returns a pruned tensor product of observables by removing
Identity
instances from the observables building up theTensor
.queue
([context, init])Append the operator to the Operator queue.
simplify
()Reduce the depth of nested operators to the minimum.
sparse_matrix
([wires, format])Computes, by default, a scipy.sparse.csr_matrix representation of this Tensor.
terms
()Representation of the operator as a linear combination of other operators.

adjoint
() → pennylane.operation.Operator¶ Create an operation that is the adjoint of this one.
Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates.
 Returns
The adjointed operation.

check_wires_partial_overlap
()[source]¶ Tests whether any two observables in the Tensor have partially overlapping wires and raise a warning if they do.
Note
Fully overlapping wires, i.e., observables with same (sets of) wires are not reported, as the
matrix
method is welldefined and implemented for this scenario.

compare
(other)¶ Compares with another
Hamiltonian
,Tensor
, orObservable
, to determine if they are equivalent.Observables/Hamiltonians are equivalent if they represent the same operator (their matrix representations are equal), and they are defined on the same wires.
Warning
The compare method does not check if the matrix representation of a
Hermitian
observable is equal to an equivalent observable expressed in terms of Pauli matrices. To do so would require the matrix form of Hamiltonians and Tensors be calculated, which would drastically increase runtime. Returns
True if equivalent.
 Return type
(bool)
Examples
>>> ob1 = qml.PauliX(0) @ qml.Identity(1) >>> ob2 = qml.Hamiltonian([1], [qml.PauliX(0)]) >>> ob1.compare(ob2) True >>> ob1 = qml.PauliX(0) >>> ob2 = qml.Hermitian(np.array([[0, 1], [1, 0]]), 0) >>> ob1.compare(ob2) False

static
compute_decomposition
(*params, wires=None, **hyperparameters)¶ Representation of the operator as a product of other operators (static method).
\[O = O_1 O_2 \dots O_n.\]Note
Operations making up the decomposition should be queued within the
compute_decomposition
method.See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributewires (Iterable[Any], Wires) – wires that the operator acts on
hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
decomposition of the operator
 Return type
list[Operator]

static
compute_diagonalizing_gates
(*params, wires, **hyperparams)¶ Sequence of gates that diagonalize the operator in the computational basis (static method).
Given the eigendecomposition \(O = U \Sigma U^{\dagger}\) where \(\Sigma\) is a diagonal matrix containing the eigenvalues, the sequence of diagonalizing gates implements the unitary \(U^{\dagger}\).
The diagonalizing gates rotate the state into the eigenbasis of the operator.
See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributewires (Iterable[Any], Wires) – wires that the operator acts on
hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
list of diagonalizing gates
 Return type
list[Operator]

static
compute_eigvals
(*params, **hyperparams)¶ Eigenvalues of the operator in the computational basis (static method).
If
diagonalizing_gates
are specified and implement a unitary \(U\), the operator can be reconstructed as\[O = U \Sigma U^{\dagger},\]where \(\Sigma\) is the diagonal matrix containing the eigenvalues.
Otherwise, no particular order for the eigenvalues is guaranteed.
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
eigenvalues
 Return type
tensor_like

static
compute_matrix
(*params, **hyperparams)¶ Representation of the operator as a canonical matrix in the computational basis (static method).
The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order.
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
matrix representation
 Return type
tensor_like

static
compute_sparse_matrix
(*params, **hyperparams)¶ Representation of the operator as a sparse matrix in the computational basis (static method).
The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order.
See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

static
compute_terms
(*params, **hyperparams)¶ Representation of the operator as a linear combination of other operators (static method).
\[O = \sum_i c_i O_i\]See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
list of coefficients and list of operations
 Return type
tuple[list[tensor_like or float], list[Operation]]

decomposition
()¶ Representation of the operator as a product of other operators.
\[O = O_1 O_2 \dots O_n\]A
DecompositionUndefinedError
is raised if no representation by decomposition is defined.See also
 Returns
decomposition of the operator
 Return type
list[Operator]

diagonalizing_gates
()[source]¶ Return the gate set that diagonalizes a circuit according to the specified tensor observable.
This method uses prestored eigenvalues for standard observables where possible and stores the corresponding eigenvectors from the eigendecomposition.
 Returns
list containing the gates diagonalizing the tensor observable
 Return type
list

eigvals
()[source]¶ Return the eigenvalues of the specified tensor product observable.
This method uses prestored eigenvalues for standard observables where possible.
 Returns
array containing the eigenvalues of the tensor product observable
 Return type
array[float]

expand
()¶ Returns a tape that has recorded the decomposition of the operator.
 Returns
quantum tape
 Return type

generator
()¶ Generator of an operator that is in singleparameterform.
For example, for operator
\[U(\phi) = e^{i\phi (0.5 Y + Z\otimes X)}\]we get the generator
>>> U.generator() (0.5) [Y0] + (1.0) [Z0 X1]
The generator may also be provided in the form of a dense or sparse Hamiltonian (using
Hermitian
andSparseHamiltonian
respectively).The default value to return is
None
, indicating that the operation has no defined generator.

