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We investigate the optimization of quantum control from a differential geometric perspective. In our approach, optimal control minimizes the cost associated with evolving a quantum state, with the cost quantified by the length of the…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While successive pseudospectral convexification combines spectral collocation with successive convexification,…
Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a…
This paper discusses the important role of controllability played on the complexity of optimizing quantum mechanical control systems. The study is based on a topology analysis of the corresponding quantum control landscape, which is…
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
Circuit optimization is a fundamental task for practical applications of near-term quantum computers. In this work we address this challenge through the powerful lenses of tensor network theory. Our approach involves the full…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold $\mathcal{M}$. Algorithms designed in this framework usually require some geometrical…
We study the time optimal control problem for the evolution operator of an n-level quantum system from the identity to any desired final condition. For the considered class of quantum systems the control couples all the energy levels to a…
We show that the second order traps in the control landscape for a three-level $\Lambda$-system found in our previous work {\it Phys. Rev. Lett.} {\bf 106}, 120402 (2011) are not local maxima: there exist directions in the space of controls…
In this paper, we propose a novel subspace learning framework for one-class classification. The proposed framework presents the problem in the form of graph embedding. It includes the previously proposed subspace one-class techniques as its…
The discovery of the SU(3) symmetry was fundamental as to establishing an ordering principle in particle physics. We already studied how to couple the SU(3) symmetry to the gravitational field in four-dimensional curved Lorentzian…
We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Gradient-flow (GF) viewpoints unify and illuminate optimization algorithms, yet most GF analyses focus on unconstrained settings. We develop a geometry-respecting framework for constrained problems by (i) reparameterizing feasible sets with…
In quantum optimal control theory the success of an optimization algorithm is highly influenced by how the figure of merit to be optimized behaves as a function of the control field, i.e. by the control landscape. Constraints on the control…
Optimization is ubiquitous in quantum information science and technology, however, the corresponding optimization landscape can encounter false traps, i.e., local but not global optima, likely to prevent used optimizers from finding optimal…
We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent…