RESEARCH CENTRE

Inria Paris Centre
at Sorbonne University

2023
ACTIVITY REPORT

IN PARTNERSHIP WITH:

CNRS, Ecole normale supérieure de Paris,
Mines ParisTech, Sorbonne Université

Project-Team

QUANTIC

QUANTum Information Circuits

IN COLLABORATION WITH: Laboratoire Pierre Aigrain, Centre
Automatique et Systèmes

DOMAIN

Applied Mathematics, Computation and
Simulation

THEME

Optimization and control of dynamic
systems

Contents

Project-Team QUANTIC

1 Team members, visitors, external collaborators

2 Overall objectives

2.1 Overall objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Research program

3.1 Hardware-efficient quantum information processing . . . . . . . . . . . . . . . . . . . . . . .
3.2 Reservoir (dissipation) engineering and autonomous stabilization of quantum systems . .
3.3 System theory for quantum information processing . . . . . . . . . . . . . . . . . . . . . . .
3.4 Stabilization by measurement-based feedback . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Filtering, quantum state and parameter estimations . . . . . . . . . . . . . . . . . . . . . . .
3.6 Stabilization by interconnections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Perturbation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 On-chip microwave engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Application domains

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4.1 Quantum engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Highlights of the year

10

6 New results

11
6.1 Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits . . . . . . . . . . . . . . . . . 11
6.2 Stabilization of approximate GHZ states with quasi-local couplings . . . . . . . . . . . . . . 11
6.3 Stability and decoherence rates of a GKP qubit protected by dissipation . . . . . . . . . . . . 11
6.4 Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination . . . . . . . 12
6.5 Correlation functions for realistic continuous quantum measurement . . . . . . . . . . . . . 12
6.6 Heisenberg formulation of adiabatic elimination for open quantum systems with two time-

scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6.7 Adiabatic elimination for composite open quantum systems: reduced model formulation

and numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.8 Convergence of bipartite open quantum systems stabilized by reservoir engineering . . . . 13
6.9 High-sensitivity AC-charge detection with a MHz-frequency fluxonium qubit . . . . . . . . 13
6.10 Quantum control of a cat-qubit with bit-flip times exceeding ten seconds
. . . . . . . . . . 13
6.11 Observation of Josephson Harmonics in Tunnel Junctions . . . . . . . . . . . . . . . . . . . . 14
6.12 Robust suppression of noise propagation in Gottesman-Kitaev-Preskill error correction . . 14
6.13 A GKP qubit protected by dissipation in a high-impedance superconducting circuit driven

by a microwave frequency comb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6.14 Robust sparse IQP sampling in constant depth . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7 Bilateral contracts and grants with industry

15
7.1 Bilateral contracts with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

8 Partnerships and cooperations

8.2 European initiatives

8.1 International research visitors

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
8.1.1 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
8.2.1 Horizon Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
8.2.2 H2020 projects
8.3 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.4 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

9 Dissemination

21
9.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
9.1.1 Scientific events: selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
9.1.2 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
9.1.3 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
9.1.4 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 22
9.1.5 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9.1.6 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3.1 Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

10 Scientific production

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10.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
10.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
10.3 Cited publications

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Project-Team QUANTIC

Creation of the Project-Team: 2015 April 01

Keywords

Computer sciences and digital sciences

A1.1.11. – Quantum architectures

A4.2. – Correcting codes

A6. – Modeling, simulation and control

A6.1. – Methods in mathematical modeling

A6.1.1. – Continuous Modeling (PDE, ODE)

A6.1.2. – Stochastic Modeling

A6.1.3. – Discrete Modeling (multi-agent, people centered)

A6.1.4. – Multiscale modeling

A6.2. – Scientific computing, Numerical Analysis & Optimization

A6.2.1. – Numerical analysis of PDE and ODE

A6.2.3. – Probabilistic methods

A6.2.6. – Optimization

A6.3.1. – Inverse problems

A6.3.2. – Data assimilation

A6.3.3. – Data processing

A6.3.4. – Model reduction

A6.4. – Automatic control

A6.4.1. – Deterministic control

A6.4.2. – Stochastic control

A6.4.3. – Observability and Controlability

A6.4.4. – Stability and Stabilization

Other research topics and application domains

B5.3. – Nanotechnology

B5.4. – Microelectronics

B6.5. – Information systems

B9.10. – Privacy

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Mazyar Mirrahimi [Team leader, INRIA, Senior Researcher]

• Philippe Campagne Ibarcq [INRIA, Researcher]

• Alain Sarlette [INRIA, Senior Researcher, from Oct 2023, HDR]

• Alain Sarlette [INRIA, Researcher, until Sep 2023, HDR]

