God does not play dice seem not to realize that a dice-playing God would be an *improvement* over the actual situation.  In quantum mechanics, a particle does not have a position, even an unknown position, until it is measured.  This means that it makes no sense to talk about a trajectory of the particle, or even a probability distribution over possible trajectories.  And without such a distribution, it is not clear how we can make even probabilistic predictions for future observations, if we ourselves belong to just one component of a larger superposition.

Hidden-variable theories try to remedy this problem by supplementing quantum mechanics with the actual values of certain observables (such as particle positions or momenta), together with rules for how those observables evolve in time.  The most famous such theory is due to Bohm [@bohm], but there are many alternatives that are equally compatible with experiment.  Indeed, a key feature of hidden-variable theories is that they reproduce the usual quantum-mechanical probabilities at any individual time, and so are empirically indistinguishable from ordinary quantum mechanics.  It does not seem, therefore, that a hidden-variable quantum computer could possibly be more powerful than a garden-variety one.

On the other hand, it 