Control of Trapped-Ion Quantum States with Optical Pulses

Abstract

We present new results on the quantum control of systems with infinitely large Hilbert spaces.A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways -one that makes the system completely uncontrollable, and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schrödinger equation controllable via bichromatic resonant pulses.Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.

Optimization of segmented linear Paul traps and transport of stored particles

“…In a similar manner in ion trap based quantum computing tailored, light pulses can speed up and improve manipulation of the ions [49,50]. In cases where analytical solution to the control problem is not available open loop optimal control methods could be applied to get optimized light pulses or electrostatic field configurations for multi ion gate operations and entangled state preparation.…”

On the control of spin-boson systems

“…or s(i) = −s(j), which implies s(k) = −s(l) and then, by (24), n(i) + n(j) = n(k) + n(l). In the latter case it must be i = k and j = l, which is excluded by assumption.…”

“…For the counterpart of the Eberly-Law model for more than one trapped ion an approximate controllability result is obtained in [4] (see also [24]), based on the analysis on a sequence of nested finite-dimensional systems. In the recent papers [15,18] the (approximate) controllability of the system is established by considering different families of controlled dynamics.…”

Controllability of the coupled spin-12harmonic oscillator system

“…Here we present a control theoretical analysis and show that in the Lamb-Dicke regime by using two resonant frequencies, any unitary transformation within a finite level of the harmonic oscillator can be generated. Unlike, e.g., [17], no fine-tuning of the Lamb-Dicke parameter is required to obtain complete control. While the proof of controllability is somewhat involved, because of the fundamental nature of the system to be controlled and because of the wide range of potential application, we present this proof in detail.…”

“…Several key features of the original proposal in [1], including the production of entangled states and the implementation of quantum controlled operations between a pair of trapped ions, have already been experimentally demonstrated (see, e.g., [8,9,10,11]). Meanwhile, several alternative theoretical schemes (see, e.g., [12,13,14,15,16,17]) have also been developed for overcoming various difficulties in realizing a practical ion-trap quantum information processor. All these [1] haidong@mit.edu proposals either require fine-tuning of the Lamb-Dicke parameter or an initial eigenstate of the vibration motion.…”