What happens when I use LRE?

As shown in the figure below, LRE works in two steps, layerwise noise scaling and extrapolation.

The noise-scaled circuits are created through the functions in mitiq.lre.multivariate_scaling.layerwise_folding while the error-mitigated expectation value is estimated by using the functions in mitiq.lre.inference.multivariate_richardson.

The diagram shows the workflow of the layerwise Richardson extrapolation (LRE) in Mitiq.

The first step involves generating and executing layerwise noise-scaled quantum circuits.

• The user provides a QPROGRAM i.e. a frontend supported quantum circuit.

• Mitiq generates a set of layerwise noise-scaled circuits by applying unitary folding based on a set of pre-determined scale factor vectors.

The noise-scaled circuits are then executed on a backend, obtaining a set of noisy expectation values.

The second step involves inferring the error mitigated expectation value from the measured results through multivariate richardson extrapolation.

The function execute_with_lre() accomplishes both steps behind the scenes to estimate the error mitigate expectation value. Additional information is available in How do I use LRE?. The linked page also has a section demonstrating how to apply each step individually.