Related papers: Holonomy control operators in classical and quantu…
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum…
We describe different strategies for using a semi-classical controller to engineer quantum Hamiltonians to solve control problems such as quantum state or process engineering or optimization of observables.
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…
In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…
We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state conical intersections. The general situation of an arbitrary number of states and…
We develop a general optimization strategy for performing a chosen unitary or non-unitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions.…
In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system.…
We provide a general framework for the identification of open quantum systems. By looking at the input-output behavior, we try to identify the system inside a black box in which some Markovian time-evolution takes place. Due to the…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…