2.1 Overall objectives

The research activities of QUANTIC team lie at the border between theoretical and experimental efforts in the emerging field of quantum systems engineering. Our research topics are in direct continuation of a historic research theme of INRIA, classical automatic control, while opening completely new perspectives toward quantum control: by developing a new mathematical system theory for quantum circuits, we will realize the components of a future quantum information processing unit.

One of the unique features of our team concerns the large spectrum of our subjects going from the mathematical analysis of the physical systems (development of systematic mathematical methods for control and estimation of quantum systems), and the numerical analysis of the proposed solutions, to the experimental implementation of the quantum circuits based on these solutions. This is made possible by the constant and profound interaction between the applied mathematicians and the physicists in the group. Indeed, this close collaboration has already brought a significant acceleration in our research efforts. In a long run, this synergy should lead to a deeper understanding of the physical phenomena behind these emerging technologies and the development of new research directions within the field of quantum information processing.

Towards this ultimate task of practical quantum digital systems, the approach of the QUANTIC team is complementary to the one taken by teams with expertise in quantum algorithms. Indeed, we start from the specific controls that can be realistically applied on physical systems, to propose designs which combine them into hardware shortcuts implementing robust behaviors useful for quantum information processing. Whenever a significant new element of quantum engineering architecture is developed, the initial motivation is to prove an enabling technology with major impact for the groups working one abstraction layer higher: on quantum algorithms but also on e.g. secure communication and metrology applications.

3.1 Hardware-efficient quantum information processing

In this scientific program, we will explore various theoretical and experimental issues concerning protection and manipulation of quantum information. Indeed, the next, critical stage in the development of Quantum Information Processing (QIP) is most certainly the active quantum error correction (QEC). Through this stage one designs, possibly using many physical qubits, an encoded logical qubit which is protected against major decoherence channels and hence admits a significantly longer effective coherence time than a physical qubit. Reliable (fault-tolerant) computation with protected logical qubits usually comes at the expense of a significant overhead in the hardware (up to thousands of physical qubits per logical qubit). Each of the involved physical qubits still needs to satisfy the best achievable properties (coherence times, coupling strengths and tunability). More remarkably, one needs to avoid undesired interactions between various subsystems. This is going to be a major difficulty for qubits on a single chip.

The usual approach for the realization of QEC is to use many qubits to obtain a larger Hilbert space of the qubit register  86, 89. By redundantly encoding quantum information in this Hilbert space of larger dimension one make the QEC tractable: different error channels lead to distinguishable error syndromes. There are two major drawbacks in using multi-qubit registers. The first, fundamental, drawback is that with each added physical qubit, several new decoherence channels are added. Because of the exponential increase of the Hilbert's space dimension versus the linear increase in the number of decay channels, using enough qubits, one is able to eventually protect quantum information against decoherence. However, multiplying the number of possible errors, this requires measuring more error syndromes. Note furthermore that, in general, some of these new decoherence channels can lead to correlated action on many qubits and this needs to be taken into account with extra care: in particular, such kind of non-local error channels are problematic for surface codes. The second, more practical, drawback is that it is still extremely challenging to build a register of more than on the order of 10 qubits where each of the qubits is required to satisfy near the best achieved properties: these properties include the coherence time, the coupling strengths and the tunability. Indeed, building such a register is not merely only a fabrication task but rather, one requirers to look for architectures such that, each individual qubit can be addressed and controlled independently from the others. One is also required to make sure that all the noise channels are well-controlled and uncorrelated for the QEC to be effective.

We have recently introduced a new paradigm for encoding and protecting quantum information in a quantum harmonic oscillator (e.g. a high-Q mode of a 3D superconducting cavity) instead of a multi-qubit register  63. The infinite dimensional Hilbert space of such a system can be used to redundantly encode quantum information. The power of this idea lies in the fact that the dominant decoherence channel in a cavity is photon damping, and no more decay channels are added if we increase the number of photons we insert in the cavity. Hence, only a single error syndrome needs to be measured to identify if an error has occurred or not. Indeed, we are convinced that most early proposals on continuous variable QIP  60, 52 could be revisited taking into account the design flexibilities of Quantum Superconducting Circuits (QSC) and the new coupling regimes that are provided by these systems. In particular, we have illustrated that coupling a qubit to the cavity mode in the strong dispersive regime provides an important controllability over the Hilbert space of the cavity mode  62. Through a recent experimental work  94, we benefit from this controllability to prepare superpositions of quasi-orthogonal coherent states, also known as Schrödinger cat states.

