460 lines
19 KiB
Plaintext
460 lines
19 KiB
Plaintext
---
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title: Stinespring
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description: API reference for qiskit.quantum_info.Stinespring
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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.Stinespring
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---
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<span id="qiskit-quantum-info-stinespring" />
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# qiskit.quantum\_info.Stinespring
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<Class id="qiskit.quantum_info.Stinespring" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.16/qiskit/quantum_info/operators/channel/stinespring.py" signature="Stinespring(data, input_dims=None, output_dims=None)" modifiers="class">
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Stinespring representation of a quantum channel.
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The Stinespring representation of a quantum channel $\mathcal{E}$ is a rectangular matrix $A$ such that the evolution of a [`DensityMatrix`](qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix") $\rho$ is given by
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$$
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\mathcal{E}(ρ) = \mbox{Tr}_2\left[A ρ A^\dagger\right]
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$$
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where $\mbox{Tr}_2$ is the [`partial_trace()`](qiskit.quantum_info.partial_trace "qiskit.quantum_info.partial_trace") over subsystem 2.
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A general operator map $\mathcal{G}$ can also be written using the generalized Stinespring representation which is given by two matrices $A$, $B$ such that
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$$
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\mathcal{G}(ρ) = \mbox{Tr}_2\left[A ρ B^\dagger\right]
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$$
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See reference \[1] for further details.
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**References**
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1. C.J. Wood, J.D. Biamonte, D.G. Cory, *Tensor networks and graphical calculus for open quantum systems*, Quant. Inf. Comp. 15, 0579-0811 (2015). [arXiv:1111.6950 \[quant-ph\]](https://arxiv.org/abs/1111.6950)
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Initialize a quantum channel Stinespring operator.
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**Parameters**
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* \*\*(\*\***QuantumCircuit or** (*data*) – Instruction or BaseOperator or matrix): data to initialize superoperator.
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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 a a list of Kraus matrices.
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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. This can fail for the Stinespring operator if the output dimension cannot be automatically determined.
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### \_\_init\_\_
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<Function id="qiskit.quantum_info.Stinespring.__init__" signature="__init__(data, input_dims=None, output_dims=None)">
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Initialize a quantum channel Stinespring operator.
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**Parameters**
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* \*\*(\*\***QuantumCircuit or** (*data*) – Instruction or BaseOperator or matrix): data to initialize superoperator.
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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 a a list of Kraus matrices.
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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. This can fail for the Stinespring operator if the output dimension cannot be automatically determined.
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</Function>
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## Methods
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| | |
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| -------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------- |
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| [`__init__`](#qiskit.quantum_info.Stinespring.__init__ "qiskit.quantum_info.Stinespring.__init__")(data\[, input\_dims, output\_dims]) | Initialize a quantum channel Stinespring operator. |
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| [`add`](#qiskit.quantum_info.Stinespring.add "qiskit.quantum_info.Stinespring.add")(other) | Return the linear operator self + other. |
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| [`adjoint`](#qiskit.quantum_info.Stinespring.adjoint "qiskit.quantum_info.Stinespring.adjoint")() | Return the adjoint of the operator. |
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| [`compose`](#qiskit.quantum_info.Stinespring.compose "qiskit.quantum_info.Stinespring.compose")(other\[, qargs, front]) | Return the composed quantum channel self @ other. |
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| [`conjugate`](#qiskit.quantum_info.Stinespring.conjugate "qiskit.quantum_info.Stinespring.conjugate")() | Return the conjugate of the QuantumChannel. |
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| [`copy`](#qiskit.quantum_info.Stinespring.copy "qiskit.quantum_info.Stinespring.copy")() | Make a deep copy of current operator. |
