Related papers: A Group-Theoretic Approach to the WSSUS Pulse Desi…
The distribution of eigenvalues of the wave equation in a bounded domain is known as Weyl's problem. We describe several computational projects related to the cumulative state number, defined as the number of states having wavenumber up to…
Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum…
We study optimal design problems for stationary diffusion involving one or more state equations and mixtures of an arbitrary number of anisotropic materials. Since such problems typically do not admit classical solutions, we adopt a…
High relative velocities and large distances in space-based quantum communication with satellites in lower earth orbits can lead to significant Doppler shifts and delays of the signal impairing the achievable performance if uncorrected. We…
We consider channel estimation within pulse-shaping multicarrier multiple-input multiple-output (MIMO) systems transmitting over doubly selective MIMO channels. This setup includes MIMO orthogonal frequency-division multiplexing (MIMO-OFDM)…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded…
Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
We consider an optimal semiconductor design problem for the quantum drift diffusion (QDD) model in the semiclassical limit. The design question is formulated as a PDE constrained optimal control problem, where the doping profile acts as…
We study rate-distortion problems of a Poisson process using a group theoretic approach. By describing a realization of a Poisson point process with either point timings or inter-event (inter-point) intervals and by choosing appropriate…
We introduce a new approach to assess the error of control problems we aim to optimize. The method offers a strategy to define new control pulses that are not necessarily optimal but still able to yield an error not larger than some fixed a…
The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator…
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…
Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates…
In this paper, we apply the framework of optimal transport to the formulation of optimal design problems. By considering the Wasserstein space as a set of design variables, we associate each probability measure with a shape configuration of…
We give a review of the most important results on optimal tomography as mathematical wave-pattern recognition theory emerged in the 70's in connection with the problems of optimal estimation and hypothesis testing in quantum theory. In…
We consider the joint design of packet forwarding policies and controllers for wireless control loops where sensor measurements are sent to the controller over an unreliable and energy-constrained multi-hop wireless network. For fixed…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are…