# Operator#

class qiskit.quantum_info.Operator(data, input_dims=None, output_dims=None)[source]#

Bases: LinearOp

Matrix operator class

This represents a matrix operator $$M$$ that will evolve() a Statevector $$|\psi\rangle$$ by matrix-vector multiplication

$|\psi\rangle \mapsto M|\psi\rangle,$

and will evolve() a DensityMatrix $$\rho$$ by left and right multiplication

$\rho \mapsto M \rho M^\dagger.$

Initialize an operator object.

Parameters:
• data (QuantumCircuit or Operation or BaseOperator or matrix) β data to initialize operator.

• input_dims (tuple) β the input subsystem dimensions. [Default: None]

• output_dims (tuple) β the output subsystem dimensions. [Default: None]

Raises:

QiskitError β if input data cannot be initialized as an operator.

If the input or output dimensions are None, they will be automatically determined from the input data. If the input data is a Numpy array of shape (2**N, 2**N) qubit systems will be used. If the input operator is not an N-qubit operator, it will assign a single subsystem with dimension specified by the shape of the input.

Attributes

atol = 1e-08#
data#

The underlying Numpy array.

dim#

Return tuple (input_shape, output_shape).

num_qubits#

Return the number of qubits if a N-qubit operator or None otherwise.

qargs#

Return the qargs for the operator.

rtol = 1e-05#
settings#

Return operator settings.

Methods

Return the adjoint of the Operator.

Return type:

Self

apply_permutation(perm, front=False)[source]#

Modifies operatorβs data by composing it with a permutation.

Parameters:
• perm (list) β permutation pattern, describing which qubits occupy the positions 0, 1, 2, etc. after applying the permutation.

• front (bool) β When set to True the permutation is applied before the operator, when set to False the permutation is applied after the operator.

Returns:

The modified operator.

Return type:

Operator

Raises:

QiskitError β if the size of the permutation pattern does not match the dimensions of the operator.

compose(other, qargs=None, front=False)[source]#

Return the operator composition with another Operator.

Parameters:
• other (Operator) β a Operator object.

• qargs (list or None) β Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

• front (bool) β If True compose using right operator multiplication, instead of left multiplication [default: False].

Returns:

The composed Operator.

Return type:

Operator

Raises:

QiskitError β if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.

Note

Composition (&) by default is defined as left matrix multiplication for matrix operators, while @ (equivalent to dot()) is defined as right matrix multiplication. That is that A & B == A.compose(B) is equivalent to B @ A == B.dot(A) when A and B are of the same type.

Setting the front=True kwarg changes this to right matrix multiplication and is equivalent to the dot() method A.dot(B) == A.compose(B, front=True).

conjugate()[source]#

Return the conjugate of the Operator.

copy()#

Make a deep copy of current operator.

dot(other, qargs=None)#

Return the right multiplied operator self * other.

Parameters:
• other (Operator) β an operator object.

• qargs (list or None) β Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

Returns:

The right matrix multiplied Operator.

Return type:

Operator

Note

The dot product can be obtained using the @ binary operator. Hence a.dot(b) is equivalent to a @ b.

equiv(other, rtol=None, atol=None)[source]#

Return True if operators are equivalent up to global phase.

Parameters:
• other (Operator) β an operator object.

• rtol (float) β relative tolerance value for comparison.

• atol (float) β absolute tolerance value for comparison.

Returns:

True if operators are equivalent up to global phase.

Return type:

bool

expand(other)[source]#

Return the reverse-order tensor product with another Operator.

Parameters:

other (Operator) β a Operator object.

Returns:

the tensor product $$b \otimes a$$, where $$a$$

is the current Operator, and $$b$$ is the other Operator.

Return type:

Operator

classmethod from_circuit(circuit, ignore_set_layout=False, layout=None, final_layout=None)[source]#

Create a new Operator object from a QuantumCircuit

While a QuantumCircuit object can passed directly as data to the class constructor this provides no options on how the circuit is used to create an Operator. This constructor method lets you control how the Operator is created so it can be adjusted for a particular use case.