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| [`dot`](#qiskit.quantum_info.Stinespring.dot "qiskit.quantum_info.Stinespring.dot")(other\[, qargs]) | Return the right multiplied quantum channel self \* other. |
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| [`expand`](#qiskit.quantum_info.Stinespring.expand "qiskit.quantum_info.Stinespring.expand")(other) | Return the tensor product channel other ⊗ self. |
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| [`input_dims`](#qiskit.quantum_info.Stinespring.input_dims "qiskit.quantum_info.Stinespring.input_dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
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| [`is_cp`](#qiskit.quantum_info.Stinespring.is_cp "qiskit.quantum_info.Stinespring.is_cp")(\[atol, rtol]) | Test if Choi-matrix is completely-positive (CP) |
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| [`is_cptp`](#qiskit.quantum_info.Stinespring.is_cptp "qiskit.quantum_info.Stinespring.is_cptp")(\[atol, rtol]) | Return True if completely-positive trace-preserving. |
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| [`is_tp`](#qiskit.quantum_info.Stinespring.is_tp "qiskit.quantum_info.Stinespring.is_tp")(\[atol, rtol]) | Test if a channel is completely-positive (CP) |
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| [`is_unitary`](#qiskit.quantum_info.Stinespring.is_unitary "qiskit.quantum_info.Stinespring.is_unitary")(\[atol, rtol]) | Return True if QuantumChannel is a unitary channel. |
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| [`multiply`](#qiskit.quantum_info.Stinespring.multiply "qiskit.quantum_info.Stinespring.multiply")(other) | Return the linear operator other \* self. |
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| [`output_dims`](#qiskit.quantum_info.Stinespring.output_dims "qiskit.quantum_info.Stinespring.output_dims")(\[qargs]) | Return tuple of output dimension for specified subsystems. |
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| [`power`](#qiskit.quantum_info.Stinespring.power "qiskit.quantum_info.Stinespring.power")(n) | The matrix power of the channel. |
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| [`reshape`](#qiskit.quantum_info.Stinespring.reshape "qiskit.quantum_info.Stinespring.reshape")(\[input\_dims, output\_dims]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
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| [`set_atol`](#qiskit.quantum_info.Stinespring.set_atol "qiskit.quantum_info.Stinespring.set_atol")(value) | Set the class default absolute tolerance parameter for float comparisons. |
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| [`set_rtol`](#qiskit.quantum_info.Stinespring.set_rtol "qiskit.quantum_info.Stinespring.set_rtol")(value) | Set the class default relative tolerance parameter for float comparisons. |
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| [`subtract`](#qiskit.quantum_info.Stinespring.subtract "qiskit.quantum_info.Stinespring.subtract")(other) | Return the linear operator self - other. |
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| [`tensor`](#qiskit.quantum_info.Stinespring.tensor "qiskit.quantum_info.Stinespring.tensor")(other) | Return the tensor product channel self ⊗ other. |
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| [`to_instruction`](#qiskit.quantum_info.Stinespring.to_instruction "qiskit.quantum_info.Stinespring.to_instruction")() | Convert to a Kraus or UnitaryGate circuit instruction. |
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| [`to_operator`](#qiskit.quantum_info.Stinespring.to_operator "qiskit.quantum_info.Stinespring.to_operator")() | Try to convert channel to a unitary representation Operator. |
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| [`transpose`](#qiskit.quantum_info.Stinespring.transpose "qiskit.quantum_info.Stinespring.transpose")() | Return the transpose of the QuantumChannel. |
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## Attributes
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| -------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------- |
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| [`atol`](#qiskit.quantum_info.Stinespring.atol "qiskit.quantum_info.Stinespring.atol") | The default absolute tolerance parameter for float comparisons. |
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| [`data`](#qiskit.quantum_info.Stinespring.data "qiskit.quantum_info.Stinespring.data") | Return data. |
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| [`dim`](#qiskit.quantum_info.Stinespring.dim "qiskit.quantum_info.Stinespring.dim") | Return tuple (input\_shape, output\_shape). |
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| [`num_qubits`](#qiskit.quantum_info.Stinespring.num_qubits "qiskit.quantum_info.Stinespring.num_qubits") | Return the number of qubits if a N-qubit operator or None otherwise. |
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| [`qargs`](#qiskit.quantum_info.Stinespring.qargs "qiskit.quantum_info.Stinespring.qargs") | Return the qargs for the operator. |
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| [`rtol`](#qiskit.quantum_info.Stinespring.rtol "qiskit.quantum_info.Stinespring.rtol") | The relative tolerance parameter for float comparisons. |
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### add
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<Function id="qiskit.quantum_info.Stinespring.add" signature="add(other)">
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Return the linear operator self + other.
