Thermal instability of the toric code in the Hamiltonian setting and implications for topological quantum computing

          @misc{ pirsa_PIRSA:09010021,
            doi = {10.48660/09010021},
            url = {https://pirsa.org/09010021},
            author = {Raussendorf, Robert},
            keywords = {Quantum Information},
            language = {en},
            title = {Thermal instability of the toric code in the Hamiltonian setting and implications for topological quantum computing},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {jan},
            note = {PIRSA:09010021 see, \url{https://pirsa.org}}
          }
          

Abstract

In topological quantum computation, a quantum algorithm is performed by braiding and fusion of certain quasi-particles called anyons. Therein, the performed quantum circuit is encoded in the topology of the braid. Thus, small inaccuracies in the world-lines of the braided anyons do not adversely affect the computation. For this reason, topological quantum computation has often been regarded as error-resilient per se, with no need for quantum error-correction. However, newer work [1], [2] shows that even topological computation is plagued with (small) errors. As a consequence, it requires error-correction, too, and in the scaling limit causes a poly-logarithmic overhead similar to systems without topological error-correction. I will discuss Nussinov and Ortiz' recent result [2] that the toric code is not fault-tolerant in a Hamiltonian setting, and outline its potential implications for topological quantum computation in general. [1] Nayak, C., Simon, S. H., Stern, A. et al. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083-1159 (2008). [2] Z. Nussinov and G. Ortiz, arXiv:0709.2717 (condmat)