156 lines
6.6 KiB
Plaintext
156 lines
6.6 KiB
Plaintext
---
|
||
title: TomographyFitter
|
||
description: API reference for qiskit.ignis.verification.TomographyFitter
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.ignis.verification.TomographyFitter
|
||
---
|
||
|
||
# TomographyFitter
|
||
|
||
<Class id="qiskit.ignis.verification.TomographyFitter" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-ignis/tree/stable/0.7/qiskit/ignis/verification/tomography/fitters/base_fitter.py" signature="TomographyFitter(result, circuits, meas_basis='Pauli', prep_basis='Pauli')" modifiers="class">
|
||
Bases: `object`
|
||
|
||
Base maximum-likelihood estimate tomography fitter class
|
||
|
||
Initialize tomography fitter with experimental data.
|
||
|
||
**Parameters**
|
||
|
||
* **result** (`Union`\[`Result`, `List`\[`Result`]]) – a Qiskit Result object obtained from executing tomography circuits.
|
||
* **circuits** (`Union`\[`List`\[`QuantumCircuit`], `List`\[`str`]]) – a list of circuits or circuit names to extract count information from the result object.
|
||
* **meas\_basis** (`Union`\[`TomographyBasis`, `str`]) – (default: ‘Pauli’) A function to return measurement operators corresponding to measurement outcomes. See Additional Information.
|
||
* **prep\_basis** (`Union`\[`TomographyBasis`, `str`]) – (default: ‘Pauli’) A function to return preparation operators. See Additional Information
|
||
|
||
## Methods
|
||
|
||
### add\_data
|
||
|
||
<Function id="qiskit.ignis.verification.TomographyFitter.add_data" signature="TomographyFitter.add_data(results, circuits)">
|
||
Add tomography data from a Qiskit Result object.
|
||
|
||
**Parameters**
|
||
|
||
* **results** (`List`\[`Result`]) – The results obtained from executing tomography circuits.
|
||
* **circuits** (`List`\[`Union`\[`QuantumCircuit`, `str`]]) – circuits or circuit names to extract count information from the result object.
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – In case some of the tomography data is not found in the results
|
||
</Function>
|
||
|
||
### fit
|
||
|
||
<Function id="qiskit.ignis.verification.TomographyFitter.fit" signature="TomographyFitter.fit(method='auto', standard_weights=True, beta=0.5, psd=True, trace=None, trace_preserving=False, **kwargs)">
|
||
Reconstruct a quantum state using CVXPY convex optimization.
|
||
|
||
**Fitter method**
|
||
|
||
The `'cvx'` fitter method uses the CVXPY convex optimization package with a SDP solver. The `'lstsq'` method uses least-squares fitting. The `'auto'` method will use `'cvx'` if the both the CVXPY and a suitable SDP solver packages are found on the system, otherwise it will default to `'lstsq'`.
|
||
|
||
**Objective function**
|
||
|
||
This fitter solves the constrained least-squares minimization: minimize: $||a \cdot x - b ||_2$
|
||
|
||
subject to:
|
||
|
||
> * $x \succeq 0$
|
||
> * $\text{trace}(x) = 1$
|
||
|
||
where:
|
||
|
||
> * a is the matrix of measurement operators $a[i] = \text{vec}(M_i).H$
|
||
> * b is the vector of expectation value data for each projector $b[i] \sim \text{Tr}[M_i.H \cdot x] = (a \cdot x)[i]$
|
||
> * x is the vectorized density matrix to be fitted
|
||
|
||
**PSD constraint**
|
||
|
||
The PSD keyword constrains the fitted matrix to be postive-semidefinite. For the `lstsq` fitter method the fitted matrix is rescaled using the method proposed in Reference \[1]. For the `cvx` fitter method the convex constraint makes the optimization problem a SDP. If PSD=False the fitted matrix will still be constrained to be Hermitian, but not PSD. In this case the optimization problem becomes a SOCP.
|
||
|
||
**Trace constraint**
|
||
|
||
The trace keyword constrains the trace of the fitted matrix. If trace=None there will be no trace constraint on the fitted matrix. This constraint should not be used for process tomography and the trace preserving constraint should be used instead.
|
||
|
||
**CVXPY Solvers:**
|
||
|
||
Various solvers can be called in CVXPY using the solver keyword argument. If `psd=True` an SDP solver is required other an SOCP solver is required. See the [CVXPY documentation](https://www.cvxpy.org/tutorial/advanced/index.html#solve-method-options) for more information on solvers. Note that the default SDP solver (‘SCS’) distributed with CVXPY will not be used for the `'auto'` method due its reduced accuracy compared to other solvers. When using the `'cvx'` method we strongly recommend installing one of the other supported SDP solvers.
|
||
|
||
References:
|
||
|
||
#### \[1] J Smolin, JM Gambetta, G Smith, Phys. Rev. Lett. 108, 070502
|
||
|
||
(2012). Open access: [arXiv:1106.5458](https://arxiv.org/abs/1106.5458) \[quant-ph].
|
||
|
||
**Parameters**
|
||
|
||
* **method** (`str`) – The fitter method ‘auto’, ‘cvx’ or ‘lstsq’.
|
||
* **standard\_weights** (`bool`) – (default: True) Apply weights to tomography data based on count probability
|
||
* **beta** (`float`) – hedging parameter for converting counts to probabilities
|
||
* **psd** (`bool`) – Enforced the fitted matrix to be positive semidefinite.
|
||
* **trace** (`Optional`\[`int`]) – trace constraint for the fitted matrix.
|
||
* **trace\_preserving** (`bool`) – Enforce the fitted matrix to be trace preserving when fitting a Choi-matrix in quantum process tomography. Note this method does not apply for ‘lstsq’ fitter method.
|
||
* **\*\*kwargs** – kwargs for fitter method.
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – In case the fitting method is unrecognized.
|
||
|
||
**Return type**
|
||
|
||
`array`
|
||
|
||
**Returns**
|
||
|
||
The fitted matrix rho that minimizes $||\text{basis_matrix} * \text{vec(rho)} - \text{data}||_2$.
|
||
</Function>
|
||
|
||
### set\_measure\_basis
|
||
|
||
<Function id="qiskit.ignis.verification.TomographyFitter.set_measure_basis" signature="TomographyFitter.set_measure_basis(basis)">
|
||
Set the measurement basis
|
||
|
||
**Parameters**
|
||
|
||
**basis** (`Union`\[`TomographyBasis`, `str`]) – measurement basis
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – In case of invalid measurement or preparation basis.
|
||
</Function>
|
||
|
||
### set\_preparation\_basis
|
||
|
||
<Function id="qiskit.ignis.verification.TomographyFitter.set_preparation_basis" signature="TomographyFitter.set_preparation_basis(basis)">
|
||
Set the preparation basis function
|
||
|
||
**Parameters**
|
||
|
||
**basis** (`Union`\[`TomographyBasis`, `str`]) – preparation basis
|
||
|
||
**Raises**
|
||
|
||
**QiskitError** – in case the basis has no preperation data
|
||
</Function>
|
||
|
||
## Attributes
|
||
|
||
### data
|
||
|
||
<Attribute id="qiskit.ignis.verification.TomographyFitter.data">
|
||
Return tomography data
|
||
</Attribute>
|
||
|
||
### measure\_basis
|
||
|
||
<Attribute id="qiskit.ignis.verification.TomographyFitter.measure_basis">
|
||
Return the tomography measurement basis.
|
||
</Attribute>
|
||
|
||
### preparation\_basis
|
||
|
||
<Attribute id="qiskit.ignis.verification.TomographyFitter.preparation_basis">
|
||
Return the tomography preparation basis.
|
||
</Attribute>
|
||
</Class>
|
||
|