Operator

class Operator(data, input_dims=None, output_dims=None)

Bases: qiskit.quantum_info.operators.linear_op.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

**(**QuantumCircuit or (data) – Instruction or BaseOperator or matrix): data to initialize operator.
input_dims (tuple) – the input subsystem dimensions. [Default: None]
output_dims (tuple) – the output subsystem dimensions. [Default: None]

Raises

QiskitError – if input data cannot be initialized as an operator.

Additional Information:

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.

Methods

adjoint

Operator.adjoint()

Return the adjoint of the Operator.

compose

Operator.compose(other, qargs=None, front=False)

Return the operator composition with another Operator.

Parameters

other (Operator) – a Operator object.
qargs (list or None) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
front (bool) – If True compose using right operator multiplication, instead of left multiplication [default: False].

Returns

The composed Operator.

Return type

Operator

Raises

QiskitError – 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 dot() is defined as right matrix multiplication. That is that A & B == A.compose(B) is equivalent to 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

Operator.conjugate()

Return the conjugate of the Operator.

copy

Operator.copy()

Make a deep copy of current operator.

dot

Operator.dot(other, qargs=None)

Return the right multiplied operator self * other.

Parameters

other (Operator) – an operator object.
qargs (list or None) – 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

equiv

Operator.equiv(other, rtol=None, atol=None)

Return True if operators are equivalent up to global phase.

Parameters

other (Operator) – an operator object.
rtol (float) – relative tolerance value for comparison.
atol (float) – absolute tolerance value for comparison.

Returns

True if operators are equivalent up to global phase.

Return type

bool

expand

Operator.expand(other)

Return the reverse-order tensor product with another Operator.

Parameters

other (Operator) – 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

from_label

classmethod Operator.from_label(label)

Return a tensor product of single-qubit operators.

Parameters

label (string) – single-qubit operator string.

Returns

The N-qubit operator.

Return type

Operator

Raises

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

Additional Information:

The labels correspond to the single-qubit matrices: ‘I’: [[1, 0], [0, 1]] ‘X’: [[0, 1], [1, 0]] ‘Y’: [[0, -1j], [1j, 0]] ‘Z’: [[1, 0], [0, -1]] ‘H’: [[1, 1], [1, -1]] / sqrt(2) ‘S’: [[1, 0], [0 , 1j]] ‘T’: [[1, 0], [0, (1+1j) / sqrt(2)]] ‘0’: [[1, 0], [0, 0]] ‘1’: [[0, 0], [0, 1]] ‘+’: [[0.5, 0.5], [0.5 , 0.5]] ‘-‘: [[0.5, -0.5], [-0.5 , 0.5]] ‘r’: [[0.5, -0.5j], [0.5j , 0.5]] ‘l’: [[0.5, 0.5j], [-0.5j , 0.5]]

input_dims

Operator.input_dims(qargs=None)

Return tuple of input dimension for specified subsystems.

is_unitary

Operator.is_unitary(atol=None, rtol=None)

Return True if operator is a unitary matrix.

output_dims

Operator.output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

power

Operator.power(n)

Return the matrix power of the operator.

Parameters

n (float) – the power to raise the matrix to.

Returns

the resulting operator O ** n.

Return type

Operator

Raises

QiskitError – if the input and output dimensions of the operator are not equal.

reshape

Operator.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) – new subsystem input dimensions. If None the original input dims will be preserved [Default: None].
output_dims (None or tuple) – new subsystem output dimensions. If None the original output dims will be preserved [Default: None].
num_qubits (None or int) – reshape to an N-qubit operator [Default: None].

Returns

returns self with reshaped input and output dimensions.

Return type

BaseOperator

Raises

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

reverse_qargs

Operator.reverse_qargs()

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

Operator.tensor(other)

Return the tensor product with another Operator.

Parameters

other (Operator) – 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

Operator.to_instruction()

Convert to a UnitaryGate instruction.

to_operator

Operator.to_operator()

Convert operator to matrix operator class

transpose

Operator.transpose()

Return the transpose of the Operator.

Attributes

atol

Default value: 1e-08

data

Return data.

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

Default value: 1e-05

settings

Return operator settings.

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