Seminar of the ICMP

In 1981, Richard Feynman proposed the idea of an analog quantum

computer, which could set up the behavior of a quantum system under the action

of a Hamiltonian and could then be probed to determine the quantum properties

of the system. Recent work with trapped ions has begun to realize this goal by

simulating interacting spins in a one-dimensional chain or in a

two-dimensional plane. Initially, researchers focused on adiabatically

creating a nontrivial ground state of a complicated Hamiltonian, but more

recent work has gone beyond this ideal to consider spectroscopically measuring

low-lying energy levels, and dynamical responses. I will describe how these

experiments work and what their successes have been in addition to describing

the role theory has played in helping shape the experimental work and where
the field is likely to go in the future.