122 lines
4.9 KiB
Plaintext
122 lines
4.9 KiB
Plaintext
---
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title: NaturalGradient
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description: API reference for qiskit.opflow.gradients.NaturalGradient
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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.opflow.gradients.NaturalGradient
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---
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# NaturalGradient
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<Class id="qiskit.opflow.gradients.NaturalGradient" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.21/qiskit/opflow/gradients/natural_gradient.py" signature="NaturalGradient(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)" modifiers="class">
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Bases: [`qiskit.opflow.gradients.gradient_base.GradientBase`](qiskit.opflow.gradients.GradientBase "qiskit.opflow.gradients.gradient_base.GradientBase")
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Convert an operator expression to the first-order gradient.
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Given an ill-posed inverse problem
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> x = arg min\{||Ax-C||^2} (1)
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one can use regularization schemes can be used to stabilize the system and find a numerical solution
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> x\_lambda = arg min\{||Ax-C||^2 + lambda\*R(x)} (2)
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where R(x) represents the penalization term.
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**Parameters**
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* **grad\_method** (`Union`\[`str`, [`CircuitGradient`](qiskit.opflow.gradients.CircuitGradient "qiskit.opflow.gradients.circuit_gradients.circuit_gradient.CircuitGradient")]) – The method used to compute the state gradient. Can be either `'param_shift'` or `'lin_comb'` or `'fin_diff'`.
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* **qfi\_method** (`Union`\[`str`, [`CircuitQFI`](qiskit.opflow.gradients.CircuitQFI "qiskit.opflow.gradients.circuit_qfis.circuit_qfi.CircuitQFI")]) – The method used to compute the QFI. Can be either `'lin_comb_full'` or `'overlap_block_diag'` or `'overlap_diag'`.
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* **regularization** (`Optional`\[`str`]) – Use the following regularization with a least square method to solve the underlying system of linear equations Can be either None or `'ridge'` or `'lasso'` or `'perturb_diag'` `'ridge'` and `'lasso'` use an automatic optimal parameter search If regularization is None but the metric is ill-conditioned or singular then a least square solver is used without regularization
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* **kwargs** (*dict*) – Optional parameters for a CircuitGradient
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## Methods Defined Here
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### convert
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<Function id="qiskit.opflow.gradients.NaturalGradient.convert" signature="NaturalGradient.convert(operator, params=None)">
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**Parameters**
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* **operator** ([`OperatorBase`](qiskit.opflow.OperatorBase "qiskit.opflow.operator_base.OperatorBase")) – The operator we are taking the gradient of.
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* **params** (`Union`\[[`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.parametervector.ParameterVector"), [`ParameterExpression`](qiskit.circuit.ParameterExpression "qiskit.circuit.parameterexpression.ParameterExpression"), `List`\[[`ParameterExpression`](qiskit.circuit.ParameterExpression "qiskit.circuit.parameterexpression.ParameterExpression")], `None`]) – The parameters we are taking the gradient with respect to. If not explicitly passed, they are inferred from the operator and sorted by name.
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**Return type**
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[`OperatorBase`](qiskit.opflow.OperatorBase "qiskit.opflow.operator_base.OperatorBase")
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**Returns**
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An operator whose evaluation yields the NaturalGradient.
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**Raises**
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* **TypeError** – If `operator` does not represent an expectation value or the quantum state is not `CircuitStateFn`.
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* **ValueError** – If `params` contains a parameter not present in `operator`.
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* **ValueError** – If `operator` is not parameterized.
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</Function>
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### nat\_grad\_combo\_fn
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<Function id="qiskit.opflow.gradients.NaturalGradient.nat_grad_combo_fn" signature="NaturalGradient.nat_grad_combo_fn(x, regularization=None)" modifiers="static">
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Natural Gradient Function Implementation.
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**Parameters**
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* **x** (`tuple`) – Iterable consisting of Gradient, Quantum Fisher Information.
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* **regularization** (`Optional`\[`str`]) – Regularization method.
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**Return type**
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`ndarray`
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**Returns**
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Natural Gradient.
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**Raises**
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**ValueError** – If the gradient has imaginary components that are non-negligible.
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</Function>
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## Attributes
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### grad\_method
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<Attribute id="qiskit.opflow.gradients.NaturalGradient.grad_method">
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Returns `CircuitGradient`.
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**Return type**
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[`CircuitGradient`](qiskit.opflow.gradients.CircuitGradient "qiskit.opflow.gradients.circuit_gradients.circuit_gradient.CircuitGradient")
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**Returns**
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`CircuitGradient`.
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</Attribute>
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### qfi\_method
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<Attribute id="qiskit.opflow.gradients.NaturalGradient.qfi_method">
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Returns `CircuitQFI`.
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Returns: `CircuitQFI`.
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**Return type**
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[`CircuitQFI`](qiskit.opflow.gradients.CircuitQFI "qiskit.opflow.gradients.circuit_qfis.circuit_qfi.CircuitQFI")
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</Attribute>
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### regularization
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<Attribute id="qiskit.opflow.gradients.NaturalGradient.regularization">
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Returns the regularization option.
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Returns: the regularization option.
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**Return type**
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`Optional`\[`str`]
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</Attribute>
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</Class>
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