17 research outputs found
Real-time Information, Uncertainty and Quantum Feedback Control
Feedback is the core concept in cybernetics and its effective use has made
great success in but not limited to the fields of engineering, biology, and
computer science. When feedback is used to quantum systems, two major types of
feedback control protocols including coherent feedback control (CFC) and
measurement-based feedback control (MFC) have been developed. In this paper, we
compare the two types of quantum feedback control protocols by focusing on the
real-time information used in the feedback loop and the capability in dealing
with parameter uncertainty. An equivalent relationship is established between
quantum CFC and non-selective quantum MFC in the form of operator-sum
representation. Using several examples of quantum feedback control, we show
that quantum MFC can theoretically achieve better performance than quantum CFC
in stabilizing a quantum state and dealing with Hamiltonian parameter
uncertainty. The results enrich understanding of the relative advantages
between quantum MFC and quantum CFC, and can provide useful information in
choosing suitable feedback protocols for quantum systems.Comment: 24 page
Nonlinear quantum input-output analysis using Volterra series
Quantum input-output theory plays a very important role for analyzing the
dynamics of quantum systems, especially large-scale quantum networks. As an
extension of the input-output formalism of Gardiner and Collet, we develop a
new approach based on the quantum version of the Volterra series which can be
used to analyze nonlinear quantum input-output dynamics. By this approach, we
can ignore the internal dynamics of the quantum input-output system and
represent the system dynamics by a series of kernel functions. This approach
has the great advantage of modelling weak-nonlinear quantum networks. In our
approach, the number of parameters, represented by the kernel functions, used
to describe the input-output response of a weak-nonlinear quantum network,
increases linearly with the scale of the quantum network, not exponentially as
usual. Additionally, our approach can be used to formulate the quantum network
with both nonlinear and nonconservative components, e.g., quantum amplifiers,
which cannot be modelled by the existing methods, such as the
Hudson-Parthasarathy model and the quantum transfer function model. We apply
our general method to several examples, including Kerr cavities, optomechanical
transducers, and a particular coherent feedback system with a nonlinear
component and a quantum amplifier in the feedback loop. This approach provides
a powerful way to the modelling and control of nonlinear quantum networks.Comment: 12 pages, 7 figure
Sliding Mode Control of Two-Level Quantum Systems
This paper proposes a robust control method based on sliding mode design for
two-level quantum systems with bounded uncertainties. An eigenstate of the
two-level quantum system is identified as a sliding mode. The objective is to
design a control law to steer the system's state into the sliding mode domain
and then maintain it in that domain when bounded uncertainties exist in the
system Hamiltonian. We propose a controller design method using the Lyapunov
methodology and periodic projective measurements. In particular, we give
conditions for designing such a control law, which can guarantee the desired
robustness in the presence of the uncertainties. The sliding mode control
method has potential applications to quantum information processing with
uncertainties.Comment: 29 pages, 4 figures, accepted by Automatic
Sampled-data design for robust control of a single qubit
This paper presents a sampled-data approach for the robust control of a
single qubit (quantum bit). The required robustness is defined using a sliding
mode domain and the control law is designed offline and then utilized online
with a single qubit having bounded uncertainties. Two classes of uncertainties
are considered involving the system Hamiltonian and the coupling strength of
the system-environment interaction. Four cases are analyzed in detail including
without decoherence, with amplitude damping decoherence, phase damping
decoherence and depolarizing decoherence. Sampling periods are specifically
designed for these cases to guarantee the required robustness. Two sufficient
conditions are presented for guiding the design of unitary control for the
cases without decoherence and with amplitude damping decoherence. The proposed
approach has potential applications in quantum error-correction and in
constructing robust quantum gates.Comment: 33 pages, 5 figures, minor correction