Travel grant to fund visit to discuss: Conducting a research program including developing novel algorithms, developing and testing code, applying new codes to optimize the dynamics of quantum systems
Abstract
The selective preparation of quantum states has primary importance in quantum engineering, particularly in quantum information and quantum computation processes. Quantum optimal control theory (QOCT) is specifically well designed to find the optimal pulses. There are general quantum controllability theorems useful to non-constructively establish the feasibility of the goal, while the study of the quantum landscapes can provide additional details regarding the topological features and hence the robustness of the optimal solutions. Control theoreticians have developed powerful tools to infer general properties of the solutions and suitable algorithms to find particular solutions. There is however, little theory or algorithmic guidance that can serve to show the efficiency and robustness of different classes of solutions applied to different types of Hamiltonian. To develop these tools in the main goal of the present project. The study will be based on the Geometrical Optimization approach (GOAP) recently proposed by the author and coworkers. In GOAP one first divides the problem as a sequence of quantum operations, some treated dynamically (finding the optimal pulses using QOCT or parameterizing the optical fields), and others statically, replacing their time0evolution operators by rotations within a subset of the Hilbert space. Then, the overall optimization of the dynamics becomes a nonlinear eigenvalue problem. Subject to constrained controllability criteria, one can always shift one particular problem from the dynamic (QOCT) to the static (GOAP) approach. The first leads to very particular solutions the second allows to classify and analyze the robustness of the yields conditioned on the type of pulses used. Our first foal will be to develop consistent algorithms that combine both techniques. Regarding the systems of study, we want to explore general features of the dynamics of systems with generic composite structures (manifolds of sublevels) that can embody quantum information or quantum computation protocols. These type of systems pose several interesting problems from the point of view of quantum control. With a large number of levels of participating in the dynamics, a multilevel structure offers more control opportunities at the expense of our ability to manipulate the wave function within the substructure. The GOAP approach is particularly suited to analyze these types of systems, as it treats the different degrees of freedom with different techniques, justified by the physical resources available to control the system (e.g. long vs short wavelengths), or the different roles that the degrees of freedom play in the process (e.g. computational basis vs ancillary states or bath states). Our final goal is to use these techniques to explore which essential features of different classes of Hamiltonians (types of couplings, etc) are required in order to control the single manifold and multi-manifold dynamics.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 22, 2018
- Source ID
- W911NF1810241
Entities
People
- Ignacio Reija
Organizations
- Army Contracting Command
- Complutense University of Madrid
- United States Army