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Luc Bouten

Publications and source records attributed to Luc Bouten.

At least 19 recordsLinked to original sources
arXiv2026

Discretisation of quantum feedback networks for implementation on a quantum computer

Quantum Feedback Network Theory (also known colloquially as the SLH-framework) is a powerful tool for modeling systems in quantum optics. This paper describes a method for discretising SLH-networks such that they can be implemented on a quantum computer. Building on a discretisation theorem for quantum stochastic differential equations, we establish strong convergence, uniformly on compact time intervals, of the discretised system to the continuous SLH-network as the discretisation mesh goes to zero.

quant-ph↗
arXiv2019

Quantum simulating an experiment: Light interference from single ions and their mirror images

We widen the range of applications for quantum computing by introducing digital quantum simulation methods for coherent light-matter interactions: We simulate an experiment where the emitted light from a single ion was interfering with its mirror image [Eschner et. al., Nature 431, 495 (2001)]. Using the quantum simulation software q1tsim we accurately reproduce the interference pattern which had been observed experimentally and also show the effect of the mirror position on the spontaneous emission rate of the ion. In order to minimize the number of required qubits we implement a qubit-reinitialization technique. We show that a digital quantum simulation of complex experiments in atomic and quantum physics is feasible with no more than seven qubits, a setting which is well within reach for advanced quantum computing platforms.

quant-ph↗
arXiv2019

Implementing quantum stochastic differential equations on a quantum computer

We study how to implement quantum stochastic differential equations (QSDEs) on a quantum computer. This is illustrated by an implementation of the QSDE that couples a laser driven two-level atom to the electromagnetic field in the vacuum state on the IBMqx4 Tenerife computer. We compare the resulting master equation and quantum filtering equations to existing theory. In this way we characterize the performance of the computer.

quant-ph↗
arXiv2018

Asymptotic Equivalence of Quantum Stochastic Models

We introduce the notion of perturbations of quantum stochastic models using the series product, and establish the asymptotic convergence of sequences of quantum stochastic models under the assumption that they are related via a right series product perturbation. While the perturbing models converge to the trivial model, we allow that the individual sequences may be divergent corresponding to large model parameter regimes that frequently occur in physical applications. This allows us to introduce the concept of asymptotically equivalent models, and we provide several examples where we replace one sequence of models with an equivalent one tailored to capture specific features. These examples include: a series product formulation of the principle of virtual work; essential commutativity of the noise in strong squeezing models; the decoupling of polarization channels in scattering by Faraday rotation driven by a strong laser field; and an application to quantum local asymptotic normality.

math-ph↗
arXiv2017

Strong squeezing limit in quantum stochastic models

In this paper we study quantum stochastic differential equations (QSDEs) that are driven by strongly squeezed vacuum noise. We show that for strong squeezing such a QSDE can be approximated (via a limit in the strong sense) by a QSDE that is driven by a single commuting noise process. We find that the approximation has an additional Hamiltonian term.

math-ph↗
arXiv2015

A Trotter-Kato Theorem for Quantum Markov Limits

Using the Trotter-Kato theorem we prove the convergence of the unitary dynamics generated by an increasingly singular Hamiltonian in the case of a single field coupling. The limit dynamics is a quantum stochastic evolution of Hudson-Parthasarathy type, and we establish in the process a graph limit convergence of the pre-limit Hamiltonian operators to the Chebotarev-Gregoratti-von Waldenfels Hamiltonian generating the quantum Ito evolution.

math-ph↗
arXiv2014

Fisher informations and local asymptotic normality for continuous-time quantum Markov processes

We consider the problem of estimating an arbitrary dynamical parameter of an quantum open system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be approximated by a quantum Gaussian state whose mean is proportional to the unknown parameter. This approximation holds locally in a neighbourhood of size $t^{-1/2}$ in the parameter space, and provides an explicit expression of the asymptotic quantum Fisher information in terms of the Markov generator. Furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical Fisher informations. The mathematical theorems are illustrated with the examples of a two-level system and the atom maser. Our results contribute towards a better understanding of the statistical and probabilistic properties of the output process, with relevance for quantum control engineering, and the theory of non-equilibrium quantum open systems.

quant-ph↗
arXiv2008

Physical model of continuous two-qubit parity measurement in a cavity-QED network

