arXiv subjects

Nina H. Amini

Publications and source records attributed to Nina H. Amini.

At least 37 records · Page 2Linked to original sources

arXiv2023

On Asymptotic Stability of Non-Demolition Quantum Trajectories with Measurement Imperfections

We consider the question of asymptotic stability of quantum trajectories undergoing quantum non-demolition imperfect measurement, that is to say the convergence of the estimated trajectory towards the true trajectory whose parameters and initial state are not necessarily known. We give conditions on the estimated initial state and regions of validity for the estimated parameters so that this convergence is ensured. We illustrate these results through numerical simulations on the physical example [1] and discuss the asymptotic stability for a more realistic general case where decoherence acts on the system. In this case, the evolution is described by new Kraus operators which do not satisfy the quantum non-demolition property.

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arXiv2022

Model robustness for feedback stabilization of open quantum systems

This paper generalizes the results in [30] concerning feedback stabilization of target states for N-level quantum angular momentum systems undergoing quantum non-demolition measurements (QND) in absence of the knowledge about initial states and parameters. Here we consider multiple measurement operators and study the stabilization toward a chosen target subspace which is a common eigenspace of measurement operators. Under the QND conditions, we show that this analysis provides necessary tools to ensure feedback stabilization based on a simplified filter whose state is a N-dimensional vector. A numerical analysis has been proposed in [18]. This paper provides a complete proof for the use of a simplified filter in feedback stabilization. This has important practical use as the dimension of quantum systems is usually high. This paper opens the way toward a complete proof concerning the robustness of a stabilizing feedback with respect to approximate filters, which is lacking.

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arXiv2022

Parameter Estimation for Quantum Trajectories: Convergence Result

A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an experimental perspective, these Kraus operators can depend on unknown physical parameters p. An interesting and powerful method has been proposed in [1] to estimate a parameter in a finite set; however, complete results of convergence were lacking. This article fills this gap by rigorously showing the consistency of the method, whereas there was only numerical evidence so far. When the parameter belongs to a continuous set, we propose an algorithm to approach its value and show simulation results.

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arXiv2021

On stability of quantum trajectories and their Cesaro mean

We address the question of stability of quantum trajectories, also referred as quantum filters}. We determine the limit of the quantum fidelity between the true quantum trajectory and the {estimated one}. Under a purification assumption we show that this limit equals to one meaning that quantum filters are stable. In the general case, under an identifiability and a spectral assumption we show that the limit of the Cesaro mean of the estimated trajectory is the same as the true one.

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arXiv2020

Feedback exponential stabilization of GHZ states of multi-qubit systems

In this paper, we consider stochastic master equations describing the evolution of a multi-qubit system interacting with electromagnetic fields undergoing continuous-time measurements. By considering multiple z-type (Pauli z matrix on different qubits) and x-type (Pauli x matrix on all qubits) measurements and one control Hamiltonian, we provide general conditions on the feedback controller and the control Hamiltonian ensuring almost sure exponential convergence to a predetermined Greenberger-Horne-Zeilinger (GHZ) state, which is assumed to be a common eigenstate of the measurement operators. We provide explicit expressions of feedback controllers satisfying such conditions. We also consider the case of only z-type measurements and multiple control Hamiltonians, and we discuss asymptotic convergence towards a predetermined GHZ state. Finally, we demonstrate the effectiveness of our methodology for a three-qubit system through numerical simulations.

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arXiv2020

Robust feedback stabilization of N-level quantum spin systems

In this paper, we consider N-level quantum angular momentum systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose unawareness of the initial state and physical parameters, entailing the introduction of an additional state representing the estimated quantum state. The evolution of the quantum state and its estimation is described by a coupled stochastic master equation. Here, we study the asymptotic behavior of such a system in presence of a feedback controller. We provide sufficient conditions on the feedback controller and on the estimated parameters that guarantee exponential stabilization of the coupled stochastic system towards an eigenstate of the measurement operator. Furthermore, we estimate the corresponding rate of convergence. We also provide parametrized feedback laws satisfying such conditions. Our results show the robustness of the feedback stabilization strategy considered in [21] in case of imprecise initialization of the estimated state and with respect to the unknown physical parameters.

math.OC↗

arXiv2020

On the robustness of stabilizing feedbacks for quantum spin-1/2 systems

In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact values of the physical parameters are unknown. We prove that the feedback stabilization strategy considered in [16] is robust to these imperfections. This is shown by studying the asymptotic behavior of the coupled stochastic master equations describing the evolutions of the actual state and the estimated one under appropriate assumptions on the feedback controller. We provide sufficient conditions on the feedback controller and a valid domain of estimated parameters which ensure exponential stabilization of the coupled system. Furthermore, our results allow us to answer positively to [15,Conjecture 4.4] in the case of spin-1/2 systems with unknown initial states, even in presence of imprecisely known physical parameters.

math.OC↗

arXiv2019

On estimation and feedback control of spin-1/2 systems with unknown initial states

In this paper, we consider stochastic master equations describing the evolutions of quantum systems interacting with electromagnetic fields undergoing continuous-time measurements. In particular, we study feedback control of quantum spin-1/2 systems in the case of unawareness of initial states and in presence of measurement imperfections. We prove that the fidelity between the actual quantum filter and its associated estimated filter converges to one under appropriate assumption on the feedback controller. This shows the asymptotic convergence of such filters. In addition, for spin-J systems, we discuss heuristically the asymptotic behavior of the actual quantum filter and its associated estimated filter and the possibility of exponentially stabilizing such systems towards an eigenvector of the measurement operator by an appropriate feedback.

