Editing Standard Randomised Benchmarking (section)

==Outline==
Randomized benchmarking method involves applying many random sequences of gates of varying lengths to a standard initial state. Each sequence ends with a randomized measurement that determines whether the correct final state was obtained. The average computationally relevant error per gate is obtained from the increase in error probability of the final measurements as a function of sequence length. 

The random gates are taken from the [[Clifford group]]. The restriction to the Clifford group ensures that the measurements can be of one-qubit Pauli operators that yield at least one deterministic one-bit answer in the absence of errors.

This method consists of the following steps:

* A fixed sequence length is selected at random. A random sequence of this length is chosen from the Clifford group.
* The operations are applied to the initial state corresponding to the selected sequence and then a final operator is applied which inverts all the previous operations.
* The final state is then measured to check if it matches the initial state. This process is performed several times with the same sequence to estimate the survival probability (the probability that the final state which returns to its initial state).
* Other random sequences of the same fixed sequence length are picked and the above-mentioned process is repeated to calculate the corresponding survival probability. This is then used to calculate the average survival probability for the sequence length.
* The same procedure is repeated for multiple different randomly selected sequence lengths.
* The observed survival probabilities are then plotted against the sequence length and then this is fit to an exponential decay curve, which is used to estimate the fidelity and also to calculate the average error rate which is the metric for randomized benchmarking.