2,873 research outputs found
On Projection-Based Model Reduction of Biochemical Networks-- Part II: The Stochastic Case
In this paper, we consider the problem of model order reduction of stochastic
biochemical networks. In particular, we reduce the order of (the number of
equations in) the Linear Noise Approximation of the Chemical Master Equation,
which is often used to describe biochemical networks. In contrast to other
biochemical network reduction methods, the presented one is projection-based.
Projection-based methods are powerful tools, but the cost of their use is the
loss of physical interpretation of the nodes in the network. In order alleviate
this drawback, we employ structured projectors, which means that some nodes in
the network will keep their physical interpretation. For many models in
engineering, finding structured projectors is not always feasible; however, in
the context of biochemical networks it is much more likely as the networks are
often (almost) monotonic. To summarise, the method can serve as a trade-off
between approximation quality and physical interpretation, which is illustrated
on numerical examples.Comment: Submitted to the 53rd CD
Constructing Qubits in Physical Systems
The notion of a qubit is ubiquitous in quantum information processing. In
spite of the simple abstract definition of qubits as two-state quantum systems,
identifying qubits in physical systems is often unexpectedly difficult. There
are an astonishing variety of ways in which qubits can emerge from devices.
What essential features are required for an implementation to properly
instantiate a qubit? We give three typical examples and propose an operational
characterization of qubits based on quantum observables and subsystems.Comment: 16 pages, no figures; IoP LaTeX2e style. Submitted to J. Phys. A:
Math. Ge
Efficient Quantum Computation using Coherent States
Universal quantum computation using optical coherent states is studied. A
teleportation scheme for a coherent-state qubit is developed and applied to
gate operations. This scheme is shown to be robust to detection inefficiency.Comment: 6 pages, 5 figures, extended and modified (in print, PRA
Protected Rabi oscillation induced by natural interactions among physical qubits
For a system composed of nine qubits, we show that natural interactions among
the qubits induce the time evolution that can be regarded, at discrete times,
as the Rabi oscillation of a logical qubit. Neither fine tuning of the
parameters nor switching of the interactions is necessary. Although
straightforward application of quantum error correction fails, we propose a
protocol by which the logical Rabi oscillation is protected against all
single-qubit errors. The present method thus opens a simple and realistic way
of protecting the unitary time evolution against noise.Comment: In this revised manuscript, new sections V, VI, VII and new
appendices A, B, C have been added to give detailed discussions. 13 pages, 4
figure
Data-driven Economic NMPC using Reinforcement Learning
Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal
control without relying on a model of the system. However, RL struggles to
provide hard guarantees on the behavior of the resulting control scheme. In
contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC)
are standard tools for the closed-loop optimal control of complex systems with
constraints and limitations, and benefit from a rich theory to assess their
closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the
quality of the model underlying the control scheme. In this paper, we show that
an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system
even when using a wrong model. This result also holds for real systems having
stochastic dynamics. This entails that ENMPC can be used as a new type of
function approximator within RL. Furthermore, we investigate our results in the
context of ENMPC and formally connect them to the concept of dissipativity,
which is central for the ENMPC stability. Finally, we detail how these results
can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply
these tools on both a classical linear MPC setting and a standard nonlinear
example from the ENMPC literature
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