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DEPRECATED: use `operator + other` instead.
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**Parameters**
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**other** (*BaseOperator*) – an operator object.
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**Returns**
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the operator self + other.
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**Return type**
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BaseOperator
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</Function>
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### adjoint
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<Function id="qiskit.quantum_info.Stinespring.adjoint" signature="adjoint()">
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Return the adjoint of the operator.
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</Function>
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### atol
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<Attribute id="qiskit.quantum_info.Stinespring.atol">
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The default absolute tolerance parameter for float comparisons.
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</Attribute>
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### compose
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<Function id="qiskit.quantum_info.Stinespring.compose" signature="compose(other, qargs=None, front=False)">
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Return the composed quantum channel self @ other.
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**Parameters**
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* **other** (*QuantumChannel*) – a quantum channel.
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* **qargs** (*list or None*) – 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 quantum channel self @ other.
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**Return type**
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[Stinespring](#qiskit.quantum_info.Stinespring "qiskit.quantum_info.Stinespring")
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**Raises**
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**QiskitError** – if other cannot be converted to a Stinespring or has incompatible dimensions.
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**Additional Information:**
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Composition (`@`) is defined as left matrix multiplication for [`SuperOp`](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") matrices. 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()`](#qiskit.quantum_info.Stinespring.dot "qiskit.quantum_info.Stinespring.dot") method.
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</Function>
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### conjugate
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<Function id="qiskit.quantum_info.Stinespring.conjugate" signature="conjugate()">
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Return the conjugate of the QuantumChannel.
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</Function>
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### copy
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<Function id="qiskit.quantum_info.Stinespring.copy" signature="copy()">
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Make a deep copy of current operator.
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</Function>
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### data
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<Attribute id="qiskit.quantum_info.Stinespring.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.Stinespring.dim">
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Return tuple (input\_shape, output\_shape).
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</Attribute>
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### dot
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<Function id="qiskit.quantum_info.Stinespring.dot" signature="dot(other, qargs=None)">
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Return the right multiplied quantum channel self \* other.
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**Parameters**
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* **other** (*QuantumChannel*) – a quantum channel.
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* **qargs** (*list or None*) – 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 quantum channel self \* other.
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**Return type**
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[Stinespring](#qiskit.quantum_info.Stinespring "qiskit.quantum_info.Stinespring")
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**Raises**
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**QiskitError** – if other cannot be converted to a Stinespring or has incompatible dimensions.
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</Function>
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### expand
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<Function id="qiskit.quantum_info.Stinespring.expand" signature="expand(other)">
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Return the tensor product channel other ⊗ self.
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**Parameters**
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**other** (*QuantumChannel*) – a quantum channel subclass.
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**Returns**
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the tensor product channel other ⊗ self as a Stinespring object.
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**Return type**
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[Stinespring](#qiskit.quantum_info.Stinespring "qiskit.quantum_info.Stinespring")
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**Raises**
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**QiskitError** – if other cannot be converted to a channel.
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</Function>
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### input\_dims
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<Function id="qiskit.quantum_info.Stinespring.input_dims" signature="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\_cp
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<Function id="qiskit.quantum_info.Stinespring.is_cp" signature="is_cp(atol=None, rtol=None)">
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Test if Choi-matrix is completely-positive (CP)
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</Function>
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### is\_cptp
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<Function id="qiskit.quantum_info.Stinespring.is_cptp" signature="is_cptp(atol=None, rtol=None)">
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Return True if completely-positive trace-preserving.
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</Function>
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### is\_tp
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<Function id="qiskit.quantum_info.Stinespring.is_tp" signature="is_tp(atol=None, rtol=None)">
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Test if a channel is completely-positive (CP)
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</Function>
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### is\_unitary
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<Function id="qiskit.quantum_info.Stinespring.is_unitary" signature="is_unitary(atol=None, rtol=None)">
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Return True if QuantumChannel is a unitary channel.
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</Function>
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### multiply
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<Function id="qiskit.quantum_info.Stinespring.multiply" signature="multiply(other)">
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Return the linear operator other \* self.
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DEPRECATED: use `other * operator` instead.
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**Parameters**
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**other** (*complex*) – a complex number.
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**Returns**
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the linear operator other \* self.
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**Return type**
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BaseOperator
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**Raises**
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**NotImplementedError** – if subclass does not support multiplication.
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</Function>
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### num\_qubits
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<Attribute id="qiskit.quantum_info.Stinespring.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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### output\_dims
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<Function id="qiskit.quantum_info.Stinespring.output_dims" signature="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.Stinespring.power" signature="power(n)">
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The matrix power of the channel.
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**Parameters**
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**n** (*int*) – compute the matrix power of the superoperator matrix.
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**Returns**
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the matrix power of the SuperOp converted to a Stinespring channel.
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**Return type**
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[Stinespring](#qiskit.quantum_info.Stinespring "qiskit.quantum_info.Stinespring")
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**Raises**
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**QiskitError** – if the input and output dimensions of the QuantumChannel are not equal, or the power is not an integer.
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</Function>
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### qargs
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<Attribute id="qiskit.quantum_info.Stinespring.qargs">
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Return the qargs for the operator.
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</Attribute>
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### reshape
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<Function id="qiskit.quantum_info.Stinespring.reshape" signature="reshape(input_dims=None, output_dims=None)">
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Return a shallow copy with reshaped input and output subsystem dimensions.
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**Arg:**
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**input\_dims (None or tuple): new subsystem input dimensions.**
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If None the original input dims will be preserved \[Default: None].
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**output\_dims (None or tuple): new subsystem output dimensions.**
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If None the original output dims will be preserved \[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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### rtol
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<Attribute id="qiskit.quantum_info.Stinespring.rtol">
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The relative tolerance parameter for float comparisons.
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</Attribute>
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### set\_atol
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<Function id="qiskit.quantum_info.Stinespring.set_atol" signature="set_atol(value)" modifiers="classmethod">
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Set the class default absolute tolerance parameter for float comparisons.
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DEPRECATED: use operator.atol = value instead
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</Function>
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### set\_rtol
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<Function id="qiskit.quantum_info.Stinespring.set_rtol" signature="set_rtol(value)" modifiers="classmethod">
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Set the class default relative tolerance parameter for float comparisons.
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DEPRECATED: use operator.rtol = value instead
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</Function>
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### subtract
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<Function id="qiskit.quantum_info.Stinespring.subtract" signature="subtract(other)">
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Return the linear operator self - other.
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DEPRECATED: use `operator - other` instead.
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**Parameters**
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**other** (*BaseOperator*) – an operator object.
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**Returns**
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the operator self - other.
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**Return type**
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BaseOperator
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</Function>
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### tensor
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<Function id="qiskit.quantum_info.Stinespring.tensor" signature="tensor(other)">
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Return the tensor product channel self ⊗ other.
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**Parameters**
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**other** (*QuantumChannel*) – a quantum channel subclass.
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**Returns**
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the tensor product channel other ⊗ self as a Stinespring object.
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**Return type**
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[Stinespring](#qiskit.quantum_info.Stinespring "qiskit.quantum_info.Stinespring")
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**Raises**
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**QiskitError** – if other cannot be converted to a channel.
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</Function>
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### to\_instruction
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<Function id="qiskit.quantum_info.Stinespring.to_instruction" signature="to_instruction()">
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Convert to a Kraus or UnitaryGate circuit instruction.
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If the channel is unitary it will be added as a unitary gate, otherwise it will be added as a kraus simulator instruction.
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**Returns**
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A kraus instruction for the channel.
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**Return type**
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[qiskit.circuit.Instruction](qiskit.circuit.Instruction "qiskit.circuit.Instruction")
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**Raises**
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**QiskitError** – if input data is not an N-qubit CPTP quantum channel.
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</Function>
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### to\_operator
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<Function id="qiskit.quantum_info.Stinespring.to_operator" signature="to_operator()">
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Try to convert channel to a unitary representation Operator.
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</Function>
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### transpose
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<Function id="qiskit.quantum_info.Stinespring.transpose" signature="transpose()">
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Return the transpose of the QuantumChannel.
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</Function>
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</Class>
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