In this Scheme, the logical qubit is encoded in a four-component Schrödinger cat state. Continuous quantum non-demolition (QND) monitoring of a single physical observable, consisting of photon number parity, enables then the tractability of single photon jumps. We obtain therefore a first-order quantum error correcting code using only a single high-Q cavity mode (for the storage of quantum information), a single qubit (providing the non-linearity needed for controllability) and a single low-Q cavity mode (for reading out the error syndrome). An earlier experiment on such QND photon-number parity measurements  90 has recently led to a first experimental realization of a full quantum error correcting code improving the coherence time of quantum information 8. As shown in Figure 1, this leads to a significant hardware economy for realization of a protected logical qubit. Our goal here is to push these ideas towards a reliable and hardware-efficient paradigm for universal quantum computation.

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3.2 Reservoir (dissipation) engineering and autonomous stabilization of quantum systems

Being at the heart of any QEC protocol, the concept of feedback is central for the protection of quantum information, enabling many-qubit quantum computation or long-distance quantum communication. However, such a closed-loop control which requires a real-time and continuous measurement of the quantum system has been for long considered as counter-intuitive or even impossible. This thought was mainly caused by properties of quantum measurements: any measurement implies an instantaneous strong perturbation to the system's state. The concept of quantum non-demolition (QND) measurement has played a crucial role in understanding and resolving this difficulty   34. In the context of cavity quantum electro-dynamics (cavity QED) with Rydberg atoms  56, a first experiment on continuous QND measurements of the number of microwave photons was performed by the group at Laboratoire Kastler-Brossel (ENS)  53. Later on, this ability of performing continuous measurements allowed the same group to realize the first continuous quantum feedback protocol stabilizing highly non-classical states of the microwave field in the cavity, the so-called photon number states 10 (this ground-breaking work was mentioned in the Nobel prize attributed to Serge Haroche). The QUANTIC team contributed to the theoretical work behind this experiment  44, 22, 88, 24. These contributions include the development and optimization of the quantum filters taking into account the quantum measurement back-action and various measurement noises and uncertainties, the development of a feedback law based on control Lyapunov techniques, and the compensation of the feedback delay.

In the context of circuit quantum electrodynamics (circuit QED)  42, recent advances in quantum-limited amplifiers  79, 92 have opened doors to high-fidelity non-demolition measurements and real-time feedback for superconducting qubits  57. This ability to perform high-fidelity non-demolition measurements of a quantum signal has very recently led to quantum feedback experiments with quantum superconducting circuits  92, 78, 36. Here again, the QUANTIC team has participated to one of the first experiments in the field where the control objective is to track a dynamical trajectory of a single qubit rather than stabilizing a stationary state. Such quantum trajectory tracking could be further explored to achieve metrological goals such as the stabilization of the amplitude of a microwave drive  70.

While all this progress has led to a strong optimism about the possibility to perform active protection of quantum information against decoherence, the rather short dynamical time scales of these systems limit, to a great amount, the complexity of the feedback strategies that could be employed. Indeed, in such measurement-based feedback protocols, the time-consuming data acquisition and post-treatment of the output signal leads to an important latency in the feedback procedure.

The reservoir (dissipation) engineering  76 and the closely related coherent feedback  68 are considered as alternative approaches circumventing the necessity of a real-time data acquisition, signal processing and feedback calculations. In the context of quantum information, the decoherence, caused by the coupling of a system to uncontrolled external degrees of freedom, is generally considered as the main obstacle to synthesize quantum states and to observe quantum effects. Paradoxically, it is possible to intentionally engineer a particular coupling to a reservoir in the aim of maintaining the coherence of some particular quantum states. In a general viewpoint, these approaches could be understood in the following manner: by coupling the quantum system to be stabilized to a strongly dissipative ancillary quantum system, one evacuates the entropy of the main system through the dissipation of the ancillary one. By building the feedback loop into the Hamiltonian, this type of autonomous feedback obviates the need for a complicated external control loop to correct errors. On the experimental side, such autonomous feedback techniques have been used for qubit reset  51, single-qubit state stabilization  71, and the creation  29 and stabilization  61, 67, 85 of states of multipartite quantum systems.

