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Pierre Rouchon - One of the best experts on this subject based on the ideXlab platform.

  • Exponential stabilization of quantum systems under continuous non-demolition Measurements
    Automatica, 2019
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a quantum Measurement Operator. In open-loop, the system converges to a random eigenstate of the Measurement Operator. The role of the feedback is to prepare a prescribed eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the Measurement Operator. Such reduced filters should play an increasing role towards advanced quantum technologies.

  • Exponential stabilization of quantum systems under continuous non-demolition Measurements
    arXiv: Quantum Physics, 2019
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) Measurement Operator. In open-loop, the system converges to a random eigenstate of the Measurement Operator. The role of the feedback is to prepare a prescribed QND eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the Measurement Operator. Such reduced filters should play an increasing role towards advanced quantum technologies.

  • Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control
    2018
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian Measurement Operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the Measurement Operator. Previous work has proposed state feed-back that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous Measurement output, our controller only depends on the single coordinate along the Measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future

  • CDC - Exponential Stochastic Stabilization of a Two-Level Quantum System via Strict Lyapunov Control
    2018 IEEE Conference on Decision and Control (CDC), 2018
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian Measurement Operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the Measurement Operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous Measurement output, our controller only depends on the single coordinate along the Measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.

Shuang Cong - One of the best experts on this subject based on the ideXlab platform.

  • Online quantum state tomography of N-qubit via continuous weak Measurement and compressed sensing
    International Journal of Quantum Information, 2020
    Co-Authors: Sajede Harraz, Shuang Cong
    Abstract:

    In this paper, we propose an online state tomography method for [Formula: see text]-qubit quantum system based on the continuous weak Measurement and compressed sensing (CS). The quantum system is described by stochastic master equation. The continuous weak Measurement Operators for the [Formula: see text]-qubit quantum system, which are indirectly acted on the quantum system, are derived according to the Measurement Operator results of two-level quantum system. The online time-varying Measurement Operators are obtained by means of the dynamic evolution equation of the system. The quantum state is online estimated by solving the optimization problem of minimizing the two-norm with the positive definite constraints of density matrix, and we use the nonnegative least squares algorithm to solve the optimization problem. CS theory is used to reduce the number of the Measurements in the process of online state estimation. In the numerical experiments, we study the effects of external control field, Measurement rate and the different numbers of qubits on the performance in the proposed method. The minimum required numbers of Measurements for 2, 3, 4 and 5 qubits are found. The normalized distance and fidelity of our proposed method can achieve satisfying accuracy with small number of Measurements.

  • MED - On-Line State Estimation of 2-qubit Quantum Systems
    2019 27th Mediterranean Conference on Control and Automation (MED), 2019
    Co-Authors: Yaru Tang, Shuang Cong
    Abstract:

    In this paper, the online estimation of 2-qubit states is studied based on the quantum continuous weak Measurement and compressed sensing (CS) theory. The stochastic master equation is used to describe the dynamic evolution of the system. The weak Measurement Operator acting on the system and the dynamic equation of the Measurement Operator over time are derived. The number of Measurements is reduced based on the CS theory. The non-negative LS algorithm is used to reconstruct the quantum system state in free evolution. At last, the numerical simulations of the on-line state estimation of 2-qubit quantum systems are carried out in MATLAB environment, and the influences of the parameters on the estimation results are analyzed by the performance comparisons.

  • Feedback stabilization of N -dimensional stochastic quantum systems based on bang-bang control
    Control Theory and Technology, 2017
    Co-Authors: Xiaqing Sun, Sen Kuang, Yanan Liu, Juan Zhou, Shuang Cong
    Abstract:

    For an N-dimensional quantum system under the influence of continuous Measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate Measurement Operator, respectively. In the switching control strategy, we divide the state space into two parts: a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate Measurement Operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous Measurement theory; while for the case of a degenerate Measurement Operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate Measurement Operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.

  • Lyapunov-Based Feedback Preparation of GHZ Entanglement of $N$ -Qubit Systems
    IEEE transactions on cybernetics, 2016
    Co-Authors: Yanan Liu, Sen Kuang, Shuang Cong
    Abstract:

