PIRSA:08100024 Scientific Series Quantum Information

DOI10.48660/08100024

Series: Perimeter Institute Quantum Discussions

Terhal, B. (2008). No-Go Theorems for Self-Correcting Quantum Memory. Perimeter Institute. https://pirsa.org/08100024

Terhal, Barbara. No-Go Theorems for Self-Correcting Quantum Memory. Perimeter Institute, Oct. 22, 2008, https://pirsa.org/08100024 

@misc{ pirsa_PIRSA:08100024,
  doi = {10.48660/08100024},
  url = {https://pirsa.org/08100024},
  author = {Terhal, Barbara},
  keywords = {Quantum Information},
  language = {en},
  title = {No-Go Theorems for Self-Correcting Quantum Memory},
  publisher = {Perimeter Institute},
  year = {2008},
  month = {oct},
  note = {PIRSA:08100024 see, \url{https://pirsa.org}}
}

Abstract

We study the possibility of a self-correcting quantum memory based on stabilizer codes with geometrically-local stabilizer generators. We prove that the distance of such stabilizer codes in D dimensions is bounded by O(L^{D-1}) where L is the linear size of the D-dimensional lattice. In addition, we prove that in D=1 and D=2, the energy barrier separating different logical states is upper-bounded by a constant independent of L. This shows that in such systems there is no natural energy dissipation mechanism which prevents errors from accumulating. Our results are in contrast with the existence of a classical 2D self-correcting memory, the 2D Ising ferromagnet.

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