Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

by A. Fabricio Albuquerque, Helmut G. Katzgraber, Matthias Troyer, Gianni Blatter

While at Aspen this summer, I had the opportunity to hear Matthias Troyer introduce this interesting study on the possibility of simply engineering a topological quantum computer. In this paper, they consider the quantum dimer model on a triangular lattice (see Moessner and Sondhi, 2000) which is known to have a gapped resonating dimer (valence bond) phase with topologically protected degenerate ground states (that could be used to store a 0 or a 1, for example). They study a "microscopic" model of a system of Josephson junctions engineered in such a way as to produce the mentioned quantum dimer model at low energies. Their central result, however, is negative: under the best circumstances, this system needs to be at or below 1 mK in order to successfully operate as a storage device of a quantum bit. The lesson to be drawn is then quite simple: to engineer such a phase, one needs to start from a system with very large energy scales so that its low energy sector can still be studied at accessible temperatures.

I find in particular that I am drawn to their numerical technique called CORE. This technique projects the lowest lying energy states of an exactly diagonalized hamiltonian onto a hoped for low energy subspace. The quality of the projection is then analyzed and if successful, provides strong evidence that a particular low energy effective model truly captures the low lying excitations of a particular system. This seems to be a particularly effective analysis of an exact diagonalization study.