pygsti.tools.rbtheory.L_matrix

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pygsti.tools.rbtheory.L_matrix#

L_matrix(model, target_model, weights=None)#

Constructs a generalization of the ‘L-matrix’ linear operator on superoperators.

From Proctor et al Phys. Rev. Lett. 119, 130502 (2017), the ‘L-matrix’ is represented as a matrix via the “stack” operation. This eigenvalues of this matrix describe the decay constant (or constants) in an RB decay curve for an RB protocol whereby random elements of the provided model are sampled according to the weights probability distribution over the model. So, this facilitates predictions of Clifford RB and direct RB decay curves.

Parameters:

  • model (Model) – The RB model. This is not necessarily the set of physical primitives – it is the model randomly sampled over in the RB protocol (e.g., the Cliffords).

  • target_model (Model) – The target model corresponding to model. This function is not invariant under swapping model and target_model: this Model must be the target model, and should consistent of perfect gates.

  • weights (dict, optional) – If not None, a dictionary of floats, whereby the keys are the gates in model and the values are the unnormalized probabilities to apply each gate at each stage of the RB protocol. If not None, the values in weights must all be non-negative, and they must not all be zero. Because, when divided by their sum, they must be a valid probability distribution. If None, the weighting defaults to an equal weighting on all gates, as this is used in many RB protocols (e.g., Clifford RB). But, this weighting is flexible in the “direct RB” protocol.

Returns:

L – A weighted version of the L operator from Proctor et al Phys. Rev. Lett. 119, 130502 (2017), represented as a matrix using the ‘stacking’ convention.

Return type:

float

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