460 lines
19 KiB
Plaintext
460 lines
19 KiB
Plaintext
---
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title: Kraus
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description: API reference for qiskit.quantum_info.Kraus
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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.Kraus
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---
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<span id="qiskit-quantum-info-kraus" />
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# qiskit.quantum\_info.Kraus
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<Class id="qiskit.quantum_info.Kraus" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.16/qiskit/quantum_info/operators/channel/kraus.py" signature="Kraus(data, input_dims=None, output_dims=None)" modifiers="class">
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Kraus representation of a quantum channel.
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The Kraus representation for a quantum channel $\mathcal{E}$ is a set of matrices $[A_0,...,A_{K-1}]$ such that
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For a quantum channel $\mathcal{E}$, the Kraus representation is given by a set of matrices $[A_0,...,A_{K-1}]$ such that the evolution of a [`DensityMatrix`](qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix") $\rho$ is given by
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$$
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\mathcal{E}(\rho) = \sum_{i=0}^{K-1} A_i \rho A_i^\dagger
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$$
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A general operator map $\mathcal{G}$ can also be written using the generalized Kraus representation which is given by two sets of matrices $[A_0,...,A_{K-1}]$, $[B_0,...,A_{B-1}]$ such that
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$$
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\mathcal{G}(\rho) = \sum_{i=0}^{K-1} A_i \rho B_i^\dagger
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$$
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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 Kraus 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. If the input data is a list of Numpy arrays of shape (2\*\*N, 2\*\*N) qubit systems will be used. If the input does not correspond to an N-qubit channel, it will assign a single subsystem with dimension specified by the shape of the input.
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### \_\_init\_\_
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<Function id="qiskit.quantum_info.Kraus.__init__" signature="__init__(data, input_dims=None, output_dims=None)">
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Initialize a quantum channel Kraus 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. If the input data is a list of Numpy arrays of shape (2\*\*N, 2\*\*N) qubit systems will be used. If the input does not correspond to an N-qubit channel, it will assign a single subsystem with dimension specified by the shape of the input.
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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.Kraus.__init__ "qiskit.quantum_info.Kraus.__init__")(data\[, input\_dims, output\_dims]) | Initialize a quantum channel Kraus operator. |
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| [`add`](#qiskit.quantum_info.Kraus.add "qiskit.quantum_info.Kraus.add")(other) | Return the linear operator self + other. |
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| [`adjoint`](#qiskit.quantum_info.Kraus.adjoint "qiskit.quantum_info.Kraus.adjoint")() | Return the adjoint of the operator. |
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| [`compose`](#qiskit.quantum_info.Kraus.compose "qiskit.quantum_info.Kraus.compose")(other\[, qargs, front]) | Return the composed quantum channel self @ other. |
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| [`conjugate`](#qiskit.quantum_info.Kraus.conjugate "qiskit.quantum_info.Kraus.conjugate")() | Return the conjugate of the QuantumChannel. |
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| [`copy`](#qiskit.quantum_info.Kraus.copy "qiskit.quantum_info.Kraus.copy")() | Make a deep copy of current operator. |
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| [`dot`](#qiskit.quantum_info.Kraus.dot "qiskit.quantum_info.Kraus.dot")(other\[, qargs]) | Return the right multiplied quantum channel self \* other. |
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| [`expand`](#qiskit.quantum_info.Kraus.expand "qiskit.quantum_info.Kraus.expand")(other) | Return the tensor product channel other ⊗ self. |
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| [`input_dims`](#qiskit.quantum_info.Kraus.input_dims "qiskit.quantum_info.Kraus.input_dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
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| [`is_cp`](#qiskit.quantum_info.Kraus.is_cp "qiskit.quantum_info.Kraus.is_cp")(\[atol, rtol]) | Test if Choi-matrix is completely-positive (CP) |
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| [`is_cptp`](#qiskit.quantum_info.Kraus.is_cptp "qiskit.quantum_info.Kraus.is_cptp")(\[atol, rtol]) | Return True if completely-positive trace-preserving. |
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| [`is_tp`](#qiskit.quantum_info.Kraus.is_tp "qiskit.quantum_info.Kraus.is_tp")(\[atol, rtol]) | Test if a channel is completely-positive (CP) |
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| [`is_unitary`](#qiskit.quantum_info.Kraus.is_unitary "qiskit.quantum_info.Kraus.is_unitary")(\[atol, rtol]) | Return True if QuantumChannel is a unitary channel. |
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| [`multiply`](#qiskit.quantum_info.Kraus.multiply "qiskit.quantum_info.Kraus.multiply")(other) | Return the linear operator other \* self. |
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| [`output_dims`](#qiskit.quantum_info.Kraus.output_dims "qiskit.quantum_info.Kraus.output_dims")(\[qargs]) | Return tuple of output dimension for specified subsystems. |
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| [`power`](#qiskit.quantum_info.Kraus.power "qiskit.quantum_info.Kraus.power")(n) | The matrix power of the channel. |
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| [`reshape`](#qiskit.quantum_info.Kraus.reshape "qiskit.quantum_info.Kraus.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.Kraus.set_atol "qiskit.quantum_info.Kraus.set_atol")(value) | Set the class default absolute tolerance parameter for float comparisons. |
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| [`set_rtol`](#qiskit.quantum_info.Kraus.set_rtol "qiskit.quantum_info.Kraus.set_rtol")(value) | Set the class default relative tolerance parameter for float comparisons. |
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| [`subtract`](#qiskit.quantum_info.Kraus.subtract "qiskit.quantum_info.Kraus.subtract")(other) | Return the linear operator self - other. |
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| [`tensor`](#qiskit.quantum_info.Kraus.tensor "qiskit.quantum_info.Kraus.tensor")(other) | Return the tensor product channel self ⊗ other. |
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| [`to_instruction`](#qiskit.quantum_info.Kraus.to_instruction "qiskit.quantum_info.Kraus.to_instruction")() | Convert to a Kraus or UnitaryGate circuit instruction. |
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| [`to_operator`](#qiskit.quantum_info.Kraus.to_operator "qiskit.quantum_info.Kraus.to_operator")() | Try to convert channel to a unitary representation Operator. |
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| [`transpose`](#qiskit.quantum_info.Kraus.transpose "qiskit.quantum_info.Kraus.transpose")() | Return the transpose of the QuantumChannel. |
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## Attributes
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| -------------------------------------------------------------------------------------------- | -------------------------------------------------------------------- |
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| [`atol`](#qiskit.quantum_info.Kraus.atol "qiskit.quantum_info.Kraus.atol") | The default absolute tolerance parameter for float comparisons. |
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| [`data`](#qiskit.quantum_info.Kraus.data "qiskit.quantum_info.Kraus.data") | Return list of Kraus matrices for channel. |
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| [`dim`](#qiskit.quantum_info.Kraus.dim "qiskit.quantum_info.Kraus.dim") | Return tuple (input\_shape, output\_shape). |
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| [`num_qubits`](#qiskit.quantum_info.Kraus.num_qubits "qiskit.quantum_info.Kraus.num_qubits") | Return the number of qubits if a N-qubit operator or None otherwise. |
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| [`qargs`](#qiskit.quantum_info.Kraus.qargs "qiskit.quantum_info.Kraus.qargs") | Return the qargs for the operator. |
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| [`rtol`](#qiskit.quantum_info.Kraus.rtol "qiskit.quantum_info.Kraus.rtol") | The relative tolerance parameter for float comparisons. |
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### add
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<Function id="qiskit.quantum_info.Kraus.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.Kraus.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.Kraus.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.Kraus.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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[Kraus](#qiskit.quantum_info.Kraus "qiskit.quantum_info.Kraus")
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**Raises**
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**QiskitError** – if other cannot be converted to a Kraus 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.Kraus.dot "qiskit.quantum_info.Kraus.dot") method.
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</Function>
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### conjugate
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<Function id="qiskit.quantum_info.Kraus.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.Kraus.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.Kraus.data">
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Return list of Kraus matrices for channel.
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</Attribute>
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### dim
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<Attribute id="qiskit.quantum_info.Kraus.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.Kraus.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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[Kraus](#qiskit.quantum_info.Kraus "qiskit.quantum_info.Kraus")
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**Raises**
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**QiskitError** – if other cannot be converted to a Kraus or has incompatible dimensions.
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</Function>
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### expand
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<Function id="qiskit.quantum_info.Kraus.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 Kraus object.
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**Return type**
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[Kraus](#qiskit.quantum_info.Kraus "qiskit.quantum_info.Kraus")
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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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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 Kraus channel.
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**Return type**
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[Kraus](#qiskit.quantum_info.Kraus "qiskit.quantum_info.Kraus")
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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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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.Kraus.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 self ⊗ other as a Kraus object.
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**Return type**
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[Kraus](#qiskit.quantum_info.Kraus "qiskit.quantum_info.Kraus")
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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.Kraus.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.Kraus.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.Kraus.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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