379 lines
18 KiB
Plaintext
379 lines
18 KiB
Plaintext
---
|
||
title: SuperOp (v0.26)
|
||
description: API reference for qiskit.quantum_info.SuperOp in qiskit v0.26
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.quantum_info.SuperOp
|
||
---
|
||
|
||
<span id="qiskit-quantum-info-superop" />
|
||
|
||
# qiskit.quantum\_info.SuperOp
|
||
|
||
<Class id="qiskit.quantum_info.SuperOp" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/quantum_info/operators/channel/superop.py" signature="SuperOp(data, input_dims=None, output_dims=None)" modifiers="class">
|
||
Superoperator representation of a quantum channel.
|
||
|
||
The Superoperator representation of a quantum channel $\mathcal{E}$ is a matrix $S$ such that the evolution of a [`DensityMatrix`](qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix") $\rho$ is given by
|
||
|
||
$$
|
||
|\mathcal{E}(\rho)\rangle\!\rangle = S |\rho\rangle\!\rangle
|
||
$$
|
||
|
||
where the double-ket notation $|A\rangle\!\rangle$ denotes a vector formed by stacking the columns of the matrix $A$ *(column-vectorization)*.
|
||
|
||
See reference \[1] for further details.
|
||
|
||
**References**
|
||
|
||
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)
|
||
|
||
Initialize a quantum channel Superoperator operator.
|
||
|
||
**Parameters**
|
||
|
||
* \*\*(\*\***QuantumCircuit or** (*data*) – Instruction or BaseOperator or matrix): data to initialize superoperator.
|
||
* **input\_dims** (*tuple*) – the input subsystem dimensions. \[Default: None]
|
||
* **output\_dims** (*tuple*) – the output subsystem dimensions. \[Default: None]
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if input data cannot be initialized as a superoperator.
|
||
|
||
**Additional Information:**
|
||
|
||
If the input or output dimensions are None, they will be automatically determined from the input data. If the input data is a Numpy array of shape (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.
|
||
|
||
### \_\_init\_\_
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.__init__" signature="__init__(data, input_dims=None, output_dims=None)">
|
||
Initialize a quantum channel Superoperator operator.
|
||
|
||
**Parameters**
|
||
|
||
* \*\*(\*\***QuantumCircuit or** (*data*) – Instruction or BaseOperator or matrix): data to initialize superoperator.
|
||
* **input\_dims** (*tuple*) – the input subsystem dimensions. \[Default: None]
|
||
* **output\_dims** (*tuple*) – the output subsystem dimensions. \[Default: None]
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if input data cannot be initialized as a superoperator.
|
||
|
||
**Additional Information:**
|
||
|
||
If the input or output dimensions are None, they will be automatically determined from the input data. If the input data is a Numpy array of shape (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.
|
||
</Function>
|
||
|
||
## Methods
|
||
|
||
| | |
|
||
| ---------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------- |
|
||
| [`__init__`](#qiskit.quantum_info.SuperOp.__init__ "qiskit.quantum_info.SuperOp.__init__")(data\[, input\_dims, output\_dims]) | Initialize a quantum channel Superoperator operator. |
|
||
| [`adjoint`](#qiskit.quantum_info.SuperOp.adjoint "qiskit.quantum_info.SuperOp.adjoint")() | Return the adjoint quantum channel. |
|
||
| [`compose`](#qiskit.quantum_info.SuperOp.compose "qiskit.quantum_info.SuperOp.compose")(other\[, qargs, front]) | Return the operator composition with another SuperOp. |
|
||
| [`conjugate`](#qiskit.quantum_info.SuperOp.conjugate "qiskit.quantum_info.SuperOp.conjugate")() | Return the conjugate quantum channel. |
|
||
