Non-Abelian Berry connections for quantum computation
Abstract
In the holonomic approach to quantum computation, information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-Abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible for a specific model to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multipartite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover, a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.
- Publication:
-
Physical Review A
- Pub Date:
- December 1999
- DOI:
- 10.1103/PhysRevA.61.010305
- arXiv:
- arXiv:quant-ph/9907103
- Bibcode:
- 1999PhRvA..61a0305P
- Keywords:
-
- 03.67.Lx;
- 03.65.Fd;
- Quantum computation;
- Algebraic methods;
- Quantum Physics;
- High Energy Physics - Theory
- E-Print:
- 5 pages, no figures, revtex, minor changes, version accepted by Phys. Rev A (rapid comm.)