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104. Dynamically enhancing qubit-oscillator interactions with anti-squeezing

Author

Villiers, Marius, Smith, W. Clarke, Petrescu, Alexandru, Borgognoni, Alvise, Delbecq, Matthieu, Sarlette, Alain, Mirrahimi, Mazyar, Campagne-Ibarcq, Philippe, Kontos, Takis, Leghtas, Zaki, QUANTum Information Circuits (QUANTIC), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre Automatique et Systèmes (CAS), Circuits Quantiques Hybrides, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, This work was sup-ported by the QuantERA grant QuCOS, by ANR 19-QUAN-0006-04. Z.L. acknowledges support from ANR project ENDURANCE, and EMERGENCES grant ENDURANCE of Ville de Paris. This work has been supported by the Paris Ile-de-France Region in the framework of DIM SIRTEQ. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreements No. 851740., ANR-16-ACHN-0012,ENDURANCE,Processus multi-photons dans des circuits supraconducteurs pour la correction d'erreur quantique(2016), and ANR-19-QUAN-0006,QuCoS,Calcul quantique avec les états de chat de Schrödinger(2019)

Subjects
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Abstract

21 pages, 15 figures; The interaction strength of an oscillator to a qubit grows with the oscillator's vacuum field fluctuations. The well known degenerate parametric oscillator has revived interest in the regime of strongly detuned squeezing, where its eigenstates are squeezed Fock states. Owing to these amplified field fluctuations, it was recently proposed that squeezing this oscillator would dynamically boost its coupling to a qubit. In a superconducting circuit experiment, we observe a two-fold increase in the dispersive interaction between a qubit and an oscillator at 5.5 dB of squeezing, demonstrating in-situ dynamical control of qubit-oscillator interactions. This work initiates the experimental coupling of oscillators of squeezed photons to qubits, and cautiously motivates their dissemination in experimental platforms seeking enhanced interactions.

Published
2023

105. Deterministic submanifolds for the backward-evolving quantum state concerning a monitored qubit

Author

Zibo Miao, Zigui Zhang, Kai Li, Yu Pan, and Alain Sarlette

Subjects
Human-Computer Interaction, Control and Optimization, Technology and Engineering, Control and Systems Engineering, Electrical and Electronic Engineering, Computer Science Applications
Abstract

The evolution of a quantum system subject to continuous weak measurement is described by a stochastic differential equation (SDE). It has been shown that the conventional density matrix rho t$\rho _t$ characterized by such SDE, under experimentally relevant settings, remains within a deterministically evolving manifold of low dimension, whose associated equations can be computed explicitly. In this paper, as a complement, it is demonstrated that the effect matrix Et$E_t$, associated to a quantum system at the time t to express its measurement during the interval [t,T]$[t,T]$, also remains confined to a deterministically evolving manifold. In particular, by using the Bloch sphere representation together with the properties of Pauli matrices (as the quantum representation of quaternions), deterministic submanifolds for the effect matrix concerning a monitored qubit are given explicitly. The qubit stays on a deterministically evolving curve in the homodyne amplitude detection scenario, and on a deterministically moving surface under heterodyne amplitude detection. This deterministic characterization should be of interest for parameter estimation and towards obtaining computationally efficient quantum filters for real-time quantum control.

Published
2023

106. Designing High-Fidelity Gates for Dissipative Cat Qubits

Author

Gautier, Ronan, Mirrahimi, Mazyar, and Sarlette, Alain

Subjects
FOS: Physical sciences, Quantum Physics (quant-ph)
Abstract

Bosonic cat qubits stabilized with a driven two-photon dissipation are systems with exponentially biased noise, opening the door to low-overhead, fault-tolerant and universal quantum computing. However, current gate proposals for such qubits induce substantial noise of the unprotected type, whose poor scaling with the relevant experimental parameters limits their practical use. In this work, we provide a new perspective on dissipative cat qubits by reconsidering the reservoir mode used to engineer the tailored two-photon dissipation, and show how it can be leveraged to mitigate gate-induced errors. Doing so, we introduce four new designs of high-fidelity and bias-preserving cat qubit gates, and compare them to the prevalent gate methods. These four designs should give a broad overview of gate engineering for dissipative systems with different and complementary ideas. In particular, we propose both already achievable low-error gate designs and longer-term implementations., 22 pages, 12 figures. All comments on the preprint are welcome

