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.
add(other)	Return the linear operator self + other.
adjoint()	Return the adjoint of the operator.
compose(other[, qargs, front])	Return the composed 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 tensor product operator other ⊗ self.
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.
multiply(other)	Return the linear operator other * self.
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])	Return a shallow copy with reshaped input and output subsystem dimensions.
set_atol(value)	Set the class default absolute tolerance parameter for float comparisons.
set_rtol(value)	Set the class default relative tolerance parameter for float comparisons.
subtract(other)	Return the linear operator self - other.
tensor(other)	Return the tensor product operator self ⊗ other.
to_instruction()	Convert to a UnitaryGate instruction.
to_operator()	Convert operator to matrix operator class
transpose()	Return the transpose of the operator.

Attributes

atol	The 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	The relative tolerance parameter for float comparisons.

add(other)

Return the linear operator self + other.

DEPRECATED: use operator + other instead.

Parameters

other (BaseOperator) – an operator object.

Returns

the operator self + other.

Return type

BaseOperator

adjoint()

Return the adjoint of the operator.

property atol

The default absolute tolerance parameter for float comparisons.

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

Return the composed operator.

Parameters

• other (Operator) – an operator object.

• qargs (list or None) – 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 operator self @ other.

Return type

Operator

Raises

QiskitError – if operators have incompatible dimensions for composition.

Additional Information:

Composition (@) is defined as left matrix multiplication for matrix operators. That is that A @ B is equal to B * A. Setting front=True returns right matrix multiplication A * B and is equivalent to the dot() method.

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) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].

Returns

The operator self * other.

Return type

Operator

Raises

QiskitError – if other cannot be converted to an Operator or has incompatible dimensions.

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 tensor product operator other ⊗ self.

Parameters

other (Operator) – an operator object.

Returns

the tensor product operator other ⊗ self.

Return type

Operator

Raises

QiskitError – if other cannot be converted to an 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.

multiply(other)

Return the linear operator other * self.

DEPRECATED: use other * operator instead.

Parameters

other (complex) – a complex number.

Returns

the linear operator other * self.

Return type

BaseOperator

Raises

NotImplementedError – if subclass does not support multiplication.

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 (int) – the power to raise the matrix to.

Returns

the n-times composed operator.

Return type

BaseOperator

Raises

QiskitError – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.

property qargs

Return the qargs for the operator.

reshape(input_dims=None, output_dims=None)

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

Arg:

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].

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.

property rtol

The relative tolerance parameter for float comparisons.

classmethod set_atol(value)

Set the class default absolute tolerance parameter for float comparisons.

DEPRECATED: use operator.atol = value instead

classmethod set_rtol(value)

Set the class default relative tolerance parameter for float comparisons.

DEPRECATED: use operator.rtol = value instead

subtract(other)

Return the linear operator self - other.

DEPRECATED: use operator - other instead.

Parameters

other (BaseOperator) – an operator object.

Returns

the operator self - other.

Return type

BaseOperator

tensor(other)

Return the tensor product operator self ⊗ other.

Parameters

other (Operator) – a operator subclass object.

Returns

the tensor product operator self ⊗ other.

Return type

Operator

Raises

QiskitError – if other cannot be converted to an operator.

to_instruction()

Convert to a UnitaryGate instruction.

to_operator()

Convert operator to matrix operator class

transpose()

Return the transpose of the operator.