Such reservoir engineering techniques could be widely revisited exploring the flexibility in the Hamiltonian design for QSC. We have recently developed theoretical proposals leading to extremely efficient, and simple to implement, stabilization schemes for systems consisting of a single, two or three qubits  51, 65, 40, 43. The experimental results based on these protocols have illustrated the efficiency of the approach  51, 85. Through these experiments, we exploit the strong dispersive interaction  83 between superconducting qubits and a single low-Q cavity mode playing the role of a dissipative reservoir. Applying continuous-wave (cw) microwave drives with well-chosen fixed frequencies, amplitudes, and phases, we engineer an effective interaction Hamiltonian which evacuates the entropy of the system interacting with a noisy environment: by driving the qubits and cavity with continuous-wave drives, we induce an autonomous feedback loop which corrects the state of the qubits every time it decays out of the desired target state. The schemes are robust against small variations of the control parameters (drives amplitudes and phase) and require only some basic calibration. Finally, by avoiding resonant interactions between the qubits and the low-Q cavity mode, the qubits remain protected against the Purcell effect, which would reduce the coherence times. We have also investigated both theoretically and experimentally the autonomous stabilization of non-classical states (such as Schrodinger cat states and Fock states) of microwave field confined in a high-Q cavity mode  81, 587, 5.

3.3 System theory for quantum information processing

In parallel and in strong interactions with the above experimental goals, we develop systematic mathematical methods for dynamical analysis, control and estimation of composite and open quantum systems. These systems are built with several quantum subsystems whose irreversible dynamics results from measurements and/or decoherence. A special attention is given to spin/spring systems made with qubits and harmonic oscillators. These developments are done in the spirit of our recent contributions  80, 22, 87, 82, 88, 249 resulting from collaborations with the cavity quantum electrodynamics group of Laboratoire Kastler Brossel.

3.4 Stabilization by measurement-based feedback

The protection of quantum information via efficient QEC is a combination of (i) tailored dynamics of a quantum system in order to protect an informational qubit from certain decoherence channels, and (ii) controlled reaction to measurements that efficiently detect and correct the dominating disturbances that are not rejected by the tailored quantum dynamics.

In such feedback scheme, the system and its measurement are quantum objects whereas the controller and the control input are classical. The stabilizing control law is based on the past values of the measurement outcomes. During our work on the LKB photon box, we have developed, for single input systems subject to quantum non-demolition measurement, a systematic stabilization method  24: it is based on a discrete-time formulation of the dynamics, on the construction of a strict control Lyapunov function and on an explicit compensation of the feedback-loop delay. Keeping the QND measurement assumptions, extensions of such stabilization schemes will be investigated in the following directions: finite set of values for the control input with application to the convergence analysis of the atomic feedback scheme experimentally tested in  95; multi-input case where the construction by inversion of a Metzler matrix of the strict Lyapunov function is not straightforward; continuous-time systems governed by diffusive master equations; stabilization towards a set of density operators included in a target subspace; adaptive measurement by feedback to accelerate the convergence towards a stationary state as experimentally tested in  74. Without the QND measurement assumptions, we will also address the stabilization of non-stationary states and trajectory tracking, with applications to systems similar to those considered in  57, 36.

3.5 Filtering, quantum state and parameter estimations

The performance of every feedback controller crucially depends on its online estimation of the current situation. This becomes even more important for quantum systems, where full state measurements are physically impossible. Therefore the ultimate performance of feedback correction depends on fast, efficient and optimally accurate state and parameter estimations.

A quantum filter takes into account imperfection and decoherence and provides the quantum state at time $t\ge 0$ from an initial value at $t=0$ and the measurement outcomes between 0 and $t$. Quantum filtering goes back to the work of Belavkin   30 and is related to quantum trajectories  37, 41. A modern and mathematical exposure of the diffusive models is given in  28. In  55 a first convergence analysis of diffusive filters is proposed. Nevertheless the convergence characterization and estimation of convergence rate remain open and difficult problems. For discrete time filters, a general stability result based on fidelity is proven in  80, 87. This stability result is extended to a large class of continuous-time filters in  23. Further efforts are required to characterize asymptotic and exponential stability. Estimations of convergence rates are available only for quantum non-demolition measurements  31. Parameter estimations based on measurement data of quantum trajectories can be formulated within such quantum filtering framework  46, 72.

