The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources required, particularly for systems with large Hilbert spaces. Prior work on unitary transformation control indicates that (i) for controllable systems, local extrema in the search landscape for optimal control of quantum gates have null measure, facilitating the convergence of local search algorithms; but (ii) the required time for convergence to optimal controls can scale exponentially with Hilbert space dimension. Depending on the control system Hamiltonian, the landscape structure and scaling may vary. This work introduces methods for quantifying Hamiltonian-dependent and kinematic effects on control optimization dynamics in order to classify quantum systems according to the search effort and control resources required to implement arbitrary unitary transformations.

Generating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many analytical and numerical studies have identified the minimum time necessary to implement a variety of quantum gates on coupled-spin qubit systems. This work focuses on exploring the Pareto front that quantifies the trade-off between the competitive objectives of maximizing the gate fidelity F and minimizing the control time T . In order to identify the critical time T * , below which the target transformation is not reachable, as well as to determine the associated Pareto front, we introduce a numerical method of Pareto front tracking (PFT). We consider closed two-and multi-qubit systems with constant inter-qubit coupling strengths and each individual qubit controlled by a separate time-dependent external field. Our analysis demonstrates that unit fidelity (to a desired numerical accuracy) can be achieved at any T ≥ T * in most cases. However, the optimization search effort rises superexponentially as T decreases and approaches T * . Furthermore, a small decrease in control time incurs a significant penalty in fidelity for T < T * , indicating that it is generally undesirable to operate below the critical time. We investigate the dependence of the critical time T * on the coupling strength between qubits and the target gate transformation. Practical consequences of these findings for laboratory implementation of quantum gates are discussed.

Fundamental selectivity limits of quantum control are pushed by introducing laser driven optimal dynamic discrimination to create distinguishing excitations on two nearly identical flavin molecules. Even with modest spectral resources, significant specificity is achieved with optimal pulse shapes, which amplify small molecular differences to create distinct, identifying signals. Rather than being a hindrance, system complexity appears to aid the control process and augments control field capability, which bodes well for implementation of quantum control in a variety of demanding applications.

Thanks to the increasing ability to coherently control quantum systems, designer Hamiltonians can be created to explore new physics and to yield a better understanding of complex phenomena.

A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum dynamics phenomena. This paper extends the concept to encompass the broader context of the environment having an influence.