Implementing Quantum Gates using the Heisenberg Ferromagnetic Quantum Spin Chain

Date:Monday, April 13, 2009
Time:10:30am - 11:30am
Location: LNBL Bldg. 50F, Room 1647

Speaker:
Jaideep Mulherkar
Department of Mathematics
University of California, Davis

Abstract:

Quantum spin systems are a natural model for quantum computation. I
will introduce the ferromagnetic Heisenberg XXZ quantum spin model
with kink boundary conditions and will talk about an interesting new
result regarding the presence of isolated eigenvalues in the low
lying spectrum of this model.The presence of isolated eigenvalues is
ideal from the point of view of quantum computation. We use the
subspace of the isolated eigenvalues to encode a qubit and
demonstrate the construction of quantum gates on this subspace,
using the time evolution of the XXZ chain under the influence of an
external magnetic field. The quantum gates are obtained using
optimal control theory and simulation results will be presented
using the Density Matrix Renormalization Group (DMRG) algorithm.

Host of Seminar:
    Esmond G. Ng