Quantum Computation and Information Seminar 

12/05/2006, 15:00 — 16:00 — Room P4.35, Mathematics Building
Pedro Ribeiro, Université Pierre et Marie Curie

Adiabatic Quantum Computation

Adiabatic Quantum Computation has been proposed in 2001 by Farhi et al. as an alternative way to perform quantum computation. The protocol consists in passing from a initial Hamiltonian with a well known and easy to prepare ground state to the ground state of a final Hamiltonian (or problem Hamiltonian) which encodes the answer to a given problem. The time taken to perform the computation is such that the adiabatic theorem applies, with a small enough probability of passing to an exited state remains limited: $T\sim {\Delta }_{\min }^{-2}$, where $T$ is the total computational time and ${\Delta }_{\min }$ is the minimum value of the energy difference between the ground and the first exited states taken along the evolution. Therefore the time scaling with $n$ will be mainly determined by the behavior of the energy gap between the two lowest energy states. In this seminar we will introduce the Adiabatic Model of Computation and present a simple model that, due to its symmetry, permits to give analytic results and see how the gap scales depending of few characteristics of the computational problem.