Published
2023
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127. Structurally stable subharmonic regime of a driven quantum Josephson circuit

Author

Michiel Burgelman, Pierre Rouchon, Alain Sarlette, Mazyar Mirrahimi, Mirrahimi, Mazyar, Calcul quantique avec les états de chat de Schrödinger - - QuCoS2019 - ANR-19-QUAN-0006 - ERA-NET Cofund QuantERA - VALID, APPEL À PROJETS GÉNÉRIQUE 2018 - Modèles réduits haute précision pour systèmes quantiques ouverts - - HAMROQS2018 - ANR-18-CE47-0005 - AAPG2018 - VALID, QUANTum Information Circuits (QUANTIC), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), Centre Automatique et Systèmes (CAS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), This work was supported by the QuantERA grant QuCOS and by the ANR grant HAMROQS. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and in-novation programme (grant agreement No. [884762])., ANR-19-QUAN-0006,QuCoS,Calcul quantique avec les états de chat de Schrödinger(2019), and ANR-18-CE47-0005,HAMROQS,Modèles réduits haute précision pour systèmes quantiques ouverts(2018)

Subjects
Quantum Physics, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], General Physics and Astronomy, FOS: Physical sciences, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Quantum Physics (quant-ph)
Abstract

International audience; Driven quantum nonlinear oscillators, while essential for quantum technologies, are generally prone to complex chaotic dynamics that fall beyond the reach of perturbative analysis. By focusing on subharmonic bifurcations of a harmonically driven oscillator, we provide a recipe for the choice of the oscillator's parameters that ensures a regular dynamical behavior independently of the driving strength. We show that this suppression of chaotic phenomena is compatible with a strong quantum nonlinear effect reflected by the confinement rate in the degenerate manifold spanned by stable subharmonic orbits.

Published
2022

130. Design and Implementation of Practical Bidirectional Texture Function Measurement Devices Focusing on the Developments at the University of Bonn

Author

Christopher Schwartz, Ralf Sarlette, Michael Weinmann, Martin Rump, and Reinhard Klein

Subjects
bidirectional texture function, BTF, bidirectional reflectance distribution functions, BRDF, light field, acquisition device, high dynamic range, HDR, camera calibration, gonioreflectometer, Chemical technology, TP1-1185
Abstract

Understanding as well as realistic reproduction of the appearance of materials play an important role in computer graphics, computer vision and industry. They enable applications such as digital material design, virtual prototyping and faithful virtual surrogates for entertainment, marketing, education or cultural heritage documentation. A particularly fruitful way to obtain the digital appearance is the acquisition of reflectance from real-world material samples. Therefore, a great variety of devices to perform this task has been proposed. In this work, we investigate their practical usefulness. We first identify a set of necessary attributes and establish a general categorization of different designs that have been realized. Subsequently, we provide an in-depth discussion of three particular implementations by our work group, demonstrating advantages and disadvantages of different system designs with respect to the previously established attributes. Finally, we survey the existing literature to compare our implementation with related approaches.

Published
2014
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131. Modified Integral Control Globally Counters Symmetry-Breaking Biases

Author

Zhifei Zhang, Zhihao Ling, and Alain Sarlette

Subjects
geometric control theory, Lie groups, symmetry breaking, coordinated swarms, Mathematics, QA1-939
Abstract

We propose a modified integral controller to treat actuation biases in nonholonomic systems. In such systems, although one cannot directly counter biases along all directions, one can still aim at restoring the symmetry of coordinated motion that the biases would break. Focusing on the example of steering controlled planar vehicles, we indeed show how to perfectly stabilize a circular trajectory coordinated with the leader, despite any unknown actuation bias. The proposed solution is a simple modified integral control term, and we prove via a detailed analysis of averaging theory that this control gadget globally stabilizes the perfect coordinated motion. The corresponding general observation is that stabilizing such symmetry-preserving situation can be viewed as rejecting a bias affecting the output measurement, instead of the input command. The symmetry-restoring control then becomes an output bias rejection, dual to the more standard input bias rejection with standard integral control.