Faculty Members

• Zaki Leghtas [ENSMP, Associate Professor]

• Tudor-Alexandru Petrescu [MINESPARISTECH]

• Pierre Rouchon [ARMINES, Professor, HDR]

• Antoine Tilloy [MINESPARISTECH]

Post-Doctoral Fellows

• Yousra Bouasria [INRIA, Post-Doctoral Fellow, until Feb 2023]

• Edoardo Lauria [ENSMP, Post-Doctoral Fellow, from Mar 2023]

• Vincent Lienhard [ENS PARIS, Post-Doctoral Fellow]

• Remi Robin [ARMINES, Post-Doctoral Fellow]

PhD Students

• Thiziri Aissaoui [ALICE ET BOB, CIFRE]

• Brieuc Beauseigneur [ARMINES, from Sep 2023]

• Leon Carde [ARMINES, CIFRE]

• Ronan Gautier [INRIA, until Aug 2023]

• Linda Greggio [INRIA]

• Pierre Guilmin [ALICE ET BOB]

• Anissa Jacob [ALICE ET BOB, CIFRE, from Nov 2023]

• François-Marie Le Regent [ALICE ET BOB]

• Louis Paletta [INRIA]

• Matthieu Praquin [ENS PARIS]

• Angela Riva [INRIA]

• Emilio Rui [ALICE ET BOB, from Oct 2023]

• Diego Ruiz [ALICE ET BOB, CIFRE]

• Lev-Arcady Sellem [ARMINES, from Sep 2023]

• Lev-Arcady Sellem [ENS PARIS-SACLAY, until Aug 2023]

• Christian Siegele [INRIA, until Feb 2023]

• Karanbir Tiwana [ARMINES]

• Aron Vanselow [INRIA]

Project QUANTIC

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Interns and Apprentices

• Brieuc Beauseigneur [INRIA, Intern, from Apr 2023 until Jul 2023]

• Leonardo Cardinale [ENSMP, Intern, from May 2023 until Aug 2023]

• Vania Clesca Dedieu [MINESPARISTECH, Intern, until Feb 2023]

• Robin Geiller [ENS DE LYON, Intern, from May 2023 until Jul 2023]

• Philippe Gigon [INRIA, Intern, from Feb 2023 until Jun 2023]

• Danilo Nascimento Guimaraes [INRIA, Intern, from Apr 2023 until Jul 2023]

• Etienne Parcollet [ENS Paris, Intern, from Apr 2023 until Jun 2023]

• Tom Perrin [MINESPARISTECH, Intern, from Dec 2023]

Administrative Assistant

• Derya Gok [INRIA]

Visiting Scientists

• Henrik Clausen [UNIV AALBORG, from Sep 2023]

• Birgitta Whaley [UNIV BERKELEY, from May 2023 until Jul 2023]

External Collaborators

• Ronan Gautier [ALICE ET BOB, from Sep 2023]

• Jeremie Guillaud [ALICE ET BOB]

2 Overall objectives

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.

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Inria Annual Report 2023

3 Research program

3.1 Hardware-efficient quantum information processing

In this scientific program, we will explore various theoretical and experimental issues concerning pro-
tection 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 co-
herence 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 [109, 113]. 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 [81]. 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 [78, 71] 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 [80]. Through a recent experimental work [120],
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. Continu-
ous 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 [114] has recently led to a first experimental realization of a full quantum error
correcting code improving the coherence time of quantum information [7]. 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.

Project QUANTIC

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Figure 1: (a) A protected logical qubit consisting of a register of many qubits: here, we see a possible
architecture for the Steane code [113] consisting of 7 qubits requiring the measurement of 6 error
syndromes. In this sketch, 7 transmon qubits in a high-Q resonator and the measurement of the 6 error
syndromes is ensured through 6 additional ancillary qubits with the possibility of individual readout of
the ancillary qubits via independent low-Q resonators. (b) Minimal architecture for a protected logical
qubit, adapted to circuit quantum electrodynamics experiments. Quantum information is encoded in a
Schrödinger cat state of a single high-Q resonator mode and a single error syndrome is measured, using a
single ancillary transmon qubit and the associated readout low-Q resonator.

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 [51]. In the context of cavity
quantum electro-dynamics (cavity QED) with Rydberg atoms [74], a first experiment on continuous QND
measurements of the number of microwave photons was performed by the group at Laboratoire Kastler-
Brossel (ENS) [72]. 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 [9] (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 [62, 41, 112, 42]. 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) [60], recent advances in quantum-
limited amplifiers [102, 117] have opened doors to high-fidelity non-demolition measurements and
real-time feedback for superconducting qubits [75]. 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 [117, 101, 53]. 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 [89].

