# Noise Reconstruction (NR)¶

The effective noise under any cycle, under both Cycle Benchmarking (CB) and Randomized Compiling (RC) protocols, is a stochastic channel of the form,

$\mathcal{E}(\rho) = \sum_P \mu(P) P \rho P^\dagger$

for some probability distribution $$\mu$$ over the $$N$$-qubit Pauli group.

Through noise reconstruction (NR), we can reconstruct the probability distribution $$\mu$$ using carefully targeted Cycle Benchmarking (CB) diagnostic sequences with additional post-processing.

We have two noise reconstruction protocols:

K-body Noise Reconstruction (KNR)

Performs noise reconstruction on various subsets of qudits which are most relevant to the cycle being benchmarked, returning error probabilities for every Pauli in each subset. See make_knr() for details.

Targeted Noise Reconstruction (TMR)

Performs noise reconstruction for a targeted set of Pauli errors, returning error probabilities for user-specified Pauli errors. See make_tnr() for details.