# Stochastic Calibration (SC)

See make_sc() for API documentation.

SC is a protocol providing a quickly measurable objective function to optimize the fidelity of a clock cycle containing any combination of gates and idle qubits.

It is nearly identical to cycle benchmarking (CB). The only difference is that in SC measurement bases (specified as eigenbases of Pauli operators) are explicitly chosen rather than randomly sampled.

The measurement bases to be characterized should be selected so that they anticommute with some error(s) which are of concern so that the error(s) contribute(s) to the element of the process matrix corresponding to the Pauli decay.

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

$$f^{(20)}_{YZXX}$$ -

The SC protocol measures how fast the non-identity Pauli of the initial density matrix

$\rho = \mathbb{I}/d + P/d$

decays under the noise model of the system, where $$P$$ is a user-selected multi-qubit Pauli operator. The value of this parameter is an estimate of the coefficient of $$P/d$$ after $$m$$ applications of the cycle of interest, interleaved with random cycles. It includes both SPAM and gate errors.

$${A}_{YZXX}$$ -

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.