Quantum computing in Fortran

Abstract

Quantum computing is the delicate art of using a quantum-mechanical system to perform some kind of computation. Such a system differs in a number of significant ways from ordinary computers:• A quantum computer actually does a lot of computations at the same time, each solution is represented by a particular possible state. This is inherent to the physical properties of such a system.• Unless you are sure that you have reached the final (unique) solution, you can not "look" at the "values" of the variables in the computer program that is being run: since all solutions are possible at the same time, observing the values will influence the system and put it into one particular, but otherwise arbitrary, state.• All computations must be reversible, that is, a statement like "a = 5" can only appear in the initialization phase of a program, because the previous value will be lost. On the other hand, a statement like "a = a + 5" is reversible, since you can retrieve the original value.The properties of such a quantum computer make it possible to devise very efficient algorithms. One such algorithm, described by L. Grover (see the references), is searching in an unsorted array of items. With ordinary computers this can not be done more efficiently than in O(N) steps (an exhaustive search: each item is examined in the worst case), with this quantum algorithm, however, the number of steps needed is O(N1/2).Devising quantum algorithms requires a thorough understanding of quantum mechanics, there is no doubt about that. Another question is: do we need quantum computers and special programming languages to program (or perhaps emulate) these algorithms? This article tries to show that, at least for the quantum search algorithm, a classical programming language like Fortran is quite fit (yes, the pun is fortunate).