A quantum information processing machine for computing by observables

Abstract

A quantum machine that accepts an input and processes it in parallel is described. The logic variables of the machine are not wavefunctions (qubits) but observables (i.e., operators) and its operation is described in the Heisenberg picture. The active core is a solid-state assembly of small nanosized colloidal quantum dots (QDs) or dimers of dots. The size dispersion of the QDs that causes fluctuations in their discrete electronic energies is a limiting factor. The input to the machine is provided by a train of very brief laser pulses, at least four in number. The coherent band width of each ultrashort pulse needs to span at least several and preferably all the single electron excited states of the dots. The spectrum of the QD assembly is measured as a function of the time delays between the input laser pulses. The dependence of the spectrum on the time delays can be Fourier transformed to a frequency spectrum. This spectrum of a finite range in time is made up of discrete pixels. These are the visible, raw, basic logic variables. The spectrum is analyzed to determine a possibly smaller number of principal components. A Lie-algebraic point of view is used to explore the use of the machine to emulate the dynamics of other quantum systems. An explicit example demonstrates the considerable quantum advantage of our scheme.