We will continue to investigate stability and convergence of quantum filtering. We will also exploit our fidelity-based stability result to justify maximum likelihood estimation and to propose, for open quantum system, parameter estimation algorithms inspired of existing estimation algorithms for classical systems. We will also investigate a more specific quantum approach: it is noticed in  35 that post-selection statistics and “past quantum” state analysis  47 enhance sensitivity to parameters and could be interesting towards increasing the precision of an estimation.

3.6 Stabilization by interconnections

In such stabilization schemes, the controller is also a quantum object: it is coupled to the system of interest and is subject to decoherence and thus admits an irreversible evolution. These stabilization schemes are closely related to reservoir engineering and coherent feedback   76, 68. The closed-loop system is then a composite system built with the original system and its controller. In fact, and given our particular recent expertise in this domain 985, 51, this subsection is dedicated to further developing such stabilization techniques, both experimentally and theoretically.

The main analysis issues are to prove the closed-loop convergence and to estimate the convergence rates. Since these systems are governed by Lindblad differential equations (continuous-time case) or Kraus maps (discrete-time case), their stability is automatically guaranteed: such dynamics are contractions for a large set of metrics (see  75). Convergence and asymptotic stability is less well understood. In particular most of the convergence results consider the case where the target steady-state is a density operator of maximum rank (see, e.g., 27[chapter 4, section 6]). When the goal steady-state is not full rank very few convergence results are available.

We will focus on this geometric situation where the goal steady-state is on the boundary of the cone of positive Hermitian operators of finite trace. A specific attention will be given to adapt standard tools (Lyapunov function, passivity, contraction and Lasalle's invariance principle) for infinite dimensional systems to spin/spring structures inspired of 9, 785, 51 and their associated Fokker-Planck equations for the Wigner functions.

We will also explore the Heisenberg point of view in connection with recent results of the INRIA project-team MAXPLUS (algorithms and applications of algebras of max-plus type) relative to Perron-Frobenius theory  50, 49. We will start with  84 and  77 where, based on a theorem due to Birkhoff  32, dual Lindblad equations and dual Kraus maps governing the Heisenberg evolution of any operator are shown to be contractions on the cone of Hermitian operators equipped with Hilbert's projective metric. As the Heisenberg picture is characterized by convergence of all operators to a multiple of the identity, it might provide a mean to circumvent the rank issues. We hope that such contraction tools will be especially well adapted to analyzing quantum systems composed of multiple components, motivated by the facts that the same geometry describes the contraction of classical systems undergoing synchronizing interactions 91 and by our recent generalized extension of the latter synchronizing interactions to quantum systems 69.

Besides these analysis tasks, the major challenge in stabilization by interconnections is to provide systematic methods for the design, from typical building blocks, of control systems that stabilize a specific quantum goal (state, set of states, operation) when coupled to the target system. While constructions exist for so-called linear quantum systems 73, this does not cover the states that are more interesting for quantum applications. Various strategies have been proposed that concatenate iterative control steps for open-loop steering 93, 66 with experimental limitations. The characterization of Kraus maps to stabilize any types of states has also been established 33, but without considering experimental implementations. A viable stabilization by interaction has to combine the capabilities of these various approaches, and this is a missing piece that we want to address.

4.1 Quantum engineering

A new field of quantum systems engineering has emerged during the last few decades. This field englobes a wide range of applications including nano-electromechanical devices, nuclear magnetic resonance applications, quantum chemical synthesis, high resolution measurement devices and finally quantum information processing devices for implementing quantum computation and quantum communication. Recent theoretical and experimental achievements have shown that the quantum dynamics can be studied within the framework of estimation and control theory, but give rise to new models that have not been fully explored yet.

The QUANTIC team's activities are defined at the border between theoretical and experimental efforts of this emerging field with an emphasis on the applications in quantum information, computation and communication. The main objective of this interdisciplinary team is to develop quantum devices ensuring a robust processing of quantum information.

On the theory side, this is done by following a system theory approach: we develop estimation and control tools adapted to particular features of quantum systems. The most important features, requiring the development of new engineering methods, are related to the concept of measurement and feedback for composite quantum systems. The destructive and partial 1 nature of measurements for quantum systems lead to major difficulties in extending classical control theory tools. Indeed, design of appropriate measurement protocols and, in the sequel, the corresponding quantum filters estimating the state of the system from the partial measurement record, are themselves building blocks of the quantum system theory to be developed.

On the experimental side, we develop new quantum information processing devices based on quantum superconducting circuits. Indeed, by realizing superconducting circuits at low temperatures and using microwave measurement techniques, the macroscopic and collective degrees of freedom such as the voltage and the current are forced to behave according to the laws of quantum mechanics. Our quantum devices are aimed to protect and process quantum information through these integrated circuits.

