qiskit.quantum_info.Operator

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

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.

__init__(data, input_dims=None, output_dims=None)

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

__init__(data[, input_dims, output_dims])	Initialize an operator object.
adjoint()	Return the adjoint of the Operator.
compose(other[, qargs, front])	Return the operator composition with another Operator.
conjugate()	Return the conjugate of the Operator.
copy()	Make a deep copy of current operator.
dot(other[, qargs])	Return the right multiplied operator self * other.
equiv(other[, rtol, atol])	Return True if operators are equivalent up to global phase.
expand(other)	Return the reverse-order tensor product with another Operator.
from_label(label)	Return a tensor product of single-qubit operators.
input_dims([qargs])	Return tuple of input dimension for specified subsystems.
is_unitary([atol, rtol])	Return True if operator is a unitary matrix.
output_dims([qargs])	Return tuple of output dimension for specified subsystems.
power(n)	Return the matrix power of the operator.
reshape([input_dims, output_dims, num_qubits])	Return a shallow copy with reshaped input and output subsystem dimensions.
reverse_qargs()	Return an Operator with reversed subsystem ordering.
tensor(other)	Return the tensor product with another Operator.
to_instruction()	Convert to a UnitaryGate instruction.
to_operator()	Convert operator to matrix operator class
transpose()	Return the transpose of the Operator.

Attributes

atol	Default absolute tolerance parameter for float comparisons.
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 relative tolerance parameter for float comparisons.
settings	Return operator settings.

adjoint()

Return the adjoint of the Operator.

property atol

Default absolute tolerance parameter for float comparisons.

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()

Return the conjugate of the Operator.

copy()

Make a deep copy of current operator.

property data

Return data.

property dim

Return tuple (input_shape, output_shape).

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(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(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

classmethod 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(qargs=None)

Return tuple of input dimension for specified subsystems.

is_unitary(atol=None, rtol=None)

Return True if operator is a unitary matrix.

property num_qubits

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

output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

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.

property qargs

Return the qargs for the 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()

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

property rtol

Default relative tolerance parameter for float comparisons.

property settings

Return operator settings.

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()

Convert to a UnitaryGate instruction.

to_operator()

Convert operator to matrix operator class

transpose()

Return the transpose of the Operator.