Published
2019
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138. Quantum fast-forwarding: Markov chains and graph property testing

Author

Simon Apers, Alain Sarlette, Department of Electronics and Information Systems - Ghent University (ELIS), Universiteit Gent = Ghent University [Belgium] (UGENT), QUANTum Information Circuits (QUANTIC), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Sarlette, Alain, Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands, Universiteit Gent = Ghent University (UGENT), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris)

Subjects
Property testing, Nuclear and High Energy Physics, Speedup, F.2, FOS: Physical sciences, General Physics and Astronomy, property testing, G.2.2, 01 natural sciences, 010305 fluids & plasmas, Theoretical Computer Science, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum state, SEARCH, 0103 physical sciences, WALKS, quantum walks, Quantum walk, ALGORITHM, 010306 general physics, quantum algorithms, [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], ComputingMilieux_MISCELLANEOUS, Mathematical Physics, Quantum walks, Mathematics, Discrete mathematics, Quantum Physics, Quantum algorithms, Markov chain, Stochastic matrix, Statistical and Nonlinear Physics, EXPANSION, HAMILTONIAN SIMULATION, Random walk, Mathematics and Statistics, Physics and Astronomy, Computational Theory and Mathematics, Quantum algorithm, Quantum Physics (quant-ph), 05C85, 60G50, 60J10, 68R10
Abstract

We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition matrix and $D = \sqrt{P\circ P^T}$ its discriminant matrix ($D=P$ if $P$ is symmetric), we construct a quantum walk algorithm that for any quantum state $|v\rangle$ and integer $t$ returns a quantum state $\epsilon$-close to the state $D^t|v\rangle/\|D^t|v\rangle\|$. The algorithm uses $O\Big(\|D^t|v\rangle\|^{-1}\sqrt{t\log(\epsilon\|D^t|v\rangle\|)^{-1}}\Big)$ expected quantum walk steps and $O(\|D^t|v\rangle\|^{-1})$ expected reflections around $|v\rangle$. This shows that quantum walks can accelerate the transient dynamics of Markov chains, complementing the line of results that proves the acceleration of their limit behavior. We show that this tool leads to speedups on random walk algorithms in a very natural way. Specifically we consider random walk algorithms for testing the graph expansion and clusterability, and show that we can quadratically improve the dependency of the classical property testers on the random walk runtime. Moreover, our quantum algorithm exponentially improves the space complexity of the classical tester to logarithmic. As a subroutine of independent interest, we use QFF for determining whether a given pair of nodes lies in the same cluster or in separate clusters. This solves a robust version of $s$-$t$ connectivity, relevant in a learning context for classifying objects among a set of examples. The different algorithms crucially rely on the quantum speedup of the transient behavior of random walks., Comment: 24 pages, 5 pages appendix. 2nd version: exponentially improved error dependency, added application to graph property testing

Published
2019

140. Quantum dynamical decoupling by shaking the close environment

Author

Michiel Burgelman, Paolo Forni, Alain Sarlette, Mirrahimi, Mazyar, QUANTum Information Circuits (QUANTIC), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), and Cambridge Mechatronics Ltd

Subjects
Quantum Physics, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Computer Networks and Communications, Control and Systems Engineering, Applied Mathematics, Signal Processing, FOS: Physical sciences, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Quantum Physics (quant-ph)
Abstract

