342 lines
11 KiB
Plaintext
342 lines
11 KiB
Plaintext
---
|
||
title: Operator
|
||
description: API reference for qiskit.quantum_info.Operator
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.quantum_info.Operator
|
||
---
|
||
|
||
# Operator
|
||
|
||
<Class id="qiskit.quantum_info.Operator" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.18/qiskit/quantum_info/operators/operator.py" signature="Operator(data, input_dims=None, output_dims=None)" modifiers="class">
|
||
Bases: `qiskit.quantum_info.operators.linear_op.LinearOp`
|
||
|
||
Matrix operator class
|
||
|
||
This represents a matrix operator $M$ that will [`evolve()`](qiskit.quantum_info.Statevector#evolve "qiskit.quantum_info.Statevector.evolve") a [`Statevector`](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector") $|\psi\rangle$ by matrix-vector multiplication
|
||
|
||
$$
|
||
|\psi\rangle \mapsto M|\psi\rangle,
|
||
$$
|
||
|
||
and will [`evolve()`](qiskit.quantum_info.DensityMatrix#evolve "qiskit.quantum_info.DensityMatrix.evolve") a [`DensityMatrix`](qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.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
|
||
|
||
<Function id="qiskit.quantum_info.Operator.adjoint" signature="Operator.adjoint()">
|
||
Return the adjoint of the Operator.
|
||
</Function>
|
||
|
||
### compose
|
||
|
||
<Function id="qiskit.quantum_info.Operator.compose" signature="Operator.compose(other, qargs=None, front=False)">
|
||
Return the operator composition with another Operator.
|
||
|
||
**Parameters**
|
||
|
||
* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.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](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
|
||
|
||
<Admonition title="Note" type="note">
|
||
Composition (`&`) by default is defined as left matrix multiplication for matrix operators, while [`dot()`](qiskit.quantum_info.Operator#dot "qiskit.quantum_info.Operator.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()`](qiskit.quantum_info.Operator#dot "qiskit.quantum_info.Operator.dot") method `A.dot(B) == A.compose(B, front=True)`.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### conjugate
|
||
|
||
<Function id="qiskit.quantum_info.Operator.conjugate" signature="Operator.conjugate()">
|
||
Return the conjugate of the Operator.
|
||
</Function>
|
||
|
||
### copy
|
||
|
||
<Function id="qiskit.quantum_info.Operator.copy" signature="Operator.copy()">
|
||
Make a deep copy of current operator.
|
||
</Function>
|
||
|
||
### dot
|
||
|
||
<Function id="qiskit.quantum_info.Operator.dot" signature="Operator.dot(other, qargs=None)">
|
||
Return the right multiplied operator self \* other.
|
||
|
||
**Parameters**
|
||
|
||
* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.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](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
</Function>
|
||
|
||
### equiv
|
||
|
||
<Function id="qiskit.quantum_info.Operator.equiv" signature="Operator.equiv(other, rtol=None, atol=None)">
|
||
Return True if operators are equivalent up to global phase.
|
||
|
||
**Parameters**
|
||
|
||
* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.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
|
||
</Function>
|
||
|
||
### expand
|
||
|
||
<Function id="qiskit.quantum_info.Operator.expand" signature="Operator.expand(other)">
|
||
Return the reverse-order tensor product with another Operator.
|
||
|
||
**Parameters**
|
||
|
||
**other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.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](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
</Function>
|
||
|
||
### from\_label
|
||
|
||
<Function id="qiskit.quantum_info.Operator.from_label" signature="Operator.from_label(label)" modifiers="classmethod">
|
||
Return a tensor product of single-qubit operators.
|
||
|
||
**Parameters**
|
||
|
||
**label** (*string*) – single-qubit operator string.
|
||
|
||
**Returns**
|
||
|
||
The N-qubit operator.
|
||
|
||
**Return type**
|
||
|
||
[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.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]]
|
||
</Function>
|
||
|
||
### input\_dims
|
||
|
||
<Function id="qiskit.quantum_info.Operator.input_dims" signature="Operator.input_dims(qargs=None)">
|
||
Return tuple of input dimension for specified subsystems.
|
||
</Function>
|
||
|
||
### is\_unitary
|
||
|
||
<Function id="qiskit.quantum_info.Operator.is_unitary" signature="Operator.is_unitary(atol=None, rtol=None)">
|
||
Return True if operator is a unitary matrix.
|
||
</Function>
|
||
|
||
### output\_dims
|
||
|
||
<Function id="qiskit.quantum_info.Operator.output_dims" signature="Operator.output_dims(qargs=None)">
|
||
Return tuple of output dimension for specified subsystems.
|
||
</Function>
|
||
|
||
### power
|
||
|
||
<Function id="qiskit.quantum_info.Operator.power" signature="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](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if the input and output dimensions of the operator are not equal.
|
||
</Function>
|
||
|
||
### reshape
|
||
|
||
<Function id="qiskit.quantum_info.Operator.reshape" signature="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.
|
||
</Function>
|
||
|
||
### reverse\_qargs
|
||
|
||
<Function id="qiskit.quantum_info.Operator.reverse_qargs" signature="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](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
</Function>
|
||
|
||
### tensor
|
||
|
||
<Function id="qiskit.quantum_info.Operator.tensor" signature="Operator.tensor(other)">
|
||
Return the tensor product with another Operator.
|
||
|
||
**Parameters**
|
||
|
||
**other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.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](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
|
||
<Admonition title="Note" type="note">
|
||
The tensor product can be obtained using the `^` binary operator. Hence `a.tensor(b)` is equivalent to `a ^ b`.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### to\_instruction
|
||
|
||
<Function id="qiskit.quantum_info.Operator.to_instruction" signature="Operator.to_instruction()">
|
||
Convert to a UnitaryGate instruction.
|
||
</Function>
|
||
|
||
### to\_operator
|
||
|
||
<Function id="qiskit.quantum_info.Operator.to_operator" signature="Operator.to_operator()">
|
||
Convert operator to matrix operator class
|
||
</Function>
|
||
|
||
### transpose
|
||
|
||
<Function id="qiskit.quantum_info.Operator.transpose" signature="Operator.transpose()">
|
||
Return the transpose of the Operator.
|
||
</Function>
|
||
|
||
## Attributes
|
||
|
||
### atol
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.atol" attributeValue="1e-08" />
|
||
|
||
### data
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.data">
|
||
Return data.
|
||
</Attribute>
|
||
|
||
### dim
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.dim">
|
||
Return tuple (input\_shape, output\_shape).
|
||
</Attribute>
|
||
|
||
### num\_qubits
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.num_qubits">
|
||
Return the number of qubits if a N-qubit operator or None otherwise.
|
||
</Attribute>
|
||
|
||
### qargs
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.qargs">
|
||
Return the qargs for the operator.
|
||
</Attribute>
|
||
|
||
### rtol
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.rtol" attributeValue="1e-05" />
|
||
|
||
### settings
|
||
|
||
<Attribute id="qiskit.quantum_info.Operator.settings">
|
||
Return operator settings.
|
||
</Attribute>
|
||
</Class>
|
||
|