  We study a model of quantum computation based on the
continuously-parameterized yet finite-dimensional Hilbert space of a spin
system. We explore the computational powers of this model by analyzing a pilot
problem we refer to as the close Hadamard problem. We prove that the close
Hadamard problem can be solved in the spin system model with arbitrarily small
error probability in a constant number of oracle queries. We conclude that this
model of quantum computation is suitable for solving certain types of problems.
The model is effective for problems where symmetries between the structure of
the information associated with the problem and the structure of the unitary
operators employed in the quantum algorithm can be exploited.
