Editing Standard Randomised Benchmarking (section)

==Notation==
* <math>p</math>: Depolarizing parameter
* <math>d</math>: Dimension of Hilbert space
* <math>F_{avg}</math>: Average fidelity, <math>F_{avg} = p + \frac{1-p}{d}</math>
* <math>r</math>: Average error rate, <math>r = 1- F_{avg}, r = \frac{(d-1)(1-p)}{d}</math>
* <math>m</math>: Selected sequence length
* <math>K_m</math>: Total randomly selected sequence of <math>m</math> sequence length
* Clif<math>_n</math>: Clifford group
* C<math>_i</math>: Random element of Clifford group
* <math>S_{(i_1, ...,i_m)}</math> = <math>S_{\mathbf{i_m}}</math>: Random sequence of operations of length <math>m</math>
* <math>M</math>: Number of different data points to get the error model
* <math>\Lambda_{i,j}</math>: Implementation of C<math>_i</math> at time j (1 <math>\leq</math> j <math>\leq</math> M) results in this error map. <math>\Lambda_{i,1}, ..., \Lambda_{i,M}</math> are the different time-dependent noise operators affecting C<math>_i</math>.
* <math>|\psi\rangle</math>: initial state
* <math>E_{\psi}</math>: POVM element which takes into account the measurement error.
* <math>F_{seq}(m, \psi) = Tr[E_{\psi}S_{\mathbf{i_m}}(\rho_\psi)]</math>: Survival probability of a sequence. <math>\rho_\psi</math>  is a quantum state that takes into account errors in preparing <math>\langle \psi |\psi \rangle</math>
* <math>F_g^{(0)}(m, |\psi\rangle)</math>: Averaged sequence fidelity for gate and time independent error model
* <math>F_g^{(1)}(m, |\psi\rangle)</math>: Averaged sequence fidelity for gate and time dependent error model. In this model, the parameter <math>(q-p^2)</math> is a measure of the degree of gate-dependence in the error.
* <math>A_0, B_0</math>:  Coefficients that absorb the state preparation and measurement errors as well as the error on the final gate for gate and time independent error model
* <math>A_1, B_1, C_1</math>:  Coefficients that absorb the state preparation and measurement errors as well as the error on the final gate for gate and time dependent error model.
* <math>R_{m+1}</math>: <math>\frac{1}{|Clif_n|}\sum_i\Lambda_{i, m+1} \otimes (C_i \otimes \Lambda \otimes C_i^{\dagger})</math>