Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find hig
h fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a holonomic phasegate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotovs method yields considerably better results than either one of the two methods alone.
Several recent studies of energy transfer in photosynthetic light harvesting complexes have revealed a subtle interplay between coherent and decoherent dynamic contributions to the overall transfer efficiency in these open quantum systems. In this wo
rk we systematically investigate the impact of temporal and spatial correlations in environmental fluctuations on excitation transport in the Fenna-Matthews-Olson photosynthetic complex. We demonstrate that the exact nature of the correlations can have a large impact on the efficiency of light harvesting. In particular, we find that (i) spatial correlations can enhance coherences in the site basis while at the same time slowing transport, and (ii) the overall efficiency of transport is optimized at a finite temporal correlation that produces maximum overlap between the environmental power spectrum and the excitonic energy differences, which in turn results in enhanced driving of transitions between excitonic states.
Fast and accurate measurement is a highly desirable, if not vital, feature of quantum computing architectures. In this work we investigate the usefulness of adaptive measurements in improving the speed and accuracy of qubit measurement. We examine a
particular class of quantum computing architectures, ones based on qubits coupled to well controlled harmonic oscillator modes (reminiscent of cavity-QED), where adaptive schemes for measurement are particularly appropriate. In such architectures, qubit measurement is equivalent to phase discrimination for a mode of the electromagnetic field, and we examine adaptive techniques for doing this. In the final section we present a concrete example of applying adaptive measurement to the particularly well-developed circuit-QED architecture.
