2011/11/06 by Daan Staudt, Staudt, Daan
Computer Science · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1111.1417
openalex publication_date 2011/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. We end our survey by briefly mentioning some more speculative objections, as put forth by Kalai [Kal08, Kal09, Kal11].