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

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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 [96] and the closely related coherent feedback [86] 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 [70], single-qubit state stabilization [90], and the
creation [45] and stabilization [79, 85, 108] of states of multipartite quantum systems.

Such reservoir engineering techniques could be widely revisited exploring the flexibility in the Hamilto-
nian 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 [70,
83, 58, 61]. The experimental results based on these protocols have illustrated the efficiency of the
approach [70, 108]. Through these experiments, we exploit the strong dispersive interaction [106]
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 [104, 76][6, 4].

3.3 System theory for quantum information processing

In parallel and in strong interactions with the above experimental goals, we develop systematic mathem-
atical 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 [103,
41, 111, 105, 112, 42][8] 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 con-
troller 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 [42]: 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

Project QUANTIC

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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 [121]; 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 [93]. 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 [75, 53].

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 ≥ 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 [47] and is related to quantum trajectories [54, 59]. A
modern and mathematical exposure of the diffusive models is given in [44]. In [73] 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 [103, 111]. This stability result is extended to a large class of continuous-
time filters in [40]. Further efforts are required to characterize asymptotic and exponential stability.
Estimations of convergence rates are available only for quantum non-demolition measurements [48].
Parameter estimations based on measurement data of quantum trajectories can be formulated within
such quantum filtering framework [65, 91].

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 [52] that post-
selection statistics and “past quantum” state analysis [66] 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 [96, 86]. 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 [8] [108, 70], 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 [95]). 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., [43][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 [8, 6] [108, 70] and their associated Fokker-Planck equations
for the Wigner functions.

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Inria Annual Report 2023

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 [69, 68]. We will start with [107] and [99] where, based on a theorem due to Birkhoff [49],
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 [116] and by our recent generalized extension of the latter synchronizing interactions to
quantum systems [88].

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 [92], 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 [119, 84] with experimental limitations. The characterization of Kraus maps
to stabilize any types of states has also been established [50], 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.

3.6.1 Perturbation methods

With this subsection we turn towards more fundamental developments that are necessary in order to
address the complexity of quantum networks with efficient reduction techniques. This should yield both
efficient mathematical methods, as well as insights towards unravelling dominant physical phenom-
ena/mechanisms in multipartite quantum dynamical systems.

In the Schrödinger point of view, the dynamics of open quantum systems are governed by master
equations, either deterministic or stochastic [74, 67]. Dynamical models of composite systems are based
on tensor products of Hilbert spaces and operators attached to the constitutive subsystems. Generally,
a hierarchy of different timescales is present. Perturbation techniques can be very useful to construct
reliable models adapted to the timescale of interest.

To eliminate high frequency oscillations possibly induced by quasi-resonant classical drives, averaging
techniques are used (rotating wave approximation). These techniques are well established for closed
systems without any dissipation nor irreversible effect due to measurement or decoherence. We will
consider in a first step the adaptation of these averaging techniques to deterministic Lindblad master
equations governing the quantum state, i.e. the system density operator. Emphasis will be put on first
order and higher order corrections based on non-commutative computations with the different operators
appearing in the Lindblad equations. Higher order terms could be of some interest for the protected
logical qubit of figure 1b. In future steps, we intend to explore the possibility to explicitly exploit averaging
or singular perturbation properties in the design of coherent quantum feedback systems; this should be
an open-systems counterpart of works like [82].

To eliminate subsystems subject to fast convergence induced by decoherence, singular perturbation
techniques can be used. They provide reduced models of smaller dimension via the adiabatic elim-
ination of the rapidly converging subsystems. The derivation of the slow dynamics is far from being
obvious (see, e.g., the computations of page 142 in [55] for the adiabatic elimination of low-Q cavity).
Conversely to the classical composite systems where we have to eliminate one component in a Cartesian
product, we here have to eliminate one component in a tensor product. We will adapt geometric singular
perturbations [63] and invariant manifold techniques [56] to such tensor product computations to
derive reduced slow approximations of any order. Such adaptations will be very useful in the context
of quantum Zeno dynamics to obtain approximations of the slow dynamics on the decoherence-free
subspace corresponding to the slow attractive manifold.

Perturbation methods are also precious to analyze convergence rates. Deriving the spectrum attached
to the Lindblad differential equation is not obvious. We will focus on the situation where the decoherence
terms of the form LρL† − (L†Lρ + ρL†L)/2 are small compared to the conservative terms −i [H /ħ, ρ]. The

Project QUANTIC

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difficulty to overcome here is the degeneracy of the unperturbed spectrum attached to the conservative
evolution d
ρ = −i [H /ħ, ρ]. The degree of degeneracy of the zero eigenvalue always exceeds the dimen-
d t
sion of the Hilbert space. Adaptations of usual perturbation techniques [77] will be investigated. They
will provide estimates of convergence rates for slightly open quantum systems. We expect that such
estimates will help to understand the dependence on the experimental parameters of the convergence
rates observed in [70, 108, 83].

