The halting problem for universal quantum computers

The halting of universal quantum computers is shown to be incompatible with the constraint of unitarity of the dynamics. The prospects of using quantum dynamics to process information have opened up new research horizon. While most of the activities is in the theoretical study and experimental realisation of quantum networks [1], the principles –and the halting problem, in particular– of a universal quantum computer [2] (qcomputer for short) are still unsettled and have generated many debates recently [3, 4, 5, 6]. Below we will discuss the general properties and the problem of halting for qcomputers. We then derive the inconsistencies between the stringent constraint of unitarity of the dynamics and other desirable properties of the general halting mechanism. Let us define a qcomputer and a general mechanism for halting sufficiently precisely for our discussion purposes. • A qcomputer is a closed quantum system governed by a time-independent, unitary dynamics U for each time step between the admission of the initial input, which is some vector in the Hilbert space of U to represent both programs and data, and the final reading-out measurements.