No-Go Theorems for Self-Correcting Quantum Memory

November 19, 2008 - 4:20 - 4:45pm

RLE Conference Center 36-428

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.

Bio
Barbara M. Terhal got her Ph.D. in Physics from the University of  Amsterdam in 1999 working on quantum computation and quantum information theory. After being a postdoc at IBM and Caltech, she joined the IBM Watson Research Center in 2002 as a Research Staff Member. She is a fellow of the American Physical Society, an associate editor of the journal `Quantum Information and Computation'. Her current active research interests are in quantum complexity theory and quantum fault-tolerance.