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Every quantum operation that takes a system from one state to another is known to have bounds on operation time, due to Heisenberg uncertainty principle. In open quantum systems (OQS), such bounds have been principally affected by system…
We derive algebraic bounds on achievable rates for quantum state transfer and entanglement generation in general quantum systems. We apply these bounds to graph-based models of local quantum spin systems to obtain speed limits on these…
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of…
The range of motion of a particle with certain energy $E$ confined in a potential is determined from the energy conservation law in classical mechanics. The counterpart of this question in quantum mechanics can be regarded as what the…
We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
A systematic scheme is proposed to numerically estimate the quantum speed limit and temporal shape of optimal control in two-level and three-level quantum systems with bounded amplitude. For the two-level system, two quantum state…
The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…
Conservation laws limit the accuracy of physical implementations of elementary quantum logic gates. If the computational basis is represented by a component of spin and physical implementations obey the angular momentum conservation law,…
Optimization of constrained quantum control problems powers quantum technologies. This task becomes very difficult when these control problems are nonconvex and plagued with dense local extrema. For such problems current optimization…
Quantum controls realize the unitary or nonunitary operations employed in quantum computers, quantum simulators, quantum communications, and other quantum information devices. They implement the desired quantum dynamics with the help of…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
Quantum optimal control has numerous important applications ranging from pulse shaping in magnetic-resonance imagining to laser control of chemical reactions and quantum computing. Our objective is to address two major challenges that have…
Control of open quantum systems is an essential ingredient to the realization of contemporary quantum science and technology. We demonstrate such control by employing a thermodynamically consistent framework, taking into account the fact…