Chrononic Computing (Time Evolution Systems)

Question

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?

Answer 1

Is universal chrononic computing possible?

There is no consensus that chronons even exist.
See the first line of this, for example.

However time (and space) is quantized in one of the most popular generalizations of quantum mechanics called loop quantum gravity.

If loop quantum gravity is an accurate description of the universe (which is not something we will be able to test for a very long time, until we can observe for example, Hawking radiation), then universal quantum computation with chronons would be possible as long as we can find a way to implement a universal set of gates such as {H,CNOT,R($\pi$/4)}.

It is hard enough to implement a useful number of {H,CNOT,R($\pi$/4)} gates with ordinary quanta that we've been working with for a century (such as spin quanta or atomic energy level quanta or photon quanta), so don't be disappointed if you don't see universal chrononic quantum computers on the market during your lifetime. But it is possible, provided that quanta of time actually do exist, which would be true if loop quantum gravity were to be true.