Editing Direct Fidelity Estimation (section)

==Outline==
In this method, we want to compare the final state created in any experiment with the initial state and hence we use fidelity as a figure of merit for this. This method works by measuring a random subset of Pauli observables chosen according to an importance weighing rule. The Pauli observables selected are most likely to detect deviations from the desired state.

This method consists of the following steps:

* A system is considered of <math>n</math> qubits with a certain space dimension and a pure quantum state is selected that is to be prepared. A group is formed of all possible [[Pauli operators]]. We have a final state, which has to be compared to the original pure quantum state.
* A Pauli observable is randomly selected from the group according to predefined importance weighing rule.
* A specific amount of copies of the final state are selected, where the amount depends on the selected Pauli observables.
* The Pauli observable is measured on each of these copies and the measurement outcome is received. An expectation value is calculated over all the random measurement outcome of all the copies.
* To estimate the fidelity with a fixed additive error and failure probability, the procedure from step 2 to step 4 is repeated <math>l</math> times, which is a function of the additive error and failure probability.
* The average of all the calculated <math>l</math> expectation values is taken which gives us the estimate of the fidelity.