From Quantum Spins to Quantum Links: Towards the Quantum Simulation of Gauge Theories

Uwe-Jens Wiese

ITP University Bern

Quantum links are gauge covariant generalizations of quantum spins that replace the classical parallel transporter matrices in Wilson's formulation of lattice gauge theory. Like Wilson's parallel transporters in an SU(N) lattice gauge theory, quantum links are N*N matrices. However, just like the components of a quantum spin vector, the elements of a quantum link matrix are non-commuting operators. In the resulting quantum link models continuous gauge symmetry is implemented on fundamental discrete quantum degrees of freedom. Ordinary gauge theories result from quantum link models by dimensional reduction. A Z(2) quantum link model is equivalent to Kitaev's toric code. If they can be implemented with ultra-cold atoms in optical lattices or with trapped Rydberg ions, quantum link models can serve as quantum simulators of dynamical gauge theories. Some (2+1)-d U(1) quantum link models can be simulated efficiently on a classical computer. In addition, small systems can be solved by exact diagonalization. This would enable us to validate corresponding quantum simulators. It is to be expected that non-Abelian Chern-Simons gauge theories arise from some (2+1)-d quantum link models. This suggests to consider quantum link models as possible realizations of a topological quantum computer.

Date: 3 November 2011

Time: 14:30 h

Place: Dpto. Física Teórica, 3rd floor seminar lecture room. Facultad de Ciencias Físicas UCM