Extended RB overview

[ShellyGarion]

Summary

• Extended RB overview to contain more explanation on how RB works and simultaneous RB
• Minor changes in Clifford_Group.ipnyb (added logo)

@dcmckayibm - please review

Details and comments

[dcmckayibm]

If you look at our papers we use $\alpha$ for $p$ here. Also you have $1-p^m$ should be $(1-p)^m$. The last equation didn't render.

[dcmckayibm]

I think the intuition paragraph would be better if you just wrote out the quantum channel

$\rho_f = \alpha \rho_i + (1-\alpha)/2^n * \mathbf{I} $

$\rho_f^m = \alpha^m \rho_i + (1-\alpha)^m/2^n * \mathbf{I} $

Then it's clear that the ground state survival probability just follows.

[ShellyGarion]

@dcmckayibm - I updated the overview following your comments above.

[dcmckayibm]

Introduction is spelled wrong

[dcmckayibm]

This sentence is a little confusing "Suppose that we have a sequence of $m$ gates, not necessarily Clifford gates. Each gate is affected by the depolarizing channel with parameter $\alpha$ (same $\alpha$ for all the gates)."

-> I would say that suppose we have gates where the error channel of the gate is a depolarizing channel.
-> I was also wrong it's not (1-alpha)^m it's (1-alpha^m)...then the last equation is exact

[ShellyGarion]

@dcmckayibm - I updated the overview again following your comments above.

[attp]

Approving since @dcmckayibm approved.