| [`copy`](#qiskit.quantum_info.SuperOp.copy "qiskit.quantum_info.SuperOp.copy")() | Make a deep copy of current operator. |
|
||
| [`dot`](#qiskit.quantum_info.SuperOp.dot "qiskit.quantum_info.SuperOp.dot")(other\[, qargs]) | Return the right multiplied operator self \* other. |
|
||
| [`expand`](#qiskit.quantum_info.SuperOp.expand "qiskit.quantum_info.SuperOp.expand")(other) | Return the reverse-order tensor product with another SuperOp. |
|
||
| [`input_dims`](#qiskit.quantum_info.SuperOp.input_dims "qiskit.quantum_info.SuperOp.input_dims")(\[qargs]) | Return tuple of input dimension for specified subsystems. |
|
||
| [`is_cp`](#qiskit.quantum_info.SuperOp.is_cp "qiskit.quantum_info.SuperOp.is_cp")(\[atol, rtol]) | Test if Choi-matrix is completely-positive (CP) |
|
||
| [`is_cptp`](#qiskit.quantum_info.SuperOp.is_cptp "qiskit.quantum_info.SuperOp.is_cptp")(\[atol, rtol]) | Return True if completely-positive trace-preserving (CPTP). |
|
||
| [`is_tp`](#qiskit.quantum_info.SuperOp.is_tp "qiskit.quantum_info.SuperOp.is_tp")(\[atol, rtol]) | Test if a channel is trace-preserving (TP) |
|
||
| [`is_unitary`](#qiskit.quantum_info.SuperOp.is_unitary "qiskit.quantum_info.SuperOp.is_unitary")(\[atol, rtol]) | Return True if QuantumChannel is a unitary channel. |
|
||
| [`output_dims`](#qiskit.quantum_info.SuperOp.output_dims "qiskit.quantum_info.SuperOp.output_dims")(\[qargs]) | Return tuple of output dimension for specified subsystems. |
|
||
| [`power`](#qiskit.quantum_info.SuperOp.power "qiskit.quantum_info.SuperOp.power")(n) | Return the power of the quantum channel. |
|
||
| [`reshape`](#qiskit.quantum_info.SuperOp.reshape "qiskit.quantum_info.SuperOp.reshape")(\[input\_dims, output\_dims, num\_qubits]) | Return a shallow copy with reshaped input and output subsystem dimensions. |
|
||
| [`tensor`](#qiskit.quantum_info.SuperOp.tensor "qiskit.quantum_info.SuperOp.tensor")(other) | Return the tensor product with another SuperOp. |
|
||
| [`to_instruction`](#qiskit.quantum_info.SuperOp.to_instruction "qiskit.quantum_info.SuperOp.to_instruction")() | Convert to a Kraus or UnitaryGate circuit instruction. |
|
||
| [`to_operator`](#qiskit.quantum_info.SuperOp.to_operator "qiskit.quantum_info.SuperOp.to_operator")() | Try to convert channel to a unitary representation Operator. |
|
||
| [`transpose`](#qiskit.quantum_info.SuperOp.transpose "qiskit.quantum_info.SuperOp.transpose")() | Return the transpose quantum channel. |
|
||
|
||
## Attributes
|
||
|
||
| | |
|
||
| ------------------------------------------------------------------------------------------------ | -------------------------------------------------------------------- |
|
||
| [`atol`](#qiskit.quantum_info.SuperOp.atol "qiskit.quantum_info.SuperOp.atol") | Default absolute tolerance parameter for float comparisons. |
|
||
| [`data`](#qiskit.quantum_info.SuperOp.data "qiskit.quantum_info.SuperOp.data") | Return data. |
|
||
| [`dim`](#qiskit.quantum_info.SuperOp.dim "qiskit.quantum_info.SuperOp.dim") | Return tuple (input\_shape, output\_shape). |
|
||
| [`num_qubits`](#qiskit.quantum_info.SuperOp.num_qubits "qiskit.quantum_info.SuperOp.num_qubits") | Return the number of qubits if a N-qubit operator or None otherwise. |
|
||
| [`qargs`](#qiskit.quantum_info.SuperOp.qargs "qiskit.quantum_info.SuperOp.qargs") | Return the qargs for the operator. |
|
||
| [`rtol`](#qiskit.quantum_info.SuperOp.rtol "qiskit.quantum_info.SuperOp.rtol") | Default relative tolerance parameter for float comparisons. |
|
||
|
||
### adjoint
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.adjoint" signature="adjoint()">
|
||
Return the adjoint quantum channel.