International audience; Quantum dynamical decoupling is a procedure to cancel the effective coupling between two systems by applying sequences of fast actuations, under which the coupling Hamiltonian averages out to leading order(s). One of its prominent uses is to drive a target system in such a way as to decouple it from a less protected one. The present manuscript investigates the dual strategy: acting on a noisy "environment" subsystem such as to decouple it from a target system. The potential advantages are that actions on the environment commute with system operations, and that imprecisions in the decoupling actuation are harmless to the target. We consider two versions of environment-side decoupling: adding an imprecise Hamiltonian drive which stirs the environment components; and, increasing the decoherence rates on the environment. The latter can be viewed as driving the environment with pure noise and our conclusions establish how, maybe counterintuitively, isolating the environment from noise sources as much as possible is often not the best option. We explicitly analyze the induced decoherence on the target system and establish how it is influenced by the parameters in both cases. The analysis combines Lindbladian derivation, adiabatic elimination, and Floquet modeling in a way that may be of independent interest.

Published
2022

141. Combined Dissipative and Hamiltonian Confinement of Cat Qubits

Author

Ronan Gautier, Alain Sarlette, Mazyar Mirrahimi, QUANTum Information Circuits (QUANTIC), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), and ANR-18-CE47-0005,HAMROQS,Modèles réduits haute précision pour systèmes quantiques ouverts(2018)

Subjects
Quantum Physics, Technology and Engineering, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], STATES, General Engineering, FOS: Physical sciences, General Earth and Planetary Sciences, Quantum Physics (quant-ph), QUANTUM, General Environmental Science
Abstract

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their non-local encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a Two-Photon Exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it only induces a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat qubit experiments., 24 pages, 18 figures

Published
2021

142. Deterministic submanifolds for the backward‐evolving quantum state concerning a monitored qubit.

Author

Miao, Zibo, Zhang, Zigui, Li, Kai, Pan, Yu, and Sarlette, Alain

Subjects
QUANTUM states, HOMODYNE detection, HETERODYNE detection, STOCHASTIC differential equations, DENSITY matrices, SUBMANIFOLDS
Abstract

The evolution of a quantum system subject to continuous weak measurement is described by a stochastic differential equation (SDE). It has been shown that the conventional density matrix ρt$\rho _t$ characterized by such SDE, under experimentally relevant settings, remains within a deterministically evolving manifold of low dimension, whose associated equations can be computed explicitly. In this paper, as a complement, it is demonstrated that the effect matrix Et$E_t$, associated to a quantum system at the time t to express its measurement during the interval [t,T]$[t,T]$, also remains confined to a deterministically evolving manifold. In particular, by using the Bloch sphere representation together with the properties of Pauli matrices (as the quantum representation of quaternions), deterministic submanifolds for the effect matrix concerning a monitored qubit are given explicitly. The qubit stays on a deterministically evolving curve in the homodyne amplitude detection scenario, and on a deterministically moving surface under heterodyne amplitude detection. This deterministic characterization should be of interest for parameter estimation and towards obtaining computationally efficient quantum filters for real‐time quantum control. [ABSTRACT FROM AUTHOR]

Published
2023
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143. Habilitationà Diriger des Recherches (HDR)

Author

Sarlette, Alain, QUANTum Information Circuits (QUANTIC), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Sorbonne Universites, UPMC University of Paris 6, Jean-Michel Coron(coron@ann.jussieu.fr), Sarlette, Alain, Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Contrôle sur variétés, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Control by interaction, Contrôle par interactions, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Quantum control, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Control on manifolds, [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Quantum walks, Marches aléatoires quantiques, Contrôle quantique
Abstract

