We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields. We determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a not quantum gate robust with respect to the pulse inhomogeneities. The method is versatile and can be applied to numerous quantum control problems, e.g., other gates, other types of imperfections, Raman processes, or dynamical decoupling of undesirable effects.

Quantum control of lossy systems is known to be achieved by adiabatic passage via an approximate dark state relatively immune to loss, such as the emblematic example of stimulated Raman adiabatic passage (STIRAP) featuring a lossy excited state. By systematic optimal control study, via the Pontryagin maximum principle, we design alternative more efficient routes that, for a given admissible loss, feature an optimal transfer with respect to the cost defined as (i) the pulse energy (energy minimization) or (ii) the pulse duration (time minimization). The optimal controls feature remarkably simple sequences in the respective cases: (i) operating far from a dark state, of $\pi$-pulse type in the limit of low admissible loss, or (ii) close to the dark state with a counterintuitive pulse configuration sandwiched by sharp intuitive sequences, referred to as the intuitive/counterintuitive/intuitive (ICI) sequence. In the case of time optimization, the resulting stimulated Raman exact passage (STIREP) outperforms STIRAP in term of speed, accuracy, and robustness for low admissible loss.

Using optimal control, we establish and link the ultimate bounds in time (referred to as the quantum speed limit) and energy of two- and three-level quantum nonlinear systems which feature 1:2 resonance. Despite the unreachable complete inversion, by using the Pontryagin maximum principle, we determine the optimal time, pulse area, or energy for a given arbitrary accuracy. We show that the third-order Kerr terms can be absorbed in the detuning in order to lock the dynamics to the resonance. In the two-level problem, we determine the nonlinear counterpart of the optimal $\pi$-pulse inversion for a given accuracy. In the three-level problem, we obtain an intuitive pulse sequence similar to the linear counterpart but with different shapes. We prove the (slow) logarithmic increasing of the optimal time as a function of the accuracy.

Many existing tag recommendation approaches ignore the social relations between users. In this paper, we investigate the role of such additional information for the task of personalized tag recommendation. We inject the social relations between users and the content similarities between resources, along with the social annotations made by collaborative users, into a graph representation. To fully explore the structure of this graph, we exploit the methodology of random-walk computation of similarities between all the objects. We develop a personalized collaborative filtering algorithm that combines both the collaborative information and the personalized tag preferences. Experiments on Delicious data demonstrate the effectiveness of the proposed methods.

Bound states in the continuum (BICs) are localized states despite in a radiation continuum, rendering the ultra-high quality factor for enhanced light–matter interactions and supporting exotic topological properties. So far, most of studied BICs in photonic crystal (PhC) slabs are only vertically localized, i.e. allowing propagations in the plane of slab therein but forbidding radiations, and the density of optical states (DOS) at their frequencies is limited due to the steep dispersion characteristics. Here, we report a BIC existing on a flatband of symmetry-broken PhC slab. The flatband, associated with largely reduced group velocity, significantly sharpens the DOS at the frequency of BIC, which can be realized via finely controlling broken vertical symmetry in the PhC slab. The effect of broken symmetry is revealed in a simple effective Hamiltonian near the second-order Γ point of such system. Our results show the simultaneous engineering of dispersion and leaky characteristics of modes, offering new opportunities to boost light–matter interactions and to enhance the performance of photonic devices.

Robust and efficient manipulation of electron spin qubits in quantum dots is of great significance for the reliable realization of quantum computers and execution of quantum algorithms. In this paper, we study the robust control on a singlet-triplet qubit based on inverse engineering, one technique of shortcuts to adiabaticity (STA), in a nanowire double quantum dot in the presence of magnetic field and strong spin-orbit coupling. The optimization of STA with respect to the systematic errors, contributed from the control field and the perturbative interaction, is explored. Moreover, we also apply optimal control techniques combining with STA, referred to as robust inverse optimization, to design optimal control fields and optimal operation time. This article is part of the theme issue ‘Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives’.