  We discuss the implementation of quantum logic in a system of strongly
interacting particles. The implementation is qubitless since ``logical qubits''
don't correspond to any physical two-state subsystems. As an illustration, we
present the results of simulations of the quantum controlled-NOT gate and
Shor's algorithm for a chain of spin-1/2 particles with Heisenberg coupling.
Our proposal extends the current theory of quantum information processing to
include systems with permanent strong coupling between the two-state
subsystems.