6.1 Error Rates and Resource Overheads of Repetition Cat Qubits

Participants: J. Guillaud, M. Mirrahimi

In 13, we estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach introduced in  54. While in  54, we show that using only bias-preserving gates on the cat-qubits, it is possible to build a universal set of fault-tolerant logical gates at the level of the repetition cat qubit, in this work, we perform Monte-Carlo simulations of all the circuits implementing the protected logical gates, using a circuit-level error model. Furthermore, we analyze two different approaches to implement a fault-tolerant Toffoli gate on repetition cat qubits. These numerical simulations indicate that very low logical error rates could be achieved with a reasonable resource overhead, and with parameters that are within the reach of near-term circuit QED experiments.

6.2 Combined Dissipative and Hamiltonian Confinement of Cat Qubits

Participants: R. Gautier, M. Mirrahimi, A. Sarlette

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. In our recent work 18, 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.

6.3 Multiplexed Photon Number Measurement

Participants: A. Sarlette, P. Rouchon, Z. Leghtas

In 12, a collaboration with our long-standing experimental partner and former QUANTIC member Benjamin Huard, a new scheme is proposed to measure the photon number operator on a superconducting cavity, thanks to a qubit dispersively coupled to the cavity and probed with a frequency comb. Thanks to this frequency multiplexing, the measurement time can be decreased compared to existing schemes. Our contribution has been to analyze the master equations modeling this experiment, in order to evaluate its benefits and clarify key elements. From a practical perspective, this has enabled us to refine the claim of the paper, identifying the use of so-called heterodyne field detectors as the main current bottleneck. From a theoretical perspective, this model has served as inspiration for developing adiabatic elimination expansions at infinite order and whose generalization we are still pursuing.

6.4 Characterizing limits and opportunities in speeding up Markov chain mixing

Participants: A. Sarlette

In our recent work 11 as a followup to our previously published work in  26, 25, we investigate an astounding point of doubt: can discrete-time quantum walks allow information to spread faster (i.e. in less steps) on a graph, than classical processes? Indeed, "quantum accelerated transport" for instance has sometimes been claimed to lay behind some fast processes, but there also exist acceleration methods for classical dynamics. We have clarified this situation by following the framework of "Lifted Markov Chains", which adds classical memory to the walker much like the quantum walk also does. We have shown that, in principle, for any evolution described by a Quantum Random Walk on a graph, there exists a classical Lifted Markov chain reproducing the same distribution over nodes in time. We have also shown that instances where particularly fast mixing Quantum Walks were known, are also those where rather intuitive Lifted Markov chains can be designed for accelerated mixing. Finally, we have clarified how much the context / constraints imposed on the Walker setting, can influence the ultimately achievable performance, hence explaining why there have been various seemingly contradictory claims in the literature. For instance, reaching a distribution that should be invariant at all time steps can be an important constraint, as well as assuming that the lifted system would start in a particular subspace of all possible distributions. This somewhat demystifies the "accelerated" evolution of Quantum Random Walks.

7.1 Bilateral contracts with industry

• New agreement with the start-up Alice&Bob defining the perimeters of our collaboration on cat qubits.
• New PhD contracts with Alice&Bob for two new students: T. Aissaoui and P. Guilmin.
• Inria-Microsoft lab funding to further study "quantum random walks". This funding has led to the hiring of Mathys Rennela.

