Introduction

The use of tailored laser fields to control quantum dynamics has been of much theoretical and experimental interest over the last 25 years, (see the recent review[1] and references therein). In general, many of the theoretical problems are posed in the form of optimal control theory (OCT)[2, 3] where monotonically convergent iterative techniques are used to find the laser field. Alternatively, and as often done in experimental implementation, closed loop feedback control is utilized, where genetic algorithms (GA) are used to determine the appropriate laser field[4]. In 2002, Tesch and de Vivie-Riedle proposed the use of a molecule's vibrational modes for quantum computation[5] and demonstrated the utility on a model of acetylene using OCT to find the laser field required to implement quantum gates. Concurrently, the work of Apkarian and co-workers appeared[6, 7], suggesting the manipulation of ro-vibronic states for quantum computing applications using time−frequency resolved coherent anti-Stokes Raman scattering or four-wave mixing. Within molecular quantum computing using OCT, various studies on polyatomics emerged incorporating: (i) quantum gates[5, 8−13], (ii) quantum algorithms[14, 15] and experimental limitations of OCT concerned with (iii) frequency constraints[16, 17, 18] and (iv) mask functions[13].

In the present chapter, the focus is on quantum computing using the internal state structure of diatomic molecules. The research involving polar diatomic molecules on a 1D array coupled by dipole−dipole interactions, as suggested by DeMille,[19] is not included in the present discussion. Table 2.1 details the theoretical and experimental studies specifically concerning diatomic quantum computing using OCT or GA shaped laser pulses. The list only includes two experimental implementations and in both cases there was no feedback loop setup. The vast majority of calculations done exploring molecular and diatomic quantum computing implement the OCT algorithm to shape laser pulses, which in general do not reflect experimental pulse shaping conditions. One of the papers by Hosaka[20] proposes an experimental setup based on available experimental techniques and explores its feasibility via numerical simulations. However, in general, there is a disconnect between computational simulations and experimental realization that needs to be bridged if further progress in molecular quantum computation is to be achieved. In this paper, we suggest areas lacking in theoretical progress that we have or are currently attempting to provide useful insights into with respect to diatomic quantum computing.