Editing Direct Fidelity Estimation (section)

==Further Information==
* For stabilizer states, the number of repetitions is constant, independent of the size of the system; and for the W state, it is only quadratic in the number of qubits <math>n</math>.
* This method can certify Clifford circuits in constant time, independent of the number of qubits and gates.
* This method performs better under some mild assumptions on the noise in the system. If the noise is depolarizing or dephasing, then we get a favourable scaling of <math>\mathcal{O} (\frac{log(1/\delta)}{\epsilon^2})</math>
* If the nonzero Pauli expectations are only inverse polynomially small, then the number of copies is polynomial.
* By truncating negligibly small probabilities from the relevance distribution, we can improve the worst-case scaling at the cost of adding a tiny (also negligible) bias to our estimate.
* An analogous method can be used for certifying any unitary quantum channel by estimating the entanglement fidelity. Most of the analysis for channels is exactly analogous to the case of states. The main difference is that we may also input a state to the channel as well as choose how to measure at the output.