# K-body Noise Reconstruction (KNR)

*See* `make_knr()`

*for API documentation.*

KNR is a protocol for estimating the probability distribution of the errors afflicting the systems targeted by a subset of the gates or idle qubits in the cycle. These probability distributions are marginals of the global distribution of all errors that occur during a cycle. The probability of a specific marginal error in the reconstructed distribution is the sum of the probabilities of all global errors that have the same action on the specified set of systems [10].

Examples of terms that may be returned from the analysis are as follows. These descriptions are also available via mouse-overs when running True-Q™ in a Jupyter or Colab notebook.

## Estimated Parameters

- \(e_{\{X,Y\}{\otimes}IZ}\) -
The sum of the probability of all global errors that act as one of the elements of the subscripted set on the specified labels during a dressed cycle of interest if the noise is stochastic, where a dressed cycle is a cycle composed with a random cycle of local gates. Note that the errors in the set are mixed by the action of the gate and so cannot be distinguished by KNR. For example, if an error rate \(e_{\{X,Y\}}=0.1\) is measured for the qubit label

`(0, )`

, then:\[\sum_Q e_{X \otimes Q} + e_{Y \otimes Q} = 0.1,\]where the sum is over all Pauli terms acting on the other qubits.

Because this protocol uses the same twirling group as randomized compiling (RC), estimates of this parameter accurately predict the in-situ characteristics of this cycle when present in a circuit that is run using RC.

Examples: \(e_{\{X\}}\), \(e_{\{XYYI\}}\), \(e_{\{ZZ\}}\), \(e_{\{XY\} \otimes \{YI\}}\), \(e_{\{Z\}\otimes \{Z\}}\), \(e_{\{X, Y\} \otimes \{I\}}\).

- \({A}_{YZXX}\) -
SPAM parameter of the exponential decay \(Ap^m\) for the given Pauli term.

Examples: \(A_X\), \(A_{XYYI}\), \(A_{ZZ}\), describing the \(A\) parameter for each of the respective Paulis.

- \({p}_{YZXX}\) -
Decay parameter of the exponential decay \(Ap^m\) for the given Pauli term.

Examples: \(p_X\), \(p_{XYYI}\), \(p_{ZZ}\), describing the \(p\) parameter for each of the respective Paulis.