    The Greenberger–Horne–Zeilinger (GHZ) entangled states are a typical class of entangled states in multiparticle systems and play an important role in the applications of quantum communication and quantum computation. For a general quantum system of ${N}$ qubits, degenerate Measurement Operators are often met, which cause the convergence obstacle in the state preparation or stabilization problem. This paper first generalizes the traditional quantum state continuous reduction theory to the case of a degenerate Measurement Operator and chooses a Measurement Operator for an arbitrarily given target GHZ entangled state, then presents a state stabilization control strategy based on the Lyapunov method and achieves the feedback preparation of the target GHZ state. In our stabilization strategy, we separate the target GHZ state and all the other GHZ states that often form the equilibrium points of the closed-loop system by dividing the state space into several different regions; and formally design a switching control law between the regions, which contains the control Hamiltonians to be constructed. By analyzing the stability of the closed-loop system in the different regions, we propose a systematic method for constructing the control Hamiltonians and solve the convergence problem caused by the degenerate Measurement Operator. The global stability of the whole closed-loop stochastic system is strictly proved. Also, we perform some simulation experiments on a three-qubit system and prepare a three-qubit GHZ entangled state. At the same time, the simulation results show the effectiveness of the switching control law and the construction method for the control Hamiltonians proposed in this paper.

Gerardo Cardona - One of the best experts on this subject based on the ideXlab platform.

  • Exponential stabilization of quantum systems under continuous non-demolition Measurements
    Automatica, 2019
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a quantum Measurement Operator. In open-loop, the system converges to a random eigenstate of the Measurement Operator. The role of the feedback is to prepare a prescribed eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the Measurement Operator. Such reduced filters should play an increasing role towards advanced quantum technologies.

  • Exponential stabilization of quantum systems under continuous non-demolition Measurements
    arXiv: Quantum Physics, 2019
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) Measurement Operator. In open-loop, the system converges to a random eigenstate of the Measurement Operator. The role of the feedback is to prepare a prescribed QND eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the Measurement Operator. Such reduced filters should play an increasing role towards advanced quantum technologies.

  • Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control
    2018
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian Measurement Operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the Measurement Operator. Previous work has proposed state feed-back that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous Measurement output, our controller only depends on the single coordinate along the Measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future

  • CDC - Exponential Stochastic Stabilization of a Two-Level Quantum System via Strict Lyapunov Control
    2018 IEEE Conference on Decision and Control (CDC), 2018
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian Measurement Operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the Measurement Operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous Measurement output, our controller only depends on the single coordinate along the Measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.

Alain Sarlette - One of the best experts on this subject based on the ideXlab platform.

  • Exponential stabilization of quantum systems under continuous non-demolition Measurements
    Automatica, 2019
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a quantum Measurement Operator. In open-loop, the system converges to a random eigenstate of the Measurement Operator. The role of the feedback is to prepare a prescribed eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the Measurement Operator. Such reduced filters should play an increasing role towards advanced quantum technologies.

  • Exponential stabilization of quantum systems under continuous non-demolition Measurements
    arXiv: Quantum Physics, 2019
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) Measurement Operator. In open-loop, the system converges to a random eigenstate of the Measurement Operator. The role of the feedback is to prepare a prescribed QND eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the amplitude of this Brownian noise input as a function of the system state. Essentially, it "shakes" the system away from undesired eigenstates by applying strong noise there, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the Measurement Operator. Such reduced filters should play an increasing role towards advanced quantum technologies.

  • Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control
    2018
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian Measurement Operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the Measurement Operator. Previous work has proposed state feed-back that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous Measurement output, our controller only depends on the single coordinate along the Measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future

  • CDC - Exponential Stochastic Stabilization of a Two-Level Quantum System via Strict Lyapunov Control
    2018 IEEE Conference on Decision and Control (CDC), 2018
    Co-Authors: Gerardo Cardona, Alain Sarlette, Pierre Rouchon
    Abstract:

    This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian Measurement Operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the Measurement Operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous Measurement output, our controller only depends on the single coordinate along the Measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.

Abraham Nitzan - One of the best experts on this subject based on the ideXlab platform.

  • simultaneous weak Measurement of non commuting observables a generalized arthurs kelly protocol
    Scientific Reports, 2018
    Co-Authors: Maicol A Ochoa, Wolfgang Belzig, Abraham Nitzan
    Abstract:

    In contrast to a projective quantum Measurement, in a weak Measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A simultaneous Measurement of non-commuting observables cannot be projective, however the strongest possible such Measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such Measurement of position and momentum, we derive a systematic extension to a corresponding weak Measurement along three steps: First, a plausible form of the weak Measurement Operator analogous to the Gaussian Kraus Operator, often used to model a weak Measurement of a single observable, is obtained by projecting a naive extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of Measurement Operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak Measurement operation, namely that this set constitutes a positive Operator valued measure (POVM) in the position-momentum space. Finally, we show that the so-obtained Measurement Operator corresponds to a generalization of the AK Measurement protocol in which the initial detector wavefunctions is suitable broadened.