How Time-Traveling Could Affect Quantum Computing

I found this article very interesting, slightly above my head interesting.
I find myself trying to reconcile the conceptual nature of "causality" with the non-causal nature of quantum mechanics and indeed quantum computing. When I say "non-causal" I mean it in a the context of linear causality as opposed to quantum causality (observational causality). It is almost as if philosophical constructs such as the grandfather paradox have to be accounted for within the realm of computing.

The type of space-time that enables time traveling involves “closed time-like curves” (CTCs), and, besides personal fates, CTCs can also provide insights into quantum information and computing. In a recent study, computer scientists Scott Aaronson of MIT and John Watrous of the University of Waterloo have discovered that, if closed time-like curves exist, then quantum computers would be no more powerful than classical computers.

But researchers shouldn’t stop working on quantum computing technology just yet, as no one has any evidence that closed time-like curves actually exist. Closed time-like curves are strange: sometimes physicists describe them as a piece of paper folded over on itself, so that opposite ends touch and create a shortcut. A person standing at the front end could then easily step onto the back end, thereby easily stepping into the past.

CTCs provide interesting but complex insights into computation. At first it may seem that, if CTCs existed, researchers could perform computations of unlimited length in an instant, by simply computing the answer, and then sending it back in time to before they started. However, this proposal, like the grandfather paradox, breaks the rules of causality, since the input could be changed, affecting the future output. Further, the computation may have actually taken 100 years, so Aaronson and Watrous don’t consider this an honest computation method

physorg

I should have paid more attention to Schrodinger.

A little elaboration on CTCs:

In a Lorentzian manifold, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is "closed," returning to its starting point. This possibility was raised by Willem Jacob van Stockum in 1937 and by Kurt Gödel in 1949. If CTCs exist, their existence would seem to imply at least the theoretical possibility of making a time machine, as well as raising the spectre of the grandfather paradox. CTCs are related to frame dragging and the Tipler time machine, one of the many interesting side-effects in general relativity.

continued

One feature of a CTC is that it opens the possibility of a worldline which is not connected to earlier times, and so the existence of events that cannot be traced to an earlier cause. Ordinarily, causality demands that each event in spacetime is preceded by its cause in every rest frame. This principle is critical in determinism, which in the language of general relativity states complete knowledge of the universe on a spacelike Cauchy surface can be used to calculate the complete state of the rest of spacetime. However, in a CTC, causality breaks down, because an event can be "simultaneous" with its cause – in some sense an event may be able to cause itself. It is impossible to determine based only on knowledge of the past whether or not something exists in the CTC that can interfere with other objects in spacetime. A CTC therefore results in a Cauchy horizon, and a region of spacetime that cannot be predicted from perfect knowledge of some past time.

No CTC can be continuously deformed as a CTC to a point (that is, a CTC and a point are not timelike homotopic), as the manifold would not be causally well behaved at that point. The topological feature which prevents the CTC from being deformed to a point is known as a timelike topological feature.

Existence of CTCs places restrictions on physically allowable states of matter-energy fields in the universe. Propagating a field configuration along the family of closed timelike worldlines must eventually result in the state that is identical to the original one. This has been explored by some scientists as a possible approach towards disproving the existence of CTCs.

wiki

And on causal structure.

In modern physics (especially general relativity) spacetime is represented by a Lorentzian manifold. The causal relations between points in the manifold are interpreted as describing which events in spacetime can influence which other events.

Minkowski spacetime is a simple example of a Lorentzian manifold. The causal relationships between points in Minkowski spacetime take a particularly simple form since the space is flat. See Causal structure of Minkowski spacetime for more information.

The causal structure of an arbitrary (possibly curved) Lorentzian manifold is made more complicated by the presence of curvature. Discussions of the causal structure for such manifolds must be phrased in terms of smooth curves joining pairs of points. Conditions on the tangent vectors of the curves then define the causal relationships.

I thought closed time-like curves were, by currently theory, considered not possible? I'm not sure I understand the explanation given, but something about virtual particle interference?

Current theory is that closed timelike curves cannot form due to destructive virtual particle interference
Link

If I understand correctly, a 'timelike' curve is one where the light-cones originating at the points of multiple-tangents do not intersect?