6,894 research outputs found
Exploring Quantum Control Landscape Structure
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
specified conditions, that the quantum control landscape should be free of
suboptimal critical points. This favorable landscape topology is one factor
contributing to the efficiency of climbing the landscape. An additional,
complementary factor is the landscape \textit{structure}, which constitutes all
non-topological features. If the landscape's structure is too complex, then
climbs may be forced to take inefficient convoluted routes to finding optimal
controls. This paper provides a foundation for understanding control landscape
structure by examining the linearity of gradient-based optimization
trajectories through the space of control fields. For this assessment, a metric
is defined as the ratio of the path length of the optimization
trajectory to the Euclidean distance between the initial control field and the
resultant optimal control field that takes an observable from the bottom to the
top of the landscape. Computational analyses for simple model quantum systems
are performed to ascertain the relative abundance of nearly straight control
trajectories encountered when optimizing a state-to-state transition
probability. The collected results indicate that quantum control landscapes
have very simple structural features. The favorable topology and the
complementary simple structure of the control landscape provide a basis for
understanding the generally observed ease of optimizing a state-to-state
transition probability.Comment: 27 pages, 7 figure
Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
This article provides a review of recent developments in the formulation and
execution of optimal control strategies for the dynamics of quantum systems. A
brief introduction to the concept of optimal control, the dynamics of of open
quantum systems, and quantum information processing is followed by a
presentation of recent developments regarding the two main tasks in this
context: state-specific and state-independent optimal control. For the former,
we present an extension of conventional theory (Pontryagin's principle) to
quantum systems which undergo a non-Markovian time-evolution. Owing to its
importance for the realization of quantum information processing, the main body
of the review, however, is devoted to state-independent optimal control. Here,
we address three different approaches: an approach which treats dissipative
effects from the environment in lowest-order perturbation theory, a general
method based on the time--evolution superoperator concept, as well as one based
on the Kraus representation of the time-evolution superoperator. Applications
which illustrate these new methods focus on single and double qubits (quantum
gates) whereby the environment is modeled either within the Lindblad equation
or a bath of bosons (spin-boson model). While these approaches are widely
applicable, we shall focus our attention to solid-state based physical
realizations, such as semiconductor- and superconductor-based systems. While an
attempt is made to reference relevant and representative work throughout the
community, the exposition will focus mainly on work which has emerged from our
own group.Comment: 27 pages, 18 figure
Quantum Control Landscapes
Numerous lines of experimental, numerical and analytical evidence indicate
that it is surprisingly easy to locate optimal controls steering quantum
dynamical systems to desired objectives. This has enabled the control of
complex quantum systems despite the expense of solving the Schrodinger equation
in simulations and the complicating effects of environmental decoherence in the
laboratory. Recent work indicates that this simplicity originates in universal
properties of the solution sets to quantum control problems that are
fundamentally different from their classical counterparts. Here, we review
studies that aim to systematically characterize these properties, enabling the
classification of quantum control mechanisms and the design of globally
efficient quantum control algorithms.Comment: 45 pages, 15 figures; International Reviews in Physical Chemistry,
Vol. 26, Iss. 4, pp. 671-735 (2007
Krotov: A Python implementation of Krotov's method for quantum optimal control
We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization
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