# Cycle Benchmarking (CB)¶

See make_cb() for API documentation.

CB is a fully scalable protocol for estimating the probability of targeted errors that occur across an entire $$n$$-qubit device during a specified clock cycle containing any combination of single gates, parallelized gates, and idle qubits (see arXiv:1902.08543 and arXiv:1907.12976).

Outline of the CB protocol. The cycle of interest (pink) is alternated with random Pauli cycles (blue) in a random measurement basis (green). The process infidelity of the dressed cycle can be inferred by measuring the decay rate of several bases.

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¶

$${e}_{P}$$ -

The total probability that an error acts 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. For example, if an error rate $$e_P=0.1$$ is measured for the qubit label (0, ), then:

$\sum_{R \neq I} \sum_Q e_{R \otimes Q} = 0.1$

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).

The probability of an error satisfies

$e_P = 1 - F_E = (1 + 1/d) r$

where $$F_E$$ is the process fidelity (also known as the entanglement fidelity), $$d$$ is the dimension of the system, and

$r = 1 - \int d\psi \operatorname{Tr}(\psi, E(\psi))$

is the average gate infidelity. Note that the process fidelity is stable under tensor products, whereas the average gate infidelity must be converted to the process fidelity to estimate the fidelity of a tensor product of processes.

$${e}_{ZXZX}$$ -

The sum of the probability of all global errors that act as the subscripted error on the specified qubit labels. For example, if an error rate $$e_X=0.1$$ is measured for the qubit label (0, ), then:

$\sum_Q e_{X \otimes Q} = 0.1$

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: $$e_{X}$$, $$e_{XYYI}$$, $$e_{ZZ}$$, $$e_{XY\otimes YI}$$, $$e_{Z\otimes Z}$$.

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

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¶

 Cycle Benchmarking (CB)¶