The Role of Correlated Noise in Quantum Computing

Understand

This paper aims to give an overview of the current state of fault-tolerant quantum computing, by surveying a number of results in the field.

• We show that thresholds can be obtained for a simple noise model as first proved in [AB97, Kit97, KLZ98], by presenting a proof for statistically independent noise, following the presentation of Aliferis, Gottesman and Preskill [AGP06].
• We also present a result by Terhal and Burkard [TB05] and later improved upon by Aliferis, Gottesman and Preskill [AGP06] that shows a threshold can still be obtained for local non-Markovian noise, where we allow the noise to be weakly correlated in space and time.
• We then turn to negative results, presenting work by Ben-Aroya and Ta-Shma [BT11] who showed conditional errors cannot be perfectly corrected.