By default this constructor method will permute the qubits based on a configured initial layout (i.e. after it was transpiled). It also provides an option to manually provide a Layout object directly.

Parameters:
• circuit (QuantumCircuit) β The QuantumCircuit to create an Operator object from.

• ignore_set_layout (bool) β When set to True if the input circuit has a layout set it will be ignored

• layout (Layout) β If specified this kwarg can be used to specify a particular layout to use to permute the qubits in the created Operator. If this is specified it will be used instead of a layout contained in the circuit input. If specified the virtual bits in the Layout must be present in the circuit input.

• final_layout (Layout) β If specified this kwarg can be used to represent the output permutation caused by swap insertions during the routing stage of the transpiler.

Returns:

An operator representing the input circuit

Return type:

Operator

classmethod from_label(label)[source]#

Return a tensor product of single-qubit operators.

Parameters:

label (string) β single-qubit operator string.

Returns:

The N-qubit operator.

Return type:

Operator

Raises:

QiskitError β if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits.

The labels correspond to the single-qubit matrices: βIβ: [[1, 0], [0, 1]] βXβ: [[0, 1], [1, 0]] βYβ: [[0, -1j], [1j, 0]] βZβ: [[1, 0], [0, -1]] βHβ: [[1, 1], [1, -1]] / sqrt(2) βSβ: [[1, 0], [0 , 1j]] βTβ: [[1, 0], [0, (1+1j) / sqrt(2)]] β0β: [[1, 0], [0, 0]] β1β: [[0, 0], [0, 1]] β+β: [[0.5, 0.5], [0.5 , 0.5]] β-β: [[0.5, -0.5], [-0.5 , 0.5]] βrβ: [[0.5, -0.5j], [0.5j , 0.5]] βlβ: [[0.5, 0.5j], [-0.5j , 0.5]]

input_dims(qargs=None)#

Return tuple of input dimension for specified subsystems.

is_unitary(atol=None, rtol=None)[source]#

Return True if operator is a unitary matrix.

output_dims(qargs=None)#

Return tuple of output dimension for specified subsystems.

power(n)[source]#

Return the matrix power of the operator.

Parameters:

n (float) β the power to raise the matrix to.

Returns:

the resulting operator O ** n.

Return type:

Operator

Raises:

QiskitError β if the input and output dimensions of the operator are not equal.

reshape(input_dims=None, output_dims=None, num_qubits=None)#

Return a shallow copy with reshaped input and output subsystem dimensions.

Parameters:
• input_dims (None or tuple) β new subsystem input dimensions. If None the original input dims will be preserved [Default: None].

• output_dims (None or tuple) β new subsystem output dimensions. If None the original output dims will be preserved [Default: None].

• num_qubits (None or int) β reshape to an N-qubit operator [Default: None].

Returns:

returns self with reshaped input and output dimensions.

Return type:

BaseOperator

Raises:

QiskitError β if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

reverse_qargs()[source]#

Return an Operator with reversed subsystem ordering.

For a tensor product operator this is equivalent to reversing the order of tensor product subsystems. For an operator $$A = A_{n-1} \otimes ... \otimes A_0$$ the returned operator will be $$A_0 \otimes ... \otimes A_{n-1}$$.

Returns:

the operator with reversed subsystem order.

Return type:

Operator

tensor(other)[source]#

Return the tensor product with another Operator.

Parameters:

other (Operator) β a Operator object.

Returns:

the tensor product $$a \otimes b$$, where $$a$$

is the current Operator, and $$b$$ is the other Operator.

Return type:

Operator

Note

The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.

to_instruction()[source]#

Convert to a UnitaryGate instruction.

to_matrix()[source]#

Convert operator to NumPy matrix.

to_operator()[source]#

Convert operator to matrix operator class

Return type:

Operator

transpose()[source]#

Return the transpose of the Operator.