366 lines
13 KiB
Plaintext
366 lines
13 KiB
Plaintext
---
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title: Operator
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description: API reference for qiskit.quantum_info.Operator
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.quantum_info.Operator
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---
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# Operator
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<Class id="qiskit.quantum_info.Operator" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.20/qiskit/quantum_info/operators/operator.py" signature="Operator(data, input_dims=None, output_dims=None)" modifiers="class">
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Bases: `qiskit.quantum_info.operators.linear_op.LinearOp`
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Matrix operator class
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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
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$$
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|\psi\rangle \mapsto M|\psi\rangle,
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$$
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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
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$$
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\rho \mapsto M \rho M^\dagger.
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$$
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Initialize an operator object.
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**Parameters**
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* \*\*(\*\***QuantumCircuit or** (*data*) – Instruction or BaseOperator or matrix): data to initialize operator.
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* **input\_dims** (*tuple*) – the input subsystem dimensions. \[Default: None]
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* **output\_dims** (*tuple*) – the output subsystem dimensions. \[Default: None]
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**Raises**
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**QiskitError** – if input data cannot be initialized as an operator.
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**Additional Information:**
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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.
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## Methods
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### adjoint
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<Function id="qiskit.quantum_info.Operator.adjoint" signature="Operator.adjoint()">
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Return the adjoint of the Operator.
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</Function>
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### compose
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<Function id="qiskit.quantum_info.Operator.compose" signature="Operator.compose(other, qargs=None, front=False)">
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Return the operator composition with another Operator.
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**Parameters**
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* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – a Operator object.
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* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
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* **front** (*bool*) – If True compose using right operator multiplication, instead of left multiplication \[default: False].
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**Returns**
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The composed Operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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**Raises**
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**QiskitError** – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
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<Admonition title="Note" type="note">
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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.
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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)`.
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</Admonition>
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</Function>
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### conjugate
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<Function id="qiskit.quantum_info.Operator.conjugate" signature="Operator.conjugate()">
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Return the conjugate of the Operator.
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</Function>
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### copy
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<Function id="qiskit.quantum_info.Operator.copy" signature="Operator.copy()">
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Make a deep copy of current operator.
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</Function>
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### dot
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<Function id="qiskit.quantum_info.Operator.dot" signature="Operator.dot(other, qargs=None)">
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Return the right multiplied operator self \* other.
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**Parameters**
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* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator object.
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* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
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**Returns**
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The right matrix multiplied Operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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</Function>
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### equiv
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<Function id="qiskit.quantum_info.Operator.equiv" signature="Operator.equiv(other, rtol=None, atol=None)">
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Return True if operators are equivalent up to global phase.
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**Parameters**
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* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator object.
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* **rtol** (*float*) – relative tolerance value for comparison.
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* **atol** (*float*) – absolute tolerance value for comparison.
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**Returns**
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True if operators are equivalent up to global phase.
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**Return type**
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bool
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</Function>
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### expand
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<Function id="qiskit.quantum_info.Operator.expand" signature="Operator.expand(other)">
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Return the reverse-order tensor product with another Operator.
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**Parameters**
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**other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – a Operator object.
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**Returns**
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**the tensor product $b \otimes a$, where $a$**
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is the current Operator, and $b$ is the other Operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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</Function>
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### from\_circuit
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<Function id="qiskit.quantum_info.Operator.from_circuit" signature="Operator.from_circuit(circuit, ignore_set_layout=False, layout=None)" modifiers="classmethod">
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Create a new Operator object from a :class\`.QuantumCircuit\`
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While a [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.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`](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator"). This constructor method lets you control how the [`Operator`](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator") is created so it can be adjusted for a particular use case.
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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`](qiskit.transpiler.Layout "qiskit.transpiler.Layout") object directly.
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**Parameters**
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* **circuit** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The [`QuantumCircuit`](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") to create an Operator object from.
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* **ignore\_set\_layout** (*bool*) – When set to `True` if the input `circuit` has a layout set it will be ignored
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* **layout** ([*Layout*](qiskit.transpiler.Layout "qiskit.transpiler.Layout")) – If specified this kwarg can be used to specify a particular layout to use to permute the qubits in the created [`Operator`](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator"). If this is specified it will be used instead of a layout contained in the `circuit` input.
