A simple proof of the threshold for fault-tolerant quantum computation

          @misc{ scivideos_PIRSA:05030120,
            doi = {10.48660/05030120},
            url = {https://pirsa.org/05030120},
            author = {Gottesman, Daniel},
            keywords = {Quantum Information},
            language = {en},
            title = {A simple proof of the threshold for fault-tolerant quantum computation},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2005},
            month = {mar},
            note = {PIRSA:05030120 see, \url{https://scivideos.org/pirsa/05030120}}
          }
          

Abstract

One of the central critical results in the theory of fault-tolerant quantum computation is that arbitrarily long reliable computation is possible provided the error rate per gate and per time step is below some threshold value. This was proved by a number of groups, but the detailed published proofs are complex and furthermore only hold for concatenation of quantum error-correcting codes able to correct 2 errors per block, while typically the best estimates of the threshold value are based on the 7-qubit code, which only corrects 1 error per block. I will describe recent work by Panos Aliferis, John Preskill, and myself which substantially simplifies existing proofs and applies as well to the concatenated 7-qubit code. The new proof also provides a nice framework in which to attempt to prove relatively high values of the threshold, which so far have only emerged as estimates from simulations