As particular outcomes for the other subsections, we expect that these developments towards simpler
dominant dynamics will guide the search for optimal control strategies, both in open-loop microwave
networks and in autonomous stabilization schemes such as reservoir engineering. It will further help
to efficiently compute explicit convergence rates and quantitative performances for all the intended
experiments.

3.7 On-chip microwave engineering

The rapid development of circuitQED over the past 20 years was enabled by commercially available
microwave components such as filters, switches and circulators, which allow experimentalists to shape
and route measurement and control signals in and out of quantum systems. However, these components
are intrinsically bulky, lossy and are imperfectly impedance-matched, leading to spurious reflections at
their ports. In order to implement a full-scale quantum computer based on superconducting circuits, it is
crucial that these functionalities be enabled reliably on-chip.

On-chip filters commonly used in circuitQED experiments are far from the level of variety and
refinement of commercially available components. The near exclusive strategy known as "Purcell-
filtering" [100] consists in placing λ/4 stubs [97] on all feed lines. This cancels the admittance of the
environment seen by a superconducting qubit at its resonance frequency, inhibiting spontaneous re-
laxation. An issue with this strategy is that given the modest width of the stub stopband, performances
are degraded as soon as the qubit is not perfectly in resonance. Moreover, this approach is not suited
for multiplexed control and measurements, in which a single feed line addresses simultaneously several
qubits. Notable alternatives include highpass waveguide filters only available in 3D circuitQED [98], and
a recent implementation of a bandpass filter [64].

On-chip non-reciprocal elements, such as isolators, circulators and gyrators are at a very early stage
of development. So far, the most promising approach to break reciprocity without resorting to strong
magnetic fields—which are incompatible with superconducting circuit technology—relies on the dif-
ferential phase impinged on a signal during parametric down-conversion with respect to the reverse
process of up-conversion. Combining coherently several conversion paths with well-chosen phases, one
obtains a constructive forward interference, and a destructive backward one. In circuitQED, frequency
conversion is enabled by a non-linear Josephson circuit [110, 57, 39], or by electromechanical coupling to
nanoresonators [46, 94]. A serious drawback of this approach is that it relies on a destructive interference
effect to obtain the reverse isolation, which limits the operational bandwidth: the highest value reported
so far is a 23 dB isolation over a 8 MHz band [39]. For completeness, we mention a recent implementation
of a forward amplifier based on resistively shunted Josephson junctions [115] that reaches a 100 MHz
bandwidth at the cost of added noise, and the long term prospect of harnessing the anomalous Hall effect
to implement a gyrator [118, 87].

In this project, we propose to develop novel on-chip filters and isolators based on 1D photonic
crystals, which could reach unprecedented bandwidth, tunable range and on/off or forward/backward
transmission ratios. The central idea is that a microwave transmission line with periodically modulated
electrical properties behaves as a robust stopband filter, with attenuation scaling exponentially with the
line length.

By fabricating lines whose properties are modulated by design, we plan to demonstrate the efficiency
of this novel type of stopband filters. These lines will be fabricated in a high-kinetic inductance material
(such as chains of Josephson junctions or granular aluminium), we will overcome the main weakness
of this approach, which is the large on-chip footprint required when fabricating with conventional su-

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Inria Annual Report 2023

perconductors. Extending the numerical simulation methods developed in thsi work, we plan to design
other types of filters (bandpass, highpass, lowpass) based on a similar technology.

We will then change perspective and modulate a line properties parametrically instead of by design
to implement non-reciprocal elements. The idea is to design a line that possesses two traveling mode 1
and 2, with different propagation phase-velocity v1 ≪ v2. If a low-frequency pump wave propagates on 1
modulates the electrical properties of the mode 2 thanks to shared non-linear inductance—for instance
Josephson junction participating in both modes inductance—we obtain a situation in which mode 2 has
spatially modulated electrical properties, with the phase of this modulation slowly evolving in time with
at the pump period. A stopband appears in the transmission of a probe signal on mode 2, whose central
frequency depends on whether the probe propagates in the same direction as the pump or not. It is then
straightforward to turn this non-reciprocal filter into an isolator on circulator.

4 Application domains

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 temperat-
ures 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.

5 Highlights of the year

• Successful PhD defense of Christian Siegele on February 24th.

• Successful PhD defense of Camille Berdou on March 14th.

• Successