387 lines
18 KiB
Plaintext
387 lines
18 KiB
Plaintext
---
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title: Choi (v0.26)
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description: API reference for qiskit.quantum_info.Choi in qiskit v0.26
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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.Choi
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---
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<span id="qiskit-quantum-info-choi" />
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# qiskit.quantum\_info.Choi
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<Class id="qiskit.quantum_info.Choi" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/quantum_info/operators/channel/choi.py" signature="Choi(data, input_dims=None, output_dims=None)" modifiers="class">
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Choi-matrix representation of a Quantum Channel.
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The Choi-matrix representation of a quantum channel $\mathcal{E}$ is a matrix
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$$
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\Lambda = \sum_{i,j} |i\rangle\!\langle j|\otimes
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\mathcal{E}\left(|i\rangle\!\langle j|\right)
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$$
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Evolution of a [`DensityMatrix`](qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix") $\rho$ with respect to the Choi-matrix is given by
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$$
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\mathcal{E}(\rho) = \mbox{Tr}_{1}\left[\Lambda
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(\rho^T \otimes \mathbb{I})\right]
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$$
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where $\mbox{Tr}_1$ is the [`partial_trace()`](qiskit.quantum_info.partial_trace "qiskit.quantum_info.partial_trace") over subsystem 1.
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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 Choi matrix 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 Choi matrix.
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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 (4\*\*N, 4\*\*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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### \_\_init\_\_
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<Function id="qiskit.quantum_info.Choi.__init__" signature="__init__(data, input_dims=None, output_dims=None)">
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Initialize a quantum channel Choi matrix 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 Choi matrix.
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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 (4\*\*N, 4\*\*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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</Function>
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## Methods
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| | |
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| ---------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------- |
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| [`__init__`](#qiskit.quantum_info.Choi.__init__ "qiskit.quantum_info.Choi.__init__")(data\[, input\_dims, output\_dims]) | Initialize a quantum channel Choi matrix operator. |
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| [`adjoint`](#qiskit.quantum_info.Choi.adjoint "qiskit.quantum_info.Choi.adjoint")() | Return the adjoint quantum channel. |
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| [`compose`](#qiskit.quantum_info.Choi.compose "qiskit.quantum_info.Choi.compose")(other\[, qargs, front]) | Return the operator composition with another Choi. |
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| [`conjugate`](#qiskit.quantum_info.Choi.conjugate "qiskit.quantum_info.Choi.conjugate")() | Return the conjugate quantum channel. |
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| [`copy`](#qiskit.quantum_info.Choi.copy "qiskit.quantum_info.Choi.copy")() | Make a deep copy of current operator. |
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| [`dot`](#qiskit.quantum_info.Choi.dot "qiskit.quantum_info.Choi.dot")(other\[, qargs]) | Return the right multiplied operator self \* other. |
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| [`expand`](#qiskit.quantum_info.Choi.expand "qiskit.quantum_info.Choi.expand")(other) | Return the reverse-order tensor product with another Choi. |
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| [`input_dims`](#qiskit.quantum_info.Choi.input_dims "qiskit.quantum_info.Choi.input_dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
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| [`is_cp`](#qiskit.quantum_info.Choi.is_cp "qiskit.quantum_info.Choi.is_cp")(\[atol, rtol]) | Test if Choi-matrix is completely-positive (CP) |
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| [`is_cptp`](#qiskit.quantum_info.Choi.is_cptp "qiskit.quantum_info.Choi.is_cptp")(\[atol, rtol]) | Return True if completely-positive trace-preserving (CPTP). |
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| [`is_tp`](#qiskit.quantum_info.Choi.is_tp "qiskit.quantum_info.Choi.is_tp")(\[atol, rtol]) | Test if a channel is trace-preserving (TP) |
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| [`is_unitary`](#qiskit.quantum_info.Choi.is_unitary "qiskit.quantum_info.Choi.is_unitary")(\[atol, rtol]) | Return True if QuantumChannel is a unitary channel. |
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| [`output_dims`](#qiskit.quantum_info.Choi.output_dims "qiskit.quantum_info.Choi.output_dims")(\[qargs]) | Return tuple of output dimension for specified subsystems. |
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| [`power`](#qiskit.quantum_info.Choi.power "qiskit.quantum_info.Choi.power")(n) | Return the power of the quantum channel. |
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| [`reshape`](#qiskit.quantum_info.Choi.reshape "qiskit.quantum_info.Choi.reshape")(\[input\_dims, output\_dims, num\_qubits]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
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| [`tensor`](#qiskit.quantum_info.Choi.tensor "qiskit.quantum_info.Choi.tensor")(other) | Return the tensor product with another Choi. |
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| [`to_instruction`](#qiskit.quantum_info.Choi.to_instruction "qiskit.quantum_info.Choi.to_instruction")() | Convert to a Kraus or UnitaryGate circuit instruction. |
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| [`to_operator`](#qiskit.quantum_info.Choi.to_operator "qiskit.quantum_info.Choi.to_operator")() | Try to convert channel to a unitary representation Operator. |
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| [`transpose`](#qiskit.quantum_info.Choi.transpose "qiskit.quantum_info.Choi.transpose")() | Return the transpose quantum channel. |
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## Attributes
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| | |
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| ------------------------------------------------------------------------------------------ | -------------------------------------------------------------------- |
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| [`atol`](#qiskit.quantum_info.Choi.atol "qiskit.quantum_info.Choi.atol") | Default absolute tolerance parameter for float comparisons. |
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| [`data`](#qiskit.quantum_info.Choi.data "qiskit.quantum_info.Choi.data") | Return data. |
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| [`dim`](#qiskit.quantum_info.Choi.dim "qiskit.quantum_info.Choi.dim") | Return tuple (input\_shape, output\_shape). |
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| [`num_qubits`](#qiskit.quantum_info.Choi.num_qubits "qiskit.quantum_info.Choi.num_qubits") | Return the number of qubits if a N-qubit operator or None otherwise. |
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| [`qargs`](#qiskit.quantum_info.Choi.qargs "qiskit.quantum_info.Choi.qargs") | Return the qargs for the operator. |
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| [`rtol`](#qiskit.quantum_info.Choi.rtol "qiskit.quantum_info.Choi.rtol") | Default relative tolerance parameter for float comparisons. |
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### adjoint
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<Function id="qiskit.quantum_info.Choi.adjoint" signature="adjoint()">
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Return the adjoint quantum channel.
