122 research outputs found
Analytic Solutions to Coherent Control of the Dirac Equation
A simple framework for Dirac spinors is developed that parametrizes
admissible quantum dynamics and also analytically constructs electromagnetic
fields, obeying Maxwell's equations, which yield a desired evolution. In
particular, we show how to achieve dispersionless rotation and translation of
wave packets. Additionally, this formalism can handle control interactions
beyond electromagnetic. This work reveals unexpected flexibility of the Dirac
equation for control applications, which may open new prospects for quantum
technologies
Dirac open quantum system dynamics: formulations and simulations
We present an open system interaction formalism for the Dirac equation.
Overcoming a complexity bottleneck of alternative formulations, our framework
enables efficient numerical simulations (utilizing a typical desktop) of
relativistic dynamics within the von Neumann density matrix and Wigner phase
space descriptions. Employing these instruments, we gain important insights
into the effect of quantum dephasing for relativistic systems in many branches
of physics. In particular, the conditions for robustness of Majorana spinors
against dephasing are established. Using the Klein paradox and tunneling as
examples, we show that quantum dephasing does not suppress negative energy
particle generation. Hence, the Klein dynamics is also robust to dephasing
Sampling-based learning control of inhomogeneous quantum ensembles
Compensation for parameter dispersion is a significant challenge for control
of inhomogeneous quantum ensembles. In this paper, we present a systematic
methodology of sampling-based learning control (SLC) for simultaneously
steering the members of inhomogeneous quantum ensembles to the same desired
state. The SLC method is employed for optimal control of the state-to-state
transition probability for inhomogeneous quantum ensembles of spins as well as
type atomic systems. The procedure involves the steps of (i) training
and (ii) testing. In the training step, a generalized system is constructed by
sampling members according to the distribution of inhomogeneous parameters
drawn from the ensemble. A gradient flow based learning and optimization
algorithm is adopted to find the control for the generalized system. In the
process of testing, a number of additional ensemble members are randomly
selected to evaluate the control performance. Numerical results are presented
showing the success of the SLC method.Comment: 8 pages, 9 figure
The role of controllability in optimizing quantum dynamics
This paper discusses the important role of controllability played on the
complexity of optimizing quantum mechanical control systems. The study is based
on a topology analysis of the corresponding quantum control landscape, which is
referred to as the optimization objective as a functional of control fields. We
find that the degree of controllability is closely relevant with the ruggedness
of the landscape, which determines the search efficiency for global optima.
This effect is demonstrated via the gate fidelity control landscape of a system
whose controllability is restricted on a SU(2) dynamic symmetry group. We show
that multiple local false traps (i.e., non-global suboptima) exist even if the
target gate is realizable and that the number of these traps is increased by
the loss of controllability, while the controllable systems are always devoid
of false traps.Comment: 13 pages, 3 figure
Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109},
190403 (2012)] is employed to analyze dynamics of spin half relativistic
particles. We arrive at the Dirac equation from specially constructed
relativistic Ehrenfest theorems by assuming that the coordinates and momenta do
not commute. Forbidding creation of antiparticles and requiring the
commutativity of the coordinates and momenta lead to classical Spohn's equation
[Ann. Phys. {\bf 282}, 420 (2000)]. Moreover, Spohn's equation turns out to be
the classical Koopman-von Neumann theory underlying the Dirac equation
The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement
This paper considers the control landscape of quantum transitions in
multi-qubit systems driven by unitary transformations with single-qubit
interaction terms. The two-qubit case is fully analyzed to reveal the features
of the landscape including the nature of the absolute maximum and minimum, the
saddle points and the absence of traps. The results permit calculating the
Schmidt state starting from an arbitrary two-qubit state following the local
gradient flow. The analysis of multi-qubit systems is more challenging, but the
generalized Schmidt states may also be located by following the local gradient
flow. Finally, we show the relation between the generalized Schmidt states and
the entanglement measure based on the Bures distance
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