LinCombQGT

class LinCombQGT(estimator, phase_fix=True, derivative_type=DerivativeType.COMPLEX, precision=None, *, transpiler=None, transpiler_options=None)[source]

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

Parameters:

  • estimator (BaseEstimatorV2) – The estimator used to compute the QGT.

  • phase_fix (bool) – 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

    \[\mathrm{QGT}_{ij}= [\langle \partial_i \psi | \partial_j \psi \rangle - \langle\partial_i \psi | \psi \rangle \langle\psi | \partial_j \psi \rangle].\]

  • precision (float | None) – Precision to be used by the underlying Estimator. If provided, this number takes precedence over the default precision of the primitive. If None, the default precision of the primitive is used. It will also be used to instantiate the internal gradient.

  • transpiler (Transpiler | None) – An optional object with a run method allowing to transpile the circuits that are produced by the internal gradient of this algorithm. If set to None, these won’t be transpiled.

  • transpiler_options (dict[str, Any] | None) – A dictionary of options to be passed to the transpiler’s run method as keyword arguments.

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.

precision

Return the precision used by the run method of the Estimator primitive. If None, the default precision of the primitive is used.

Returns:

The default precision.

Methods

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

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]]) – 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.

  • precision (float | Sequence[float] | None) – Precision to be used by the underlying Estimator. If a single float is provided, this number will be used for all circuits. If a sequence of floats is provided, they will be used on a per-circuit basis. If not set, the gradient’s default precision will be used for all circuits, and if that is None (not set) then the underlying primitive’s (default) precision will be used for all circuits.

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 – Invalid arguments are given.

Return type:

AlgorithmJob