Related papers: Analytic Approach for Controlling Quantum States i…
We numerically study a particle in a box with moving walls. In the case where the walls are oscillating sinusoidally with small amplitude, we show that states up to the fourth state can be populated with more than 80 percent population,…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
Optimal Control (OC) is the process of determining control and state trajectories for a dynamic system, over a period of time, in order to optimize a given performance index. With the increasing of variables and complexity, OC problems can…
Quantum optimal control involves setting up an objective function that evaluates the quality of an operator representing the realized process w.r.t. the target process. Here we propose a stronger objective function which incorporates not…
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly…
Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this…
In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control enters into…
In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher "spin" operators. We construct an effective field theory (EFT)…
Optimal control theory is developed for the task of obtaining a primary objective in a subspace of the Hilbert space while avoiding other subspaces of the Hilbert space. The primary objective can be a state-to-state transition or a unitary…
Motivated by the control of invasive biological populations, we consider a class of optimization problems for moving sets $t\mapsto \Omega(t)\subset\mathbb{R}^2$. Given an initial set $\Omega_0$, the goal is to minimize the area of the…
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…
We propose a multi-scale approach for computing abstractions of dynamical systems, that incorporates both local and global optimal control to construct a goal-specific abstraction. For a local optimal control problem, we not only design the…
The capability to control molecular rotation for field-free orientation, which arranges molecules in specific spatial directions without external fields, is crucial in physics, chemistry, and quantum information science. However,…
The wave-function Monte-Carlo method, also referred to as the use of "quantum-jump trajectories", allows efficient simulation of open systems by independently tracking the evolution of many pure-state "trajectories". This method is ideally…
Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the…
The Rabi model, a two-level atom coupled to a harmonic oscillator, can undergo a second-order quantum phase transition (QPT) [M. -J. Hwang et al, Phys. Rev. Lett. 115, 180404 (2015)]. Here we show that the Rabi QPT accompanies critical…
We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
A two-level quantum system coherently driven by a resonant electromagnetic field oscillates sinusoidally between the two levels at frequency $\Omega$ which is proportional to the field amplitude [1]. This phenomenon, known as the Rabi…