Related papers: Quantum Riemannian Cubics with Obstacle Avoidance …
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the…
This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently,…
This paper summarizes several recent developments in the area of estimation and robust control of quantum systems and outlines several directions for future research. Quantum state tomography via linear regression estimation and adaptive…
In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to…
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to…
Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to…
We introduce an efficient iterative method to prepare a target state in Hilbert spaces with high dimensionality using a combination of unitary evolution, measurements, and quantum Zeno dynamics. The latter confines the evolution within Zeno…
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…