Related papers: Integrability and chaos in the quantum brachistoch…
We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system…
Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian $\cal PT$-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state $|\psi_i\rangle$…
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this…
Advancing quantum technologies requires precise and robust coherent control of quantum systems. Robust higher-order Hamiltonian engineering is essential for high-precision control and for accessing effective dynamics absent at zeroth order.…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations in the system Hamiltonian. We present a method to design a coherent robust H-infinity controller so that the closed loop system is robustly…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Transforming an initial quantum state into a target state through the fastest possible route---a quantum brachistochrone---is a fundamental challenge for many technologies based on quantum mechanics. Here, we demonstrate fast coherent…
In this brief comment we attempt to clarify the apparent discrepancy between the papers [1] and [2] on the quantum brachistochrone, namely whether it is possible to use a judicious mixture of Hermitian and non-Hermitian quantum mechanics to…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a…
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
This work presents an exactly soluble scheme to address the problem of optimal transfer of quantum states through a set of $s$ harmonic oscillators composing a network with connected ends as a closed quantum circuit. For this purpose we…
We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of…
It is shown that if one can perform a restricted set of fast manipulations on a quantum system, one can implement a large class of dynamical evolutions by effectively removing or introducing selected Hamiltonians. The procedure can be used…
We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system with bounded input. We completely solve the…