This manuscript is meant to provide an overview of most of my research activities, taking a step back to highlight the links between my contributions and suggest perspectives for future research directions. A central element on which I have focussed turns out to be controlled interactions, with an approach at the boundary between applied mathematics, theoretical physics, and control theory. Other recurrent elements are nonlinear manifolds, and most importantly tools towards developing quantum technology. The overarching theme is the interplay between information and physical systems modeled by differential equations.A first type of work establishes some fundamental limitations, as a help to guide further research focus. These results include- fundamental bounds on rejecting disturbances in linear systems due to distributed sensing (with European Extremely Large Telescope primary mirror application);- impossibility results on achieving so-called \string stability" in long chains of systems, with the first results in presence of strong nonlinearities (including any form of digital communication);- a structural bound, showing that a rst-order memory already achieves optimal convergence speed in consensus algorithms when the network spectrum can span a given interval (with an opening to accelerate the convergence for clustered spectra)- comprehensive and tight results on the ultimately achievable mixing speed of Quantum Random Walks (QRWs), compared to Markov Chains and so-called Lifted Markov Chains: once memory is allowed, in principle QRWs provide no further speedup.A second type of work has been developing tools for the analysis of few-body, controlled quantum systems, like those built in the experiments of my physics colleagues. Results along these lines include:- results on Lyapunov functions for proving convergence of dissipative quantum systems towards a unique steady state, with an aim for general results and for covering infinite-dimensional systems;- procedures for high-accuracy model reduction in open quantum systems, on the basis of series expansions, extending the usual adiabatic elimination method;- characterizing the presence of low-dimensional deterministic manifolds on which some typical quantum stochastic dierential equations remain conned with probability 1.A third type of work has been the proposal of particular designs or algorithmic procedures. - In the sense of generalizing simple linear procedures, we have proposed principles for applying integral control on nonlinear manifolds; and to formulate \consensus" as an abstract symmetrization procedure that can be extended among others to quantum systems;- Towards stabilizing quantum systems, we have proposed a way to tune the repeated interaction with a stream of auxiliary systems in order to stabilize a target quantum system into a desired state, like so-called Schroedinger cat states of harmonic oscillators, Fock states or squeezed sates- For the same goal, we have developed some improved quantum feedback schemes based on Quantum Non-Demolition measurements: stabilizing highly entangled states between remote systems despite decoherence along the line; and proving how injecting noise of controlled amplitude can achieve the so-far elusive exponential stabilization of eigenstates under weak continuous-time measurement.- While working towards a better understanding of quantum algorithms, in particular QRWs, we have proposed a Quantum Fast-Forwarding algorithm (QFF) which provides an accelerated evolution of a classical Markov chain, without requiring to compute the associated lifted Markov chain as would be needed for designing a classical forwarding algorithm. This algorithm is shown to accelerate primitives on graphs provided via quantum query.The main drive behind all this research has been to understand the essence and limitations of various procedures towards taking decisions in complex dynamical systems, on the basis of continuous physical variables. In this sense, the extraction of some most fundamental elements of quantum technology, combining both hardware level and logical level into a consistent and robust system-theoretic picture, remains a guiding objective for the years to come. This shall involve further intense collaboration with quantum physics experimentalists, and also with algorithm experts as I have started doing more recently. On the way, we plan to develop fundamental tools for approximate analysis and control design guidelines, tailored to the needs of interacting quantum systems.Much of this work has been carried out in collaboration with outstanding and friendly scientific colleagues, whom I most warmly thank for this experience. Those whose work is missing here should please just consider that I had to leave out some things in the process of keeping the present document precise and concise.

Published
2020

144. About strong string stability of a vehicle chain with time-headway control

Author

Alain Sarlette, Arash Farnam, Universiteit Gent = Ghent University [Belgium] (UGENT), QUANTum Information Circuits (QUANTIC), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office., École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Universiteit Gent = Ghent University (UGENT), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), and Sarlette, Alain

Subjects
Time headway, 050210 logistics & transportation, 0209 industrial biotechnology, String length, Technology and Engineering, Proportional derivative, SUBJECT, PLATOONS, 05 social sciences, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], 02 engineering and technology, Chain length, 020901 industrial engineering & automation, Control theory, Optimization and Control (math.OC), Norm (mathematics), Bounded function, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0502 economics and business, FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Absolute velocity, Mathematics - Optimization and Control, [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, Mathematics
Abstract