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<Admonition title="Note" type="note">
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This is equivalent to the matrix Hermitian conjugate in the [`SuperOp`](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") representation ie. for a channel $\mathcal{E}$, the SuperOp of the adjoint channel $\mathcal{{E}}^\dagger$ is $S_{\mathcal{E}^\dagger} = S_{\mathcal{E}}^\dagger$.
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</Admonition>
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</Function>
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### atol
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<Attribute id="qiskit.quantum_info.Choi.atol">
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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.Choi.compose" signature="compose(other, qargs=None, front=False)">
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Return the operator composition with another Choi.
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**Parameters**
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* **other** ([*Choi*](#qiskit.quantum_info.Choi "qiskit.quantum_info.Choi")) – a Choi 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 Choi.
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**Return type**
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[Choi](#qiskit.quantum_info.Choi "qiskit.quantum_info.Choi")
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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.Choi.dot "qiskit.quantum_info.Choi.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.Choi.dot "qiskit.quantum_info.Choi.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.Choi.conjugate" signature="conjugate()">
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Return the conjugate quantum channel.
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<Admonition title="Note" type="note">
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This is equivalent to the matrix complex conjugate in the [`SuperOp`](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") representation ie. for a channel $\mathcal{E}$, the SuperOp of the conjugate channel $\overline{{\mathcal{{E}}}}$ is $S_{\overline{\mathcal{E}^\dagger}} = \overline{S_{\mathcal{E}}}$.
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</Admonition>
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</Function>
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### copy
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<Function id="qiskit.quantum_info.Choi.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.Choi.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.Choi.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.Choi.dot" signature="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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### expand
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<Function id="qiskit.quantum_info.Choi.expand" signature="expand(other)">
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Return the reverse-order tensor product with another Choi.
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**Parameters**
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**other** ([*Choi*](#qiskit.quantum_info.Choi "qiskit.quantum_info.Choi")) – a Choi 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 Choi, and $b$ is the other Choi.
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**Return type**
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[Choi](#qiskit.quantum_info.Choi "qiskit.quantum_info.Choi")
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</Function>
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### input\_dims
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<Function id="qiskit.quantum_info.Choi.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.Choi.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.Choi.is_cptp" signature="is_cptp(atol=None, rtol=None)">
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Return True if completely-positive trace-preserving (CPTP).
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</Function>
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### is\_tp
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<Function id="qiskit.quantum_info.Choi.is_tp" signature="is_tp(atol=None, rtol=None)">
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Test if a channel is trace-preserving (TP)
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</Function>
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### is\_unitary
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<Function id="qiskit.quantum_info.Choi.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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### num\_qubits
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<Attribute id="qiskit.quantum_info.Choi.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.Choi.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.Choi.power" signature="power(n)">
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Return the power of the quantum channel.
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**Parameters**
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**n** (*float*) – the power exponent.
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**Returns**
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the channel $\mathcal{{E}} ^n$.
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**Return type**
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[SuperOp](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")
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**Raises**
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**QiskitError** – if the input and output dimensions of the SuperOp are not equal.
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<Admonition title="Note" type="note">
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For non-positive or non-integer exponents the power is defined as the matrix power of the [`SuperOp`](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") representation ie. for a channel $\mathcal{{E}}$, the SuperOp of the powered channel $\mathcal{{E}}^\n$ is $S_{{\mathcal{{E}}^n}} = S_{{\mathcal{{E}}}}^n$.
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</Admonition>
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</Function>
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### qargs
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<Attribute id="qiskit.quantum_info.Choi.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.Choi.reshape" signature="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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### rtol
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<Attribute id="qiskit.quantum_info.Choi.rtol">
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Default relative tolerance parameter for float comparisons.
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</Attribute>
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### tensor
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<Function id="qiskit.quantum_info.Choi.tensor" signature="tensor(other)">
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Return the tensor product with another Choi.
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**Parameters**
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**other** ([*Choi*](#qiskit.quantum_info.Choi "qiskit.quantum_info.Choi")) – a Choi 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 Choi, and $b$ is the other Choi.
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**Return type**
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[Choi](#qiskit.quantum_info.Choi "qiskit.quantum_info.Choi")
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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.Choi.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.Choi.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.Choi.transpose" signature="transpose()">
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Return the transpose quantum channel.
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<Admonition title="Note" type="note">
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This is equivalent to the matrix transpose in the [`SuperOp`](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") representation, ie. for a channel $\mathcal{E}$, the SuperOp of the transpose channel $\mathcal{{E}}^T$ is $S_{mathcal{E}^T} = S_{\mathcal{E}}^T$.
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</Admonition>
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</Function>
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</Class>
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