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**Returns**
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An operator representing the input circuit
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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</Function>
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### from\_label
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<Function id="qiskit.quantum_info.Operator.from_label" signature="Operator.from_label(label)" modifiers="classmethod">
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Return a tensor product of single-qubit operators.
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**Parameters**
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**label** (*string*) – single-qubit operator string.
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**Returns**
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The N-qubit operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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**Raises**
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**QiskitError** – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num\_qubits.
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#### Additional Information:
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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]]
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</Function>
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### input\_dims
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<Function id="qiskit.quantum_info.Operator.input_dims" signature="Operator.input_dims(qargs=None)">
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Return tuple of input dimension for specified subsystems.
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</Function>
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### is\_unitary
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<Function id="qiskit.quantum_info.Operator.is_unitary" signature="Operator.is_unitary(atol=None, rtol=None)">
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Return True if operator is a unitary matrix.
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</Function>
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### output\_dims
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<Function id="qiskit.quantum_info.Operator.output_dims" signature="Operator.output_dims(qargs=None)">
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Return tuple of output dimension for specified subsystems.
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</Function>
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### power
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<Function id="qiskit.quantum_info.Operator.power" signature="Operator.power(n)">
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Return the matrix power of the operator.
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**Parameters**
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**n** (*float*) – the power to raise the matrix to.
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**Returns**
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the resulting operator `O ** n`.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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**Raises**
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**QiskitError** – if the input and output dimensions of the operator are not equal.
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</Function>
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### reshape
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<Function id="qiskit.quantum_info.Operator.reshape" signature="Operator.reshape(input_dims=None, output_dims=None, num_qubits=None)">
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Return a shallow copy with reshaped input and output subsystem dimensions.
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**Parameters**
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* **input\_dims** (*None or tuple*) – new subsystem input dimensions. If None the original input dims will be preserved \[Default: None].
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* **output\_dims** (*None or tuple*) – new subsystem output dimensions. If None the original output dims will be preserved \[Default: None].
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* **num\_qubits** (*None or int*) – reshape to an N-qubit operator \[Default: None].
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**Returns**
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returns self with reshaped input and output dimensions.
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**Return type**
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BaseOperator
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**Raises**
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**QiskitError** – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.
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</Function>
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### reverse\_qargs
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<Function id="qiskit.quantum_info.Operator.reverse_qargs" signature="Operator.reverse_qargs()">
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Return an Operator with reversed subsystem ordering.
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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 $A_0 \otimes ... \otimes A_{n-1}$.
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**Returns**
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the operator with reversed subsystem order.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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</Function>
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### tensor
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<Function id="qiskit.quantum_info.Operator.tensor" signature="Operator.tensor(other)">
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Return the tensor product with another Operator.
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**Parameters**
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**other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – a Operator object.
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**Returns**
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**the tensor product $a \otimes b$, where $a$**
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is the current Operator, and $b$ is the other Operator.
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**Return type**
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[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
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<Admonition title="Note" type="note">
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The tensor product can be obtained using the `^` binary operator. Hence `a.tensor(b)` is equivalent to `a ^ b`.
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</Admonition>
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</Function>
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### to\_instruction
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<Function id="qiskit.quantum_info.Operator.to_instruction" signature="Operator.to_instruction()">
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Convert to a UnitaryGate instruction.
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</Function>
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### to\_operator
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<Function id="qiskit.quantum_info.Operator.to_operator" signature="Operator.to_operator()">
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Convert operator to matrix operator class
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</Function>
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### transpose
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<Function id="qiskit.quantum_info.Operator.transpose" signature="Operator.transpose()">
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Return the transpose of the Operator.
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</Function>
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## Attributes
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### atol
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<Attribute id="qiskit.quantum_info.Operator.atol" attributeValue="1e-08" />
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### data
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<Attribute id="qiskit.quantum_info.Operator.data">
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Return data.
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</Attribute>
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### dim
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<Attribute id="qiskit.quantum_info.Operator.dim">
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Return tuple (input\_shape, output\_shape).
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.quantum_info.Operator.num_qubits">
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Return the number of qubits if a N-qubit operator or None otherwise.
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</Attribute>
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### qargs
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<Attribute id="qiskit.quantum_info.Operator.qargs">
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Return the qargs for the operator.
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</Attribute>
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### rtol
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<Attribute id="qiskit.quantum_info.Operator.rtol" attributeValue="1e-05" />
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### settings
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<Attribute id="qiskit.quantum_info.Operator.settings">
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Return operator settings.
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</Attribute>
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</Class>
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