8.1 European initiatives

8.2 National initiatives

• ANR project HAMROQS: In the framework of the ANR program JCJC, Alain Sarlette has received a funding for his research program "High-accuracy model reduction for open quantum systems". This grant of 212k euros started on april 2019 and will run for 4 years.
• ANR project SYNCAMIL: In the framework of the ANR program JCJC, Philippe Campagne-Ibarcq has received a funding for his research program "Synthetic Non-Local Hamiltonians for the protection of quantum information". This grant of 380k euros has allowed us to purchase the experimental equipment to perform an experiment on stabilization of GKP grid states at ENS Paris, and to hire a postdoctoral associate, Vincent Lienhard, for 2 years. The project started in December 2020 for 48 months.
• ANR project Mecaflux: Alain Sarlette is a PI of this newly obtained ANR Grant. This project aims to couple mechanical oscillators with superconduncting circuits at the quantum level, using a new circuit architecture allowing near-resonant coupling. The project is coordinated by mechanical oscillators expert Samuel Deléglise (LKB, U.Sorbonne), other project PIs are Alain Sarlette and Zaki Leghtas (QUANTIC project-team), Emmanuel Flurin and Hélène LeSueur (CEA Saclay). Our new recruit Antoine Tilloy may join with quantum gravity expertise if the level of control attains the objective where those effects become significant.
• ANR project OCTAVES: Mazyar Mirrahimi is a PI of this newly obtained ANR Grant. This project aims in studying the measurement problem in circuit QED (non QND effects in presence of probe drives) as well as limitations to the parametric driving for cat qubit stabilization. The project is coordinated by Olivier Buisson (Institut Néel, Grenoble) and other project PIs are Benjamin Huard (ENS Lyon), Mazyar Mirrahimi (Quantic project-team), and Dima Shepelyansky (LPT, Toulouse).

8.3 Regional initiatives

• In the framework of the project “DIM SIRTEQ Domaine d’intérêt Majeur: Science et Ingénierie Quantique” of Ile de France Region, we have received two half PhD fellowships covering the PhDs of Jérémie Guillaud and Marius Villiers.
• In the framework of the project “DIM SIRTEQ Domaine d’intérêt Majeur: Science et Ingénierie Quantique” of Ile de France Region, we have received a 109k€ grant to co-fund the purchase of a fast laser lithography system in the frame of the collaborative project "Chip-In" which aims at designing and testing on-chip microwave components for high-coherence and scalable superconducting circuits.
• PSL Jeune Equipe Grant: Antoine Tilloy has obtained a PSL grant to start his activity as an associate professor in our team working on the topic of tensor networks.

9.1 Promoting scientific activities

9.2 Teaching - Supervision - Juries

9.3 Popularization

10.1 Major publications

• 1 articleS.Simon Apers and A.Alain Sarlette. Quantum Fast-Forwarding: Markov chains and graph property testing.Quantum Information & ComputationApril 2019
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• 2 articleP.Philippe Campagne-Ibarcq, A.Alec Eickbusch, S.Steven Touzard, E.Evan Zalys-Geller, N. E.Nicholas E. Frattini, V. V.Volodymyr V. Sivak, P.Philip Reinhold, S.Shruti Puri, S.Shyam Shankar, R. J.Robert J. Schoelkopf, L.Luigi Frunzio, M.Mazyar Mirrahimi and M. H.Michel H. Devoret. Quantum error correction of a qubit encoded in grid states of an oscillator.Nature584Text and figures edited for clarity. The claims of the paper remain the same. Author list fixedAugust 2020
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• 3 articleG.Gerardo Cardona, A.Alain Sarlette and P.Pierre Rouchon. Exponential stabilization of quantum systems under continuous non-demolition measurements.AutomaticaDecember 2019
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• 4 articleJ.Jérémie Guillaud and M.Mazyar Mirrahimi. Repetition Cat Qubits for Fault-Tolerant Quantum Computation.Physical Review Xhttps://arxiv.org/abs/1904.09474 - 22 pages, 11 figuresDecember 2019
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• 5 articleZ.Zaki Leghtas, S.Steven Touzard, I. M.Ioan M. Pop, A.Angela Kou, B.Brian Vlastakis, A.Andrei Petrenko, K. M.Katrina M. Sliwa, A.Anirudh Narla, S.Shyam Shankar, M. J.Michael J. Hatridge, M.Matthew Reagor, L.Luigi Frunzio, R. J.Robert J. Schoelkopf, M.Mazyar Mirrahimi and M. H.Michel H. Devoret. Confining the state of light to a quantum manifold by engineered two-photon loss.Science3476224February 2015, 853-857
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• 6 articleR.Raphaël Lescanne, M.Marius Villiers, T.Théau Peronnin, A.Alain Sarlette, M.Matthieu Delbecq, B.Benjamin Huard, T.Takis Kontos, M.Mazyar Mirrahimi and Z.Zaki Leghtas. Exponential suppression of bit-flips in a qubit encoded in an oscillator.Nature PhysicsMarch 2020
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• 7 articleM.Mazyar Mirrahimi, Z.Zaki Leghtas, V. V.Victor V Albert, S.Steven Touzard, R. J.Robert J Schoelkopf, L.Liang Jiang and M. H.Michel H Devoret. Dynamically protected cat-qubits: a new paradigm for universal quantum computation.New Journal of Physics164apr 2014, 045014
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• 8 articleN.N. Ofek, A.A. Petrenko, R.R. Heeres, P.P. Reinhold, Z.Z. Leghtas, B.B. Vlastakis, Y.Y. Liu, L.L. Frunzio, S.S.M. Girvin, L.L. Jiang, M.M. Mirrahimi, M. H.M. H. Devoret and R. J.R. J. Schoelkopf. Extending the lifetime of a quantum bit with error correction in superconducting circuits.Nature5362016, 5
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• 9 articleA.A. Sarlette, J.-M.J.-M. Raimond, M.M. Brune and P.P. Rouchon. Stabilization of nonclassical states of the radiation field in a cavity by reservoir engineering.Phys. Rev. Lett.1070104022011
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• 10 articleC.C. Sayrin, I.I. Dotsenko, X.X. Zhou, B.B. Peaudecerf, T.T. Rybarczyk, S.S. Gleyzes, P.P. Rouchon, M.M. Mirrahimi, H.H. Amini, M.M. Brune, J.-M.J.-M. Raimond and S.S. Haroche. Real-time quantum feedback prepares and stabilizes photon number states.Nature4772011, 73--77
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10.2 Publications of the year