This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles, i.e. how input disturbances affect the distributed system for very long chains. There exist variants of string stability, like avoiding that a local disturbance gets amplified along the chain, or more strongly ensuring that the output vector's p-norm remains bounded for any bounded vector of input disturbances independently of the string length. They are all impossible to achieve with any linear controller if the vehicles only use relative information of few vehicles in front. Previous work has shown that adding absolute velocity into the controller, allows to at least avoid amplification of a local disturbance. In this paper, we consider the stronger definitions of string stability, under this same relaxation of using absolute velocity in the controller. We prove that the influence from input vector to output vector cannot be bounded independently of chain length in the most popular 2-norm sense, with any bounded stabilizing linear controller; while a proportional derivative (PD) controller can guarantee it in the practically relevant infinity-norm sense. Moreover, we identify the disturbance acting on the leader as the main issue for string stability., Comment: presented at IEEE-CDC 2018, Miami; more complete version and correcting a few typos

Published
2019

145. Minimizing decoherence on target in bipartite open quantum systems

Author

Alain Sarlette, Paolo Forni, Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), QUANTum Information Circuits (QUANTIC), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This work has been supported by the ANR project HAMROQS, ANR-18-CE47-0005,HAMROQS,Modèles réduits haute précision pour systèmes quantiques ouverts(2018), Sarlette, Alain, APPEL À PROJETS GÉNÉRIQUE 2018 - Modèles réduits haute précision pour systèmes quantiques ouverts - - HAMROQS2018 - ANR-18-CE47-0005 - AAPG2018 - VALID, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, and Université Paris sciences et lettres (PSL)

Subjects
Coupling, Physics, 0209 industrial biotechnology, Quantum decoherence, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], 02 engineering and technology, Dissipation, Topology, Hermitian matrix, 020901 industrial engineering & automation, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Hardware_GENERAL, Bipartite graph, Quantum system, Quadratic programming, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Quantum, [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]
Abstract

International audience; We consider a target quantum system, coupled to an auxiliary quantum system which dissipates rapidly at somewhat adjustable rates. The goal is to minimize the dissipation induced on the target system by this coupling. We use explicit model reduction formulas to express this as a quadratic optimization problem. We prove that maybe counterintuitively, when the auxiliary system dissipates along Hermitian (entropy-increasing) channels, the minimum induced dissipation is reached by maximizing the dissipation rate of the auxiliary system.

Published
2019

146. Multiplexed Photon Number Measurement

Author

Essig, Antoine, Ficheux, Quentin, Peronnin, Théau, Cottet, Nathanaël, Lescanne, Raphaël, Sarlette, Alain, Rouchon, Pierre, Leghtas, Zaki, Huard, Benjamin, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), QUANTum Information Circuits (QUANTIC), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), Department of Electronics and Information Systems - Ghent University (ELIS), Universiteit Gent = Ghent University (UGENT), Centre Automatique et Systèmes (CAS), This work is made possible through the support of Fondation Del Duca, IDEX Lyon (Contract No. ANR-16-IDEX-0005) and Contract No. ANR JCJC-HAMROQS., ANR-16-IDEX-0005,IDEXLYON,IDEXLYON(2016), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Physique Mésoscopique, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), MINES ParisTech - École nationale supérieure des mines de Paris, Universiteit Gent = Ghent University [Belgium] (UGENT), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris)

Subjects
Quantum Physics, Technology and Engineering, Condensed Matter - Mesoscale and Nanoscale Physics, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Physics, QC1-999, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Physical sciences, Quantum Physics (quant-ph), [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

When a two-level system -- a qubit -- is used as a probe of a larger system, it naturally leads to answering a single yes-no question about the system state. Here we propose a method where a single qubit is able to extract, not a single, but many bits of information about the photon number of a microwave resonator using continuous measurement. We realize a proof-of-principle experiment by recording the fluorescence emitted by a superconducting qubit reflecting a frequency comb, thus implementing multiplexed photon counting where the information about each Fock state -- from 0 to 8 -- is simultaneously encoded in independent measurement channels. Direct Wigner tomography of the quantum state of the resonator evidences the back-action of the measurement as well as the optimal information extraction parameters. Our experiment unleashes the full potential of quantum meters by replacing a sequential quantum measurements with simultaneous and continuous measurements separated in the frequency domain., Comment: This new version of the manuscript adds several results compared to the first versions