label
(decimals=None, base_label=None, cache=None)[source]¶ How the operator is represented in diagrams and drawings.
 Parameters
decimals=None (Int) – If
None
, no parameters are included. Else, how to round the parameters.base_label=None (Iterable[str]) – overwrite the nonparameter component of the label. Must be same length as
obs
attribute.cache=None (dict) – dictionary that carries information between label calls in the same drawing
 Returns
label to use in drawings
 Return type
str
>>> T = qml.PauliX(0) @ qml.Hadamard(2) >>> T.label() '[email protected]' >>> T.label(base_label=["X0", "H2"]) '[email protected]'

matrix
(wire_order=None)[source]¶ Matrix representation of the Tensor operator in the computational basis.
Note
The wire_order argument is added for compatibility, but currently not implemented. The Tensor class is planned to be removed soon.
 Parameters
wire_order (Iterable) – global wire order, must contain all wire labels in the operator’s wires
 Returns
matrix representation
 Return type
array
Example
>>> O = qml.PauliZ(0) @ qml.PauliZ(2) >>> O.matrix() array([[ 1, 0, 0, 0], [ 0, 1, 0, 0], [ 0, 0, 1, 0], [ 0, 0, 0, 1]])
To get the full \(2^3\times 2^3\) Hermitian matrix acting on the 3qubit system, the identity on wire 1 must be explicitly included:
>>> O = qml.PauliZ(0) @ qml.Identity(1) @ qml.PauliZ(2) >>> O.matrix() array([[ 1., 0., 0., 0., 0., 0., 0., 0.], [ 0., 1., 0., 0., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0., 0., 0., 0.], [ 0., 0., 0., 1., 0., 0., 0., 0.], [ 0., 0., 0., 0., 1., 0., 0., 0.], [ 0., 0., 0., 0., 0., 1., 0., 0.], [ 0., 0., 0., 0., 0., 0., 1., 0.], [ 0., 0., 0., 0., 0., 0., 0., 1.]])

pow
(z) → List[pennylane.operation.Operator]¶ A list of new operators equal to this one raised to the given power.
 Parameters
z (float) – exponent for the operator
 Returns
list[
Operator
]

prune
()[source]¶ Returns a pruned tensor product of observables by removing
Identity
instances from the observables building up theTensor
.The
return_type
attribute is preserved while pruning.If the tensor product only contains one observable, then this observable instance is returned.
Note that, as a result, this method can return observables that are not a
Tensor
instance.Example:
Pruning that returns a
Tensor
:>>> O = qml.PauliZ(0) @ qml.Identity(1) @ qml.PauliZ(2) >>> O.prune() <pennylane.operation.Tensor at 0x7fc1642d1590 >>> [(o.name, o.wires) for o in O.prune().obs] [('PauliZ', [0]), ('PauliZ', [2])]
Pruning that returns a single observable:
>>> O = qml.PauliZ(0) @ qml.Identity(1) >>> O_pruned = O.prune() >>> (O_pruned.name, O_pruned.wires) ('PauliZ', [0])
 Returns
the pruned tensor product of observables
 Return type
Observable

queue
(context=<class 'pennylane.queuing.QueuingContext'>, init=False)[source]¶ Append the operator to the Operator queue.

simplify
() → pennylane.operation.Operator¶ Reduce the depth of nested operators to the minimum.
 Returns
simplified operator
 Return type

sparse_matrix
(wires=None, format='csr')[source]¶ Computes, by default, a scipy.sparse.csr_matrix representation of this Tensor.
This is useful for larger qubit numbers, where the dense matrix becomes very large, while consisting mostly of zero entries.
 Parameters
wires (Iterable) – Wire labels that indicate the order of wires according to which the matrix is constructed. If not provided,
self.wires
is used.format – the output format for the sparse representation. All scipy sparse formats are accepted.
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix
Example
Consider the following tensor:
>>> t = qml.PauliX(0) @ qml.PauliZ(1)
Without passing wires, the sparse representation is given by:
>>> print(t.sparse_matrix()) (0, 2) 1 (1, 3) 1 (2, 0) 1 (3, 1) 1
If we define a custom wire ordering, the matrix representation changes accordingly: >>> print(t.sparse_matrix(wires=[1, 0])) (0, 1) 1 (1, 0) 1 (2, 3) 1 (3, 2) 1
We can also enforce implicit identities by passing wire labels that are not present in the constituent operations:
>>> res = t.sparse_matrix(wires=[0, 1, 2]) >>> print(res.shape) (8, 8)

terms
()¶ Representation of the operator as a linear combination of other operators.
\[O = \sum_i c_i O_i\]A
TermsUndefinedError
is raised if no representation by terms is defined.See also
 Returns
list of coefficients \(c_i\) and list of operations \(O_i\)
 Return type
tuple[list[tensor_like or float], list[Operation]]
