101 research outputs found
Quantum Internal Model Principle: Decoherence Control
In this article, we study the problem of designing a Decoherence Control for
quantum systems with the help of a scalable ancillary quantum control and
techniques from geometric control theory, in order to successfully and
completely decouple an open quantum system from its environment. We
re-formulate the problem of decoherence control as a disturbance rejection
scheme which also leads us to the idea of Internal Model Principle for quantum
control systems which is first of its kind in the literature.
It is shown that decoupling a quantum disturbance from an open quantum
system, is possible only with the help of a quantum controller which takes into
account the model of the environmental interaction. This is demonstrated for a
simple 2-qubit system wherein the effects of decoherence are completely
eliminated. The theory provides conditions to be imposed on the controller to
ensure perfect decoupling. Hence the problem of decoherence control naturally
gives rise to the quantum internal model principle which relates the
disturbance rejecting control to the model of the environmental interaction.
Classical internal model principle and disturbance decoupling focus on
different aspects viz. perfect output tracking and complete decoupling of
output from external disturbances respectively. However for quantum systems,
the two problems come together and merge in order to produce an effective
platform for decoherence control. In this article we introduce a seminal
connection between disturbance decoupling and the corresponding analog for
internal model principle for quantum systems.Comment: Submitted to IEEE Transactions on Automatic Control, Mar 15 2010. A
basic introduction appeared in 46th IEEE CDC 2007. Acknowledgements: The
authors would like to thank the Center for Quantum Information Science and
Technology at Tsinghua University, R.-B. Wu, J. Zhang, J.-W. Wu, M. Jiang,
C.-W. Li and G.-L. Long for their valuable comments and suggestion
Strong Analytic Controllability for Hydrogen Control Systems
The realization and representation of so(4,2) associated with the hydrogen
atom Hamiltonian are derived. By choosing operators from the realization of
so(4,2) as interacting Hamiltonians, a hydrogen atom control system is
constructed, and it is proved that this control system is strongly analytically
controllable based on a time-dependent strong analytic controllability theorem.Comment: 6 pages; corrected typo; added equations in section III for
representation states of so(4,2). accepted by CDC 200
Optimal Control of Gene Mutation in DNA Replication
We propose a molecular-level control system view of the gene mutations in
DNA replication from the finite field concept. By treating DNA sequences as state variables,
chemical mutagens and radiation as control inputs, one cell cycle as a step increment, and the
measurements of the resulting DNA sequence as outputs, we derive system equations for both
deterministic and stochastic discrete-time, finite-state systems of different scales. Defining the
cost function as a summation of the costs of applying mutagens and the off-trajectory penalty,
we solve the deterministic and stochastic optimal control problems by dynamic programming
algorithm. In addition, given that the system is completely controllable, we find that the
global optimum of both base-to-base and codon-to-codon deterministic mutations can always
be achieved within a finite number of steps
Genetic Code Based Coding and Mathematical Formulation for DNA Computation
DNA computation is to use DNA molecules for information storing and processing. Challenges currently faced by DNA computation are (1) lack of theoretical computational models for applications, and (2) high error rate for implementation. This paper attempts to address these problems from genetic coding and mathematical modeling aspects. The proposed genetic coding approach provides a promising alternative to reduce high error rate. The mathematical formulation lays down groundwork for studying theoretical aspects of DNA computation
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