Published
2021

147. Characterizing limits and opportunities in speeding up Markov chain mixing

Author

Alain Sarlette, Simon Apers, Francesco Ticozzi, Universiteit Gent = Ghent University [Belgium] (UGENT), Universita degli Studi di Padova, QUANTum Information Circuits (QUANTIC), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universiteit Gent = Ghent University (UGENT), Università degli Studi di Padova = University of Padua (Unipd), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), and Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Subjects
Statistics and Probability, Speedup, Markov chains, Markov chain, Applied Mathematics, Mixing time, 010102 general mathematics, Algorithm design and analysis, Network theory (graphs), Conductance, Random walk, 01 natural sciences, 010104 statistics & probability, Consensus, Modeling and Simulation, Simulated annealing, Convergence (routing), Statistical physics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mixing (physics), Mathematics
Abstract

International audience; Lifted Markov chains are Markov chains on graphs with added local "memory" and can be used to mix towards a target distribution faster than their memoryless counterparts. Upper and lower bounds on the achievable performance have been provided under specific assumptions. In this paper, we analyze which assumptions and constraints are relevant for mixing, and how changing these assumptions affects those bounds. Explicitly, we find that requesting mixing on either the original or the full lifted graph, and allowing for reducible lifted chains or not, have no essential influence on mixing time bounds. On the other hand, allowing for suitable initialization of the lifted dynamics and/or imposing invariance of the target distribution for any initialization do significantly affect the convergence performance. The achievable convergence speed for a lifted chain goes from diameter-time to no acceleration over a standard Markov chain, with conductance bounds limiting the effectiveness of the intermediate cases. In addition, we show that the relevance of imposing ergodic flows depends on the other criteria. The presented analysis allows us to clarify in which scenarios designing lifted dynamics can lead to better mixing, and provide a flexible framework to compare lifted walks with other acceleration methods.

Published
2021

148. Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback

Author

Gerardo Cardona, Alain Sarlette, and Pierre Rouchon

Subjects
Lyapunov function, 0209 industrial biotechnology, Time quantum, Automatic control, Computer science, Quantum feedback, 020208 electrical & electronic engineering, 02 engineering and technology, Filter (signal processing), symbols.namesake, Noise, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Quantum error correction, Quantum state, Control theory, 0202 electrical engineering, electronic engineering, information engineering, symbols, Error detection and correction
Abstract

We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive. Previous feedback designs could feature spurious equilibria, or resort to discrete kicks pushing the system away from these equilibria to ensure global asymptotic stability. We present a new approach that consists of introducing controls driven by Brownian motions. Unlike the previous methods, the resulting closed-loop dynamics can be shown to stabilize the target manifold exponentially. We further present a reduced-order filter formulation with classical probabilities. The exponential property is important to quantify the protection induced by the closed-loop error-correction dynamics against disturbances. We study numerically the performance of this control law and of the reduced filter. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Published
2019

150. Construire une machine quantique

Author

Sarlette, Alain, QUANTum Information Circuits (QUANTIC), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Interstices, inria, MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris)

Subjects
[PHYS]Physics [physics], [INFO.INFO-AR]Computer Science [cs]/Hardware Architecture [cs.AR], [INFO.INFO-AR] Computer Science [cs]/Hardware Architecture [cs.AR], Calcul Quantique, Physique domaines classiques de la physique, Calculateur analogique, Quantiques, Calculateur numérique, [PHYS] Physics [physics]
Abstract

National audience; Si l’histoire nous dit que le chat de Schrödinger était à la fois mort et vivant, elle ne nous dit pas s’il était obéissant... Or, sans élément capable de les exécuter, l’utilité des algorithmes (suites d’instructions) demeurerait bien limitée.

Published
2021

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