10.3 Other

10.4 Cited publications

• 22 articleH.H. Amini, M.M. Mirrahimi and P.P. Rouchon. Stabilization of a delayed quantum system: the Photon Box case-study.IEEE Trans. Automatic Control5782012, 1918--1930
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• 23 articleH.H Amini, C.C. Pellegrini and P.P. Rouchon. Stability of continuous-time quantum filters with measurement imperfections.Russian Journal of Mathematical Physics212014, 297--315
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• 24 articleH.H. Amini, A.A. Somaraju, I.I. Dotsenko, C.C. Sayrin, M.M. Mirrahimi and P.P. Rouchon. Feedback stabilization of discrete-time quantum systems subject to non-demolition measurements with imperfections and delays.Automatica4992013, 2683--2692
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• 25 articleS.Simon Apers, A.Alain Sarlette and F.Francesco Ticozzi. Simulation of quantum walks and fast mixing with classical processes.Physical Review A983September 2018, 032115
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• 26 inproceedings S.Simon Apers, A.Alain Sarlette and F.Francesco Ticozzi. When Does Memory Speed-up Mixing? IEEE Conference on Decision and Control Melbourne, Australia December 2017
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• 27 bookS.S. AttalA.A. JoyeC.-A.C.-A. PilletOpen Quantum Systems III: Recent Developments.Springer, Lecture notes in Mathematics 18802006
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• 28 bookA.A. Barchielli and M.M. Gregoratti. Quantum Trajectories and Measurements in Continuous Time: the Diffusive Case.Springer Verlag2009
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• 29 articleJ.J.T. Barreiro, M.M. Muller, P.P. Schindler, D.D. Nigg, T.T. Monz, M.M. Chwalla, M.M. Hennrich, C.C.F. Roos, P.P. Zoller and R.R. Blatt. An open-system quantum simulator with trapped ions.Nature4704862011
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• 30 articleV.V.P. Belavkin. Quantum stochastic calculus and quantum nonlinear filtering.Journal of Multivariate Analysis4221992, 171--201
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• 31 articleT.T. Benoist and C.C. Pellegrini. Large Time Behavior and Convergence Rate for Quantum Filters Under Standard Non Demolition Conditions.Communications in Mathematical Physics2014, 1-21URL: http://dx.doi.org/10.1007/s00220-014-2029-6
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• 32 articleG.G. Birkhoff. Extensions of Jentzch's theorem.Trans. Amer. Math. Soc.851957, 219--227
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• 33 articleS.S. Bolognani and F.F. Ticozzi. Engineering stable discrete-time quantum dynamics via a canonical QR decomposition.IEEE Trans. Autom. Control552010
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• 34 bookV.V. Braginski and F.F. Khalili. Quantum Measurements.Cambridge University Press1992
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• 35 articleP.P. Campagne-Ibarcq, L.L. Bretheau, E.E. Flurin, A.A. Auffèves, F.F. Mallet and B.B. Huard. Observing Interferences between Past and Future Quantum States in Resonance Fluorescence.Phys. Rev. Lett.11218040218May 2014, URL: http://link.aps.org/doi/10.1103/PhysRevLett.112.180402
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