Computing With Quantum Mechanical Oscillators

Abstract

Abstract : Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations. The purpose of this report is to describe one such idealized system-the quantum harmonic computer. As its name might suggest, this theoretical device employs the well known energy characteristics of quantum mechanical oscillators; the associated creation and annihilation operators; and the quantum mechanical axioms of state preparation and observability to perform computations. It is demonstrated that programs can be written for this device in terms of quantum mechanical observables and creation and annihilation operators which will algorithmically manipulate oscillator energy states to perform the desired calculations, the results of which are eigenvalues of a well defined system observable. By definition, these programs are equivalent to Turing machines, so that anything that is Turing computable is also computable with this device.