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# LinCombQGT

qiskit.algorithms.gradients.LinCombQGT(estimator, phase_fix=True, derivative_type=DerivativeType.COMPLEX, options=None) GitHub(opens in a new tab)

Bases: BaseQGT

Computes the Quantum Geometric Tensor (QGT) given a pure, parameterized quantum state.

This method employs a linear combination of unitaries [1].

Reference:

[1]: Schuld et al., “Evaluating analytic gradients on quantum hardware” (2018).

arXiv:1811.11184(opens in a new tab)

Parameters

• estimator (BaseEstimator) – The estimator used to compute the QGT.

• phase_fix (bool(opens in a new tab)) – Whether to calculate the second term (phase fix) of the QGT, which is $\langle\partial_i \psi | \psi \rangle \langle\psi | \partial_j \psi \rangle$. Default to True.

• derivative_type (DerivativeType) –

The type of derivative. Can be either DerivativeType.REAL DerivativeType.IMAG, or DerivativeType.COMPLEX. Defaults to DerivativeType.REAL.

• DerivativeType.REAL computes
$\mathrm{Re(QGT)}_{ij}= \mathrm{Re}[\langle \partial_i \psi | \partial_j \psi \rangle - \langle\partial_i \psi | \psi \rangle \langle\psi | \partial_j \psi \rangle].$
• DerivativeType.IMAG computes
$\mathrm{Re(QGT)}_{ij}= \mathrm{Im}[\langle \partial_i \psi | \partial_j \psi \rangle - \langle\partial_i \psi | \psi \rangle \langle\psi | \partial_j \psi \rangle].$
• DerivativeType.COMPLEX computes
$\mathrm{QGT}_{ij}= [\langle \partial_i \psi | \partial_j \psi \rangle - \langle\partial_i \psi | \psi \rangle \langle\psi | \partial_j \psi \rangle].$
• options (Options | None) – Backend runtime options used for circuit execution. The order of priority is: options in run method > QGT’s default options > primitive’s default setting. Higher priority setting overrides lower priority setting.

## Attributes

### SUPPORTED_GATES

= ['rx', 'ry', 'rz', 'rzx', 'rzz', 'ryy', 'rxx', 'cx', 'cy', 'cz', 'ccx', 'swap', 'iswap', 'h', 't', 's', 'sdg', 'x', 'y', 'z']

### derivative_type

The derivative type.

### options

Return the union of estimator options setting and QGT default options, where, if the same field is set in both, the QGT’s default options override the primitive’s default setting.

Returns

The QGT default + estimator options.

## Methods

### run

run(circuits, parameter_values, parameters=None, **options)

Run the job of the QGTs on the given circuits.

Parameters

• circuits (Sequence[QuantumCircuit]) – The list of quantum circuits to compute the QGTs.
• parameter_values (Sequence[Sequence[float(opens in a new tab)]]) – The list of parameter values to be bound to the circuit.
• parameters (Sequence[Sequence[Parameter] | None] | None) – The sequence of parameters to calculate only the QGTs of the specified parameters. Each sequence of parameters corresponds to a circuit in circuits. Defaults to None, which means that the QGTs of all parameters in each circuit are calculated.
• options – Primitive backend runtime options used for circuit execution. The order of priority is: options in run method > QGT’s default options > primitive’s default setting. Higher priority setting overrides lower priority setting.

Returns

The job object of the QGTs of the expectation values. The i-th result corresponds to circuits[i] evaluated with parameters bound as parameter_values[i].

Raises

ValueError(opens in a new tab) – Invalid arguments are given.

Return type

AlgorithmJob

### update_default_options

update_default_options(**options)

Update the gradient’s default options setting.

Parameters

**options – The fields to update the default options.