We propose and analyze a physical implementation of two-qubit parity measurements as required for continuous error correction, assuming a setup in which the individual qubits are strongly coupled to separate optical cavities. A single optical probe beam scatters sequentially from the two cavities and the continuous parity measurement is realized via fixed quadrature homodyne photo-detection. We present models based on quantum stochastic differential equations (QSDE's) for both an ideal continuous parity measurement and our proposed cavity quantum electrodynamics (cavity QED) implementation; a recent adiabatic elimination theorem for QSDE's is used to assert strong convergence of the latter to the former in an appropriate limit of physical parameters. Performance of the cavity QED scheme is studied via numerical simulation with experimentally realistic parameters.

quant-ph↗
arXiv2008

Discrete Approximation of Quantum Stochastic Models

We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main theorem, which is based on the Trotter-Kato theorem, is not restricted to a specific noise model and does not require boundedness of the limit coefficients.

math-ph↗
arXiv2008

Quantum risk-sensitive estimation and robustness

This paper studies a quantum risk-sensitive estimation problem and investigates robustness properties of the filter. This is a direct extension to the quantum case of analogous classical results. All investigations are based on a discrete approximation model of the quantum system under consideration. This allows us to study the problem in a simple mathematical setting. We close the paper with some examples that demonstrate the robustness of the risk-sensitive estimator.

quant-ph↗
arXiv2007

Adiabatic elimination in quantum stochastic models

We consider a physical system with a coupling to bosonic reservoirs via a quantum stochastic differential equation. We study the limit of this model as the coupling strength tends to infinity. We show that in this limit the solution to the quantum stochastic differential equation converges strongly to the solution of a limit quantum stochastic differential equation. In the limiting dynamics the excited states are removed and the ground states couple directly to the reservoirs.

math-ph↗
arXiv2007

Optimality of feedback control strategies for qubit purification

Recently two papers [K. Jacobs, Phys. Rev. A {\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\bf 8}, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various goals. In the former paper the proof of optimality was not mathematically rigorous, while the latter gave only heuristic arguments for optimality. In this paper we provide rigorous proofs of optimality in all cases, by applying simple concepts from optimal control theory, including Bellman equations and verification theorems.

quant-ph↗
arXiv2007

Scattering of polarized laser light by an atomic gas in free space: a QSDE approach

We propose a model, based on a quantum stochastic differential equation (QSDE), to describe the scattering of polarized laser light by an atomic gas. The gauge terms in the QSDE account for the direct scattering of the laser light into different field channels. Once the model has been set, we can rigorously derive quantum filtering equations for balanced polarimetry and homodyne detection experiments, study the statistics of output processes and investigate a strong driving, weak coupling limit.

quant-ph↗
arXiv2006

A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory, while remaining completely within the setting of finite-dimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.

math.PR↗
arXiv2006

On the separation principle of quantum control

It is well known that quantum continuous observations and nonlinear filtering can be developed within the framework of the quantum stochastic calculus of Hudson-Parthasarathy. The addition of real-time feedback control has been discussed by many authors, but the foundations of the theory still appear to be relatively undeveloped. Here we introduce the notion of a controlled quantum flow, where feedback is taken into account by allowing the coefficients of the quantum stochastic differential equation to be adapted processes in the observation algebra. We then prove a separation theorem for quantum control: the admissible control that minimizes a given cost function is a memoryless function of the filter, provided that the associated Bellman equation has a sufficiently regular solution. Along the way we obtain results on existence and uniqueness of the solutions of controlled quantum filtering equations and on the innovations problem in the quantum setting.

math-ph↗
arXiv2006

Optimal Pointers for Joint Measurement of sigma-x and sigma-z via Homodyne Detection

We study a model of a two-level system (i.e. a qubit) in interaction with the electromagnetic field. By means of homodyne detection, one field-quadrature is observed continuously in time. Due to the interaction, information about the initial state of the qubit is transferred into the field, thus influencing the homodyne measurement results. We construct random variables (pointers) on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of sigma-x and sigma-z. Using variational calculus, we find the pointers that are optimal. These optimal pointers are very close to hitting the bound imposed by Heisenberg's uncertainty relation on joint measurement of two non-commuting observables. We close the paper by giving the probability densities of the pointers.

quant-ph↗
arXiv2006

Quantum filtering: a reference probability approach

These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. Next we describe the Hudson-Parthasarathy quantum Ito calculus and its use in the modelling of physical systems. Finally, we use a reference probability method to obtain quantum filtering equations, in the Belavkin-Zakai (unnormalized) form, for several system-observation models from quantum optics. The normalized (Belavkin-Kushner-Stratonovich) form is obtained through a noncommutative analogue of the Kallianpur-Striebel formula.

math-ph↗