PIRSA:09010021

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

Raussendorf, R. (2009). Thermal instability of the toric code in the Hamiltonian setting and implications for topological quantum computing. Perimeter Institute. https://pirsa.org/09010021

Raussendorf, Robert. Thermal instability of the toric code in the Hamiltonian setting and implications for topological quantum computing. Perimeter Institute, Jan. 19, 2009, https://pirsa.org/09010021 

          @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}}
          }

Robert Raussendorf

Leibniz University Hannover

Talk number
PIRSA:09010021
Collection
Talk Type
Subject
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)