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arXiv2019

On the response of a two-level system to two-photon inputs

The purpose of this paper is to study the interaction between a two-level system and two continuous-mode photons. Two scenarios are investigated: Case 1, how a two-level system changes the pulse shapes of two input photons propagating in a single input channel; and Case 2, how a two-level system responds to two counter-propagating photons. By means of a transfer function approach, the steady-state output field states for both cases are derived analytically. In Example 1, a two-photon input state of Gaussian pulse shape is used to excite a two-level atom. The simulation demonstrates that in the time domain the atom tends to stretch out the two photons. Moreover, the striking difference between the joint probability distribution of the output two-photon state and that of the input two-photon state occurs exactly under the setting when the two-level atom is most efficiently excited. In Example 2, a two-photon input state of rising exponential pulse shape is used to excite a two-level atom. Strong anti-correlation of the output two-photon state is observed, which is absent in Example 1 for the Gaussian pulse shape. Such difference indicates that different pulse shapes give rise to drastically different frequency entanglement of the output two-photon state. Example 3 is used to illustrate Case 2, where two counter-propagating single photons of rising exponential pulse shapes are input to a two-level atom. The frequency-dependent Hong-Ou-Mandel (HOM) interference phenomenon is observed. The simulation results base on the analytic forms of output two-photon states are consistent with those based on quantum master or filter equations [43,11]. Similar physical phenomena have been observed in physical settings such as cavity opto-mechanical systems and Keer nonlinear cavities.

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arXiv2019

On exponential stabilization of two-qubit systems

In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to a predetermined Bell state. This is obtained by applying stochastic tools, Lyapunov methods and geometric control tools. With one channel, we establish asymptotic convergence towards a predetermined Bell state. In both cases, we provide explicit expressions of feedback control laws satisfying the above-mentioned conditions. Finally, we demonstrate the effectiveness of our methodology through numerical simulations.

math.OC↗

arXiv2019

Quantum filtering for a two-level atom driven by two counter-propagating photons

The purpose of this paper is to propose quantum filters for a two-level atom driven by two continuous-mode counter-propagating photons and under continuous measurements. Two scenarios of multiple measurements, 1) homodyne detection plus photodetection, and 2) two homodyne detections, are discussed. Filtering equations for both cases are derived explicitly. As demonstration, the two input photons with rising exponential and Gaussian pulse shapes are used to excite a two-level atom under two homodyne detection measurements. Simulations reveal scaling relations between atom-photon coupling and photonic pulse shape for maximum atomic excitation.

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arXiv2019

On exponential stabilization of N-level quantum angular momentum systems

In this paper, we consider the feedback stabilization problem for N-level quantum angular momentum systems undergoing continuous-time measurements. By using stochastic and geometric control tools, we provide sufficient conditions on the feedback control law ensuring almost sure exponential convergence to a predetermined eigenstate of the measurement operator. In order to achieve these results, we establish general features of quantum trajectories which are of interest by themselves. We illustrate the results by designing a class of feedback control laws satisfying the above-mentioned conditions and finally we demonstrate the effectiveness of our methodology through numerical simulations for three-level quantum angular momentum systems.

math.OC↗

arXiv2019

On Exponential Stabilization of Spin-1/2 Systems

In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.

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arXiv2018

Single-photon quantum filtering with multiple measurements

The single-photon quantum filtering problems have been investigated recently with applications in quantum computing. In practice, the detector responds with a quantum efficiency of less than unity since there exists some mode mismatch between the detector and the system, and the single-photon signal may be corrupted by quantum white noise. Consequently, quantum filters based on multiple measurements are designed in this paper to improve the estimation performance. More specifically, the filtering equations for a two-level quantum system driven by a single-photon input state and under multiple measurements are presented in this paper. Four scenarios, 1) two diffusive measurements with Q-P quadrature form, 2) two diffusive measurements with Q-Q quadrature form, 3) diffusive plus Poissonian measurements, and 4) two Poissonian measurements, are considered. It is natural to compare the filtering results, i.e., measuring single channel or both channels, which one is better? By the simulation where we use a single photon to excite an atom, it seems that multiple measurements enable us to excite the atom with higher probability than only measuring single channel. In addition, measurement back-action phenomenon is revealed by the simulation results.

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arXiv2017

Entropy Production and Information Flow for Markov Diffusions with Filtering

Filtering theory gives an explicit models for the flow of information and thereby quantifies the rates of change of information supplied to and dissipated from the filter's memory. Here we extend the analysis of Mitter and Newton from linear Gaussian models to general nonlinear filters involving Markov diffusions.The rates of entropy production are now generally the average squared-field (co-metric) of various logarithmic probability densities, which may be interpreted as Fisher information associate with Gaussian perturbations (via de Bruijn's identity). We show that the central connection is made through the Mayer-Wolf and Zakai Theorem for the rate of change of the mutual information between the filtered state and the observation history. In particular, we extend this Theorem to cover a Markov diffusion controlled by observations process, which may be interpreted as the filter acting as a Maxwell's Daemon applying feedback to the system.

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arXiv2016

How To Build A Quantum Coherent Observer

We give an explicit construction for a quantum observer coherently mimicking the dynamics of a cavity mode system and without any disturbance of the system's dynamics. This gives the exact analogue of the Luenberger observer used in controller design in engineering

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arXiv2015

Quantum filtering for multiple measurements driven by fields in single-photon states

In this paper, we derive the stochastic master equations for quantum systems driven by a single-photon input state which is contaminated by quantum vacuum noise. To improve estimation performance, quantum filters based on multiple-channel measurements are designed. Two cases, namely diffusive plus Poissonian measurements and two diffusive measurements, are considered.

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arXiv2015

Interpolation Approach to Hamiltonian-varying Quantum Systems and the Adiabatic Theorem

Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure could be taken as the error of adiabatic approximation. We prove under certain conditions, this error can be precisely estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example on which the applicability of the adiabatic theorem is questionable.

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