Related papers: Toward a Theory of Phase Transitions in Quantum Co…
In optimal quantum control, control landscape phase transitions (CLPTs) indicate sharp changes occurring in the set of optimal protocols, as a physical model parameter is varied. Here, we demonstrate the existence of a new class of CLPTs,…
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing.…
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 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…
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…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
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…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a…
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…
Quantum Phase Transition (QPT) is a phase transition between different quantum states by adjusting some control parameters. Based on the Principle of Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a general QPT…
Quantum critical states exhibit strong quantum fluctuations and are therefore highly susceptible to perturbations. In this work we study the dynamical stability against a sudden coupling to these strong fluctuations by quenching the order…
Considerable theoretical and experimental efforts have been devoted to the quench dynamics, in particular, the dynamical quantum phase transition (DQPT) and the steady-state transition. These developments have motivated us to study the…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
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 study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glass-like…
This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers…
This paper explores the mechanisms behind extreme financial events, specifically market crashes, by employing the theoretical framework of phase transitions. We focus on endogenous crashes, driven by internal market dynamics, and model…
Dynamical quantum phase transitions (DQPTs) at critical times appear as non-analyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase…
This Report discusses a recently developed concept of Limiting Phase Trajectories (LPTs) providing a unified description of resonant energy transport in a wide range of classical and quantum dynamical systems with constant and time-varying…