In a recent question about quantum speed-up @DaftWullie says:
My research, for example, is very much about "how do we design Hamiltonians $H$ so that their time evolution $e^{-iHt_0}$ creates the operations that we want?", aiming to do everything we can in a language that is "natural" for a given quantum system, rather than having to coerce it into performing a whole weird sequence of quantum gates.
This makes me think of chronons, which are a proposed quantum of time.
"There are physical limits that prevent the distinction of arbitrarily close successive states in the time evolution of a quantum system.
If a discretization is to be introduced in the description of a quantum system, it cannot possess a universal value, since those limitations depend on the characteristics of the particular system under consideration. In other words, the value of the fundamental interval of time has to change a priori from system to system."
Introduction of a Quantum of Time ("chronon"), and its Consequences for Quantum Mechanics
Is universal chrononic computing possible?