The clock of a quantum computer

Abstract

If the physical agent (the 'pointer', or 'cursor', or 'clocking mechanism') that sequentially scans the T lines of a long computer program is a microscopic system, two quantum phenomena become relevant: spreading of the probability distribution of the pointer along the program lines, and scattering of the probability amplitude at the two endpoints of the physical space allowed for its motion. We show that the first effect determines an upper bound O(T−2/3) on the probability of finding the pointer exactly at the END line. By adding an adequate number δ of further empty lines ('telomers'), one can store the result of the computation up to the moment in which the pointer is scattered back into the active region. This leads to a less severe upper bound O(√δ/T) on the probability of finding the pointer either at the END line or within the additional empty lines. Our analysis is performed in the context of Feynman's model of quantum computation, the only model, to our knowledge, that explicitly includes a physically plausible quantum clocking mechanism in its considerations.