LinCombQGT

class LinCombQGT(estimator, phase_fix=True, derivative_type=DerivativeType.COMPLEX, options=None)

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 (BaseEstimator) -- 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

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

• 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.

Methods

run	Run the job of the QGTs on the given circuits.
update_default_options	Update the gradient's default options 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.