|
||
|
||
<Admonition title="Note" type="note">
|
||
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 $S_{\mathcal{E}^\dagger} = S_{\mathcal{E}}^\dagger$.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### atol
|
||
|
||
<Attribute id="qiskit.quantum_info.SuperOp.atol">
|
||
Default absolute tolerance parameter for float comparisons.
|
||
</Attribute>
|
||
|
||
### compose
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.compose" signature="compose(other, qargs=None, front=False)">
|
||
Return the operator composition with another SuperOp.
|
||
|
||
**Parameters**
|
||
|
||
* **other** ([*SuperOp*](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")) – a SuperOp object.
|
||
* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
|
||
* **front** (*bool*) – If True compose using right operator multiplication, instead of left multiplication \[default: False].
|
||
|
||
**Returns**
|
||
|
||
The composed SuperOp.
|
||
|
||
**Return type**
|
||
|
||
[SuperOp](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
|
||
|
||
<Admonition title="Note" type="note">
|
||
Composition (`&`) by default is defined as left matrix multiplication for matrix operators, while [`dot()`](#qiskit.quantum_info.SuperOp.dot "qiskit.quantum_info.SuperOp.dot") is defined as right matrix multiplication. That is that `A & B == A.compose(B)` is equivalent to `B.dot(A)` when `A` and `B` are of the same type.
|
||
|
||
Setting the `front=True` kwarg changes this to right matrix multiplication and is equivalent to the [`dot()`](#qiskit.quantum_info.SuperOp.dot "qiskit.quantum_info.SuperOp.dot") method `A.dot(B) == A.compose(B, front=True)`.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### conjugate
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.conjugate" signature="conjugate()">
|
||
Return the conjugate quantum channel.
|
||
|
||
<Admonition title="Note" type="note">
|
||
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 $S_{\overline{\mathcal{E}^\dagger}} = \overline{S_{\mathcal{E}}}$.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### copy
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.copy" signature="copy()">
|
||
Make a deep copy of current operator.
|
||
</Function>
|
||
|
||
### data
|
||
|
||
<Attribute id="qiskit.quantum_info.SuperOp.data">
|
||
Return data.
|
||
</Attribute>
|
||
|
||
### dim
|
||
|
||
<Attribute id="qiskit.quantum_info.SuperOp.dim">
|
||
Return tuple (input\_shape, output\_shape).
|
||
</Attribute>
|
||
|
||
### dot
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.dot" signature="dot(other, qargs=None)">
|
||
Return the right multiplied operator self \* other.
|
||
|
||
**Parameters**
|
||
|
||
* **other** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator object.
|
||
* **qargs** (*list or None*) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).
|
||
|
||
**Returns**
|
||
|
||
The right matrix multiplied Operator.
|
||
|
||
**Return type**
|
||
|
||
[Operator](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")
|
||
</Function>
|
||
|
||
### expand
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.expand" signature="expand(other)">
|
||
Return the reverse-order tensor product with another SuperOp.
|
||
|
||
**Parameters**
|
||
|
||
**other** ([*SuperOp*](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")) – a SuperOp object.
|
||
|
||
**Returns**
|
||
|
||
**the tensor product $b \otimes a$, where $a$**
|
||
|
||
is the current SuperOp, and $b$ is the other SuperOp.
|
||
|
||
**Return type**
|
||
|
||
[SuperOp](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")
|
||
</Function>
|
||
|
||
### input\_dims
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.input_dims" signature="input_dims(qargs=None)">
|
||
Return tuple of input dimension for specified subsystems.
|
||
</Function>
|
||
|
||
### is\_cp
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.is_cp" signature="is_cp(atol=None, rtol=None)">
|
||
Test if Choi-matrix is completely-positive (CP)
|
||
</Function>
|
||
|
||
### is\_cptp
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.is_cptp" signature="is_cptp(atol=None, rtol=None)">
|
||
Return True if completely-positive trace-preserving (CPTP).
|
||
</Function>
|
||
|
||
### is\_tp
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.is_tp" signature="is_tp(atol=None, rtol=None)">
|
||
Test if a channel is trace-preserving (TP)
|
||
</Function>
|
||
|
||
### is\_unitary
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.is_unitary" signature="is_unitary(atol=None, rtol=None)">
|
||
Return True if QuantumChannel is a unitary channel.
|
||
</Function>
|
||
|
||
### num\_qubits
|
||
|
||
<Attribute id="qiskit.quantum_info.SuperOp.num_qubits">
|
||
Return the number of qubits if a N-qubit operator or None otherwise.
|
||
</Attribute>
|
||
|
||
### output\_dims
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.output_dims" signature="output_dims(qargs=None)">
|
||
Return tuple of output dimension for specified subsystems.
|
||
</Function>
|
||
|
||
### power
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.power" signature="power(n)">
|
||
Return the power of the quantum channel.
|
||
|
||
**Parameters**
|
||
|
||
**n** (*float*) – the power exponent.
|
||
|
||
**Returns**
|
||
|
||
the channel $\mathcal{{E}} ^n$.
|
||
|
||
**Return type**
|
||
|
||
[SuperOp](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if the input and output dimensions of the SuperOp are not equal.
|
||
|
||
<Admonition title="Note" type="note">
|
||
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 $S_{{\mathcal{{E}}^n}} = S_{{\mathcal{{E}}}}^n$.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### qargs
|
||
|
||
<Attribute id="qiskit.quantum_info.SuperOp.qargs">
|
||
Return the qargs for the operator.
|
||
</Attribute>
|
||
|
||
### reshape
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.reshape" signature="reshape(input_dims=None, output_dims=None, num_qubits=None)">
|
||
Return a shallow copy with reshaped input and output subsystem dimensions.
|
||
|
||
**Parameters**
|
||
|
||
* **input\_dims** (*None or tuple*) – new subsystem input dimensions. If None the original input dims will be preserved \[Default: None].
|
||
* **output\_dims** (*None or tuple*) – new subsystem output dimensions. If None the original output dims will be preserved \[Default: None].
|
||
* **num\_qubits** (*None or int*) – reshape to an N-qubit operator \[Default: None].
|
||
|
||
**Returns**
|
||
|
||
returns self with reshaped input and output dimensions.
|
||
|
||
**Return type**
|
||
|
||
BaseOperator
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.
|
||
</Function>
|
||
|
||
### rtol
|
||
|
||
<Attribute id="qiskit.quantum_info.SuperOp.rtol">
|
||
Default relative tolerance parameter for float comparisons.
|
||
</Attribute>
|
||
|
||
### tensor
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.tensor" signature="tensor(other)">
|
||
Return the tensor product with another SuperOp.
|
||
|
||
**Parameters**
|
||
|
||
**other** ([*SuperOp*](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")) – a SuperOp object.
|
||
|
||
**Returns**
|
||
|
||
**the tensor product $a \otimes b$, where $a$**
|
||
|
||
is the current SuperOp, and $b$ is the other SuperOp.
|
||
|
||
**Return type**
|
||
|
||
[SuperOp](#qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp")
|
||
|
||
<Admonition title="Note" type="note">
|
||
The tensor product can be obtained using the `^` binary operator. Hence `a.tensor(b)` is equivalent to `a ^ b`.
|
||
</Admonition>
|
||
</Function>
|
||
|
||
### to\_instruction
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.to_instruction" signature="to_instruction()">
|
||
Convert to a Kraus or UnitaryGate circuit instruction.
|
||
|
||
If the channel is unitary it will be added as a unitary gate, otherwise it will be added as a kraus simulator instruction.
|
||
|
||
**Returns**
|
||
|
||
A kraus instruction for the channel.
|
||
|
||
**Return type**
|
||
|
||
[qiskit.circuit.Instruction](qiskit.circuit.Instruction "qiskit.circuit.Instruction")
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – if input data is not an N-qubit CPTP quantum channel.
|
||
</Function>
|
||
|
||
### to\_operator
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.to_operator" signature="to_operator()">
|
||
Try to convert channel to a unitary representation Operator.
|
||
</Function>
|
||
|
||
### transpose
|
||
|
||
<Function id="qiskit.quantum_info.SuperOp.transpose" signature="transpose()">
|
||
Return the transpose quantum channel.
|
||
|
||
<Admonition title="Note" type="note">
|
||
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 $S_{mathcal{E}^T} = S_{\mathcal{E}}^T$.
|
||
</Admonition>
|
||
</Function>
|
||
</Class>
|
||
|