8,268 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
Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity
We propose a mean to obtain computationally useful resource states also known
as cluster states, for measurement-based quantum computation, via
transitionless quantum driving algorithm. The idea is to cool the system to its
unique ground state and tune some control parameters to arrive at
computationally useful resource state, which is in one of the degenerate ground
states. Even though there is set of conserved quantities already present in the
model Hamiltonian, which prevents the instantaneous state to go to any other
eigenstate subspaces, one cannot quench the control parameters to get the
desired state. In that case, the state will not evolve. With involvement of the
shortcut Hamiltonian, we obtain cluster states in fast-forward manner. We
elaborate our proposal in the one-dimensional Kitaev honeycomb model, and show
that the auxillary Hamiltonian needed for the counterdiabatic driving is of
M-body interaction.Comment: 13 pages, 3 figures. Added detailed derivation to arrive at the
shortcut Hamiltonian plus numerical simulations. Invited manuscript to be
appeared in Focus on Shortcuts to Adiabaticity, NJP (IOP
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