143 research outputs found
Dissipation-induced continuous quantum error correction for superconducting circuits
Quantum error correction (QEC) is a crucial step towards long coherence times
required for efficient quantum information processing (QIP). One major
challenge in this direction concerns the fast real-time analysis of error
syndrome measurements and the associated feedback control. Recent proposals on
autonomous QEC (AQEC) have opened new perspectives to overcome this difficulty.
Here, we design an AQEC scheme based on quantum reservoir engineering adapted
to superconducting qubits. We focus on a three-qubit bit-flip code, where three
transmon qubits are dispersively coupled to a few low-Q resonator modes. By
applying only continuous-wave drives of fixed but well-chosen frequencies and
amplitudes, we engineer an effective interaction Hamiltonian to evacuate the
entropy created by eventual bit-flip errors. We provide a full analytical and
numerical study of the protocol, while introducing the main limitations on the
achievable error correction rates.Comment: 9 pages, 6 figure
Singular perturbations and Lindblad-Kossakowski differential equations
We consider an ensemble of quantum systems whose average evolution is
described by a density matrix, solution of a Lindblad-Kossakowski differential
equation. We focus on the special case where the decoherence is only due to a
highly unstable excited state and where the spontaneously emitted photons are
measured by a photo-detector. We propose a systematic method to eliminate the
fast and asymptotically stable dynamics associated to the excited state in
order to obtain another differential equation for the slow part. We show that
this slow differential equation is still of Lindblad-Kossakowski type, that the
decoherence terms and the measured output depend explicitly on the amplitudes
of quasi-resonant applied field, i.e., the control. Beside a rigorous proof of
the slow/fast (adiabatic) reduction based on singular perturbation theory, we
also provide a physical interpretation of the result in the context of
coherence population trapping via dark states and decoherence-free subspaces.
Numerical simulations illustrate the accuracy of the proposed approximation for
a 5-level systems.Comment: 6 pages, 2 figure
Distributed source identification for wave equations: an observer-based approach
In this paper, we consider a wave equation on a bounded interval where the
initial conditions are known (are zero) and we are rather interested in
identifying an unknown source term thanks to the measurement output
which is the Neumann derivative on one of the boundaries. We use a
back-and-forth iterative procedure and construct well-chosen observers which
allow to retrieve from in the minimal observation time.Comment: 6 pages, 3 figures, MTNS 201
Stabilizing feedback controls for quantum systems
No quantum measurement can give full information on the state of a quantum
system; hence any quantum feedback control problem is neccessarily one with
partial observations, and can generally be converted into a completely observed
control problem for an appropriate quantum filter as in classical stochastic
control theory. Here we study the properties of controlled quantum filtering
equations as classical stochastic differential equations. We then develop
methods, using a combination of geometric control and classical probabilistic
techniques, for global feedback stabilization of a class of quantum filters
around a particular eigenstate of the measurement operator
Feedback generation of quantum Fock states by discrete QND measures
A feedback scheme for preparation of photon number states in a microwave
cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity
field provides information on its actual state. The control consists in
injecting into the cavity mode a microwave pulse adjusted to maximize the
population of the desired target photon number. In the ideal case (perfect
cavity and measures), we present the feedback scheme and its detailed
convergence proof through stochastic Lyapunov techniques based on
super-martingales and other probabilistic arguments. Quantum Monte-Carlo
simulations performed with experimental parameters illustrate convergence and
robustness of such feedback scheme.Comment: submitted, update version with feedback law of arXiv:0905.0114
[quant-ph
On stability of continuous-time quantum-filters
We prove that the fidelity between the quantum state governed by a continuous
time stochastic master equation driven by a Wiener process and its associated
quantum-filter state is a sub-martingale. This result is a generalization to
non-pure quantum states where fidelity does not coincide in general with a
simple Frobenius inner product. This result implies the stability of such
filtering process but does not necessarily ensure the asymptotic convergence of
such quantum-filters
Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements
We consider discrete-time quantum systems subject to Quantum Non-Demolition
(QND) measurements and controlled by an adjustable unitary evolution between
two successive QND measures. In open-loop, such QND measurements provide a
non-deterministic preparation tool exploiting the back-action of the
measurement on the quantum state. We propose here a systematic method based on
elementary graph theory and inversion of Laplacian matrices to construct strict
control-Lyapunov functions. This yields an appropriate feedback law that
stabilizes globally the system towards a chosen target state among the
open-loop stable ones, and that makes in closed-loop this preparation
deterministic. We illustrate such feedback laws through simulations
corresponding to an experimental setup with QND photon counting
Approximate stabilization of an infinite dimensional quantum stochastic system
We propose a feedback scheme for preparation of photon number states in a
microwave cavity. Quantum Non-Demolition (QND) measurements of the cavity field
and a control signal consisting of a microwave pulse injected into the cavity
are used to drive the system towards a desired target photon number state.
Unlike previous work, we do not use the Galerkin approximation of truncating
the infinite-dimensional system Hilbert space into a finite-dimensional
subspace. We use an (unbounded) strict Lyapunov function and prove that a
feedback scheme that minimizes the expectation value of the Lyapunov function
at each time step stabilizes the system at the desired photon number state with
(a pre-specified) arbitrarily high probability. Simulations of this scheme
demonstrate that we improve the performance of the controller by reducing
"leakage" to high photon numbers.Comment: Submitted to CDC 201
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