The following is a solution to the halting problem, which asks the question: given a description of a program, decide whether the program finishes running or will run forever. This problem is generally believed to be insoluble, however I believe it is possible to conceive a theoretical solution as follows.


Consider a thought experiment, in which quantum scientists, though sub atomic particle tunneling are able to perform a single logical operation in zero time.  Using this technology they are able to construct a quantum computer which is able to run sequential operation in zero time.  This quantum computer is set up as follows:  a light bulb goes on while the program is loaded into the computer.  The start button is pressed, and the computer starts to execute the program.  As soon as the lightbulb goes off, the program is finished and you can look at the result as well as the time taken to complete.  Now it is immediately apparent that the light bulb will go off after zero time if the program halts.  It is also easy to imagine that the machine keeps on processing if the program enters an infinite loop and the lightbulb will remain on.  Iff we observe that the lightbulb remains on we know that the program does not halt.  Hence we have a theoretical solution to the halting problem.


QED