Related papers: Singularities of Quantum Control Landscapes
A proof that almost all quantum systems have trap free (that is, free from local optima) landscapes is presented for a large and physically general class of quantum system. This result offers an explanation for why gradient methods succeed…
Many quantum control problems are formulated as a search for an optimal field that maximizes a physical objective. This search is performed over a landscape defined as the objective as a function of the control field. A recent Letter [A. N.…
We investigate the control landscapes of closed, finite level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. Theoretical analysis is presented for the $n$ level case and formulas for…
Quantum optimal control has enjoyed wide success for a variety of theoretical and experimental objectives. These favorable results have been attributed to advantageous properties of the corresponding control landscapes, which are free from…
The ability to control quantum systems using shaped fields as well as to infer the states of such controlled systems from measurement data are key tasks in the design and operation of quantum devices. Here we associate the success of…
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic…
The reliable and precise generation of quantum unitary transformations is essential to the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal…
A common goal of quantum control is to maximize a physical observable through the application of a tailored field. The observable value as a function of the field constitutes a quantum control landscape. Previous works have shown, under…
The control landscape for various canonical quantum control problems is considered. For the class of pure-state transfer problems, analysis of the fidelity as a functional over the unitary group reveals no suboptimal attractive critical…
The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum…
A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a…
The control of quantum systems has been proven to possess trap-free optimization landscapes under the satisfaction of proper assumptions. However, many details of the landscape geometry and their influence on search efficiency still need to…
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…
A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum…
The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls.…
A quantum control landscape is defined as the physical objective as a function of the control variables to be optimized. Analyzing the topology of these landscapes is important for understanding the origins of the increasing number of…
We present a comprehensive analysis of the landscape for full quantum-quantum control associated with the expectation value of an arbitrary observable of one quantum system controlled by another quantum system. It is shown that such full…
The control of quantum system dynamics is generally performed by seeking a suitable applied field. The physical objective as a functional of the field forms the quantum control landscape, whose topology, under certain conditions, has been…
There has been great interest in recent years in quantum control landscapes. Given an objective $J$ that depends on a control field $\varepsilon$ the dynamical landscape is defined by the properties of the Hessian $\delta^2…
A controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability Pif between the states of a finite level…