# 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 (see arXiv:1907.12976).

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.

The assumption that the noise is stochastic can be enforced using randomized compiling, so that the probability of an error accurately characterizes errors in circuits run using randomized compiling. The probability of an error can also be used as a heuristic for the performance of circuits run without randomized compiling, however, the resulting predictions are substantially less accurate for even small coherent or calibration errors (as a percentage of the fidelity).

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.

## Examples¶

 K-body Noise Reconstruction (KNR)¶