Related papers: Trap-free manipulation in the Landau-Zener system
There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal…
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…
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…
We analyze a recent claim that almost all closed, finite dimensional quantum systems have trap-free (i.e., free from local optima) landscapes (B. Russell et.al. J. Phys. A: Math. Theor. 50, 205302 (2017)). We point out several errors in the…
We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point…
In this work we study extrema of objective functionals for ultrafast manipulation by a qubit. Traps are extrema of the objective functionals which are optimal for manipulation by quantum systems only locally but not globally. Much effort in…
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.…
The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive…
We consider manipulation of the transmission coefficient for a quantum particle moving in one dimension where the shape of the potential is taken as the control. We show that the control landscape---the transmission as a functional of the…
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…
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 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…
Nonselective quantum measurements, i.e., measurements without reading the results, are often considered as a resource for manipulating quantum systems. In this work, we investigate optimal acceleration of the Landau-Zener (LZ) transitions…
In the present work the extrema of the objective functional for the problem of generation of quantum gates (logical elements for quantum computations) for two--level systems are investigated for short duration of the control. The problem of…
Quantum control is necessary for a variety of modern quantum technologies as it allows to optimally manipulate quantum systems. An important problem in quantum control is to establish whether the control objective functional has trapping…
In this work, we consider the problem of ultrafast controlled generation of single-qubit phase shift quantum gates. Globally optimal control is a control which realizes the gate with maximal possible fidelity. Trap is a control which is…
We exploit the concept of Landau-Zener transitions at avoided energy crossings as a quantum-control tool. In an avoided crossing the two quantum states interchange their characteristics as an external parameter is varied. Depending on the…
The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expectation of value of some physical observable. The functional which maps the control…
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…
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…