160 lines
9.2 KiB
Plaintext
160 lines
9.2 KiB
Plaintext
---
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title: NaturalGradient
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description: API reference for qiskit.aqua.operators.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.aqua.operators.gradients.NaturalGradient
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---
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# qiskit.aqua.operators.gradients.NaturalGradient
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<Class id="qiskit.aqua.operators.gradients.NaturalGradient" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.9/qiskit/aqua/operators/gradients/natural_gradient.py" signature="NaturalGradient(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)" modifiers="class">
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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`]) – 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`]) – 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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### \_\_init\_\_
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<Function id="qiskit.aqua.operators.gradients.NaturalGradient.__init__" signature="__init__(grad_method='lin_comb', qfi_method='lin_comb_full', regularization=None, **kwargs)">
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**Parameters**
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* **grad\_method** (`Union`\[`str`, `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`]) – 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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</Function>
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## Methods
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| | |
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| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------- |
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| [`__init__`](#qiskit.aqua.operators.gradients.NaturalGradient.__init__ "qiskit.aqua.operators.gradients.NaturalGradient.__init__")(\[grad\_method, qfi\_method, …]) | **type grad\_method**`Union`\[`str`, `CircuitGradient`] |
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| [`convert`](#qiskit.aqua.operators.gradients.NaturalGradient.convert "qiskit.aqua.operators.gradients.NaturalGradient.convert")(operator\[, params]) | **type operator**`OperatorBase` |
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| [`gradient_wrapper`](#qiskit.aqua.operators.gradients.NaturalGradient.gradient_wrapper "qiskit.aqua.operators.gradients.NaturalGradient.gradient_wrapper")(operator, bind\_params\[, …]) | Get a callable function which provides the respective gradient, Hessian or QFI for given parameter values. |
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| [`parameter_expression_grad`](#qiskit.aqua.operators.gradients.NaturalGradient.parameter_expression_grad "qiskit.aqua.operators.gradients.NaturalGradient.parameter_expression_grad")(param\_expr, param) | Get the derivative of a parameter expression w\.r.t. |
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## Attributes
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| | |
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| ---------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------- |
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| [`grad_method`](#qiskit.aqua.operators.gradients.NaturalGradient.grad_method "qiskit.aqua.operators.gradients.NaturalGradient.grad_method") | Returns `CircuitGradient`. |
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| [`qfi_method`](#qiskit.aqua.operators.gradients.NaturalGradient.qfi_method "qiskit.aqua.operators.gradients.NaturalGradient.qfi_method") | Returns `CircuitQFI`. |
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| [`regularization`](#qiskit.aqua.operators.gradients.NaturalGradient.regularization "qiskit.aqua.operators.gradients.NaturalGradient.regularization") | Returns the regularization option. |
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### convert
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<Function id="qiskit.aqua.operators.gradients.NaturalGradient.convert" signature="convert(operator, params=None)">
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**Parameters**
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* **operator** (`OperatorBase`) – The operator we are taking the gradient of.
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* **params** (`Union`\[`ParameterVector`, `ParameterExpression`, `List`\[`ParameterExpression`], `None`]) – The parameters we are taking the gradient with respect to.
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**Return type**
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`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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</Function>
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### grad\_method
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<Attribute id="qiskit.aqua.operators.gradients.NaturalGradient.grad_method">
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Returns `CircuitGradient`.
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**Return type**
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`CircuitGradient`
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**Returns**
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`CircuitGradient`.
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</Attribute>
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### gradient\_wrapper
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<Function id="qiskit.aqua.operators.gradients.NaturalGradient.gradient_wrapper" signature="gradient_wrapper(operator, bind_params, grad_params=None, backend=None)">
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Get a callable function which provides the respective gradient, Hessian or QFI for given parameter values. This callable can be used as gradient function for optimizers.
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**Parameters**
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* **operator** (`OperatorBase`) – The operator for which we want to get the gradient, Hessian or QFI.
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* **bind\_params** (`Union`\[`ParameterExpression`, `ParameterVector`, `List`\[`ParameterExpression`]]) – The operator parameters to which the parameter values are assigned.
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* **grad\_params** (`Union`\[`ParameterExpression`, `ParameterVector`, `List`\[`ParameterExpression`], `Tuple`\[`ParameterExpression`, `ParameterExpression`], `List`\[`Tuple`\[`ParameterExpression`, `ParameterExpression`]], `None`]) – The parameters with respect to which we are taking the gradient, Hessian or QFI. If grad\_params = None, then grad\_params = bind\_params
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* **backend** (`Union`\[`BaseBackend`, `QuantumInstance`, `None`]) – The quantum backend or QuantumInstance to use to evaluate the gradient, Hessian or QFI.
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**Returns**
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Function to compute a gradient, Hessian or QFI. The function takes an iterable as argument which holds the parameter values.
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**Return type**
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callable(param\_values)
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</Function>
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### parameter\_expression\_grad
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<Function id="qiskit.aqua.operators.gradients.NaturalGradient.parameter_expression_grad" signature="parameter_expression_grad(param_expr, param)" modifiers="static">
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Get the derivative of a parameter expression w\.r.t. the given parameter.
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**Parameters**
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* **param\_expr** (`ParameterExpression`) – The Parameter Expression for which we compute the derivative
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* **param** (`ParameterExpression`) – Parameter w\.r.t. which we want to take the derivative
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**Return type**
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`Union`\[`ParameterExpression`, `float`]
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**Returns**
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ParameterExpression representing the gradient of param\_expr w\.r.t. param
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</Function>
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### qfi\_method
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<Attribute id="qiskit.aqua.operators.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`
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</Attribute>
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### regularization
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<Attribute id="qiskit.aqua.operators.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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