Counterfactual Computation may allow super-Turing hypercomputation (imo, bigger news than “the program didn’t run”):
hxxp://www.cs.auckland.ac.nz/CDMTCS//researchreports/107cds.pdf

It is vain to look in expectation, or believe ourselves in the hereditary possession, of a treasure, without so much as opening or suspecting even the casket in which it is shut up. The common elements of Nature obscure their Divine Original, and Chemistry and all our experimental physics drive it forcibly without the means of Identification. Yet as the experienced Chemist knows how, by a skillful application of his art, to analyze the common elements, and distill them to a high virtue and strength of refinement, so the Alchemists long since have taught by a more subtle apparatus and artifice, and tests more cogent than all, to rectify the Universal Element, and compress its invisible vapor into a tangible Form.

-Mary Anne Atwood

Wow! “to search a region of space without actually entering that region of space.” - Aren’t they describing intuition?

No. We all (including professional physicists) need to be very careful when trying to intuit the results of quantum experiments. The amount of distance between the final machine readout and the quantum phenomenon that makes the algorithm work is HUGE, and the distance between our symbolic mind has to go to produce some narrative out of these readouts is perhaps even longer.

Read this (short, with easy math) article to understand how ‘entanglement’ and ‘observation’ are related, afterwards, you will hardly be able to read a single pop-sci article without getting angry at the absurd interpretations they come up with just because they

Quantum Mysteries Disentangled:
hxxp://www.flownet.com/ron/QM.pdf

Here is another short article explaining Bell’s Theorem.
hxxp://world.std.com/~reinhold/bellsinequalities.html

Now, to understand a little how the quantum algorithm can “run without running” (try to) read this link, the example they use to illustrate the point should raise your eyebrows! (Since they provide adequate caveats, this is in fact a reasonable illustration of the phenomenon!)
hxxp://en.wikipedia.org/wiki/Quantum_Zeno_effect

QM is very interesting and teaches us a lot, but it is such an indirect science, we cannot really trust our intuitions regarding it one whit.

does that mean that thinking about them made the phone ring? No: but thinking about them made the phone’s ringing /significant/

Yes! And I sort of have another post on this tomorrow.

he has no rational explanation for where hypotheses come from

Whoa! Awesome - right there in the core of science!

nd self-supporting cycles are an important property of living creatures…

YES! Feedback loops! Wait for my post tomorrow!

what else is an omen but an effect of something that hasn’t happened yet?

Very succintly put. Man, good stuff. Gotta go to bed though.

If you’re thinking about someone, and the phone rings, does that mean that thinking about them made the phone ring? No: but thinking about them made the phone’s ringing /significant/. In fact, it’s no more than science: you choose to make observations based on hypotheses. Where do hypotheses come from? People making observations. One of the best bits of Zen & the Art of Motorcycle Maintenance is where Phaedrus realises he has no rational explanation for where hypotheses come from. I’m inclined to agree with him - they’re definitely trans-rational. Observations and hypotheses exist in a self-stoking cycle (there’s cyclic time for you!). And self-supporting cycles are an important property of living creatures… lots of interesting connections to be made here. The Ouroboros is an interesting thing to ponder. A serpent with its tail in its mouth: what is happening?

It’s worth noting that ancient civilisations had less of a problem with reversed cause and effect: what else is an omen but an effect of something that hasn’t happened yet?