  We propose a (theoretical ;-) model for quantum computation where the result
can be read out from the time average of the Hamiltonian dynamics of a
2-dimensional crystal on a cylinder. The Hamiltonian is a spatially local
interaction among Wigner-Seitz cells containing 6 qubits. The quantum circuit
that is simulated is specified by the initialization of program qubits. As in
Margolus' Hamiltonian cellular automaton (implementing classical circuits), a
propagating wave in a clock register controls asynchronously the application of
the gates. However, in our approach all required initializations are basis
states. After a while the synchronizing wave is essentially spread around the
whole crystal. The circuit is designed such that the result is available with
probability about 1/4 despite of the completely undefined computation step.
This model reduces quantum computing to preparing basis states for some qubits,
waiting, and measuring in the computational basis. Even though it may be
unlikely to find our specific Hamiltonian in real solids, it is possible that
also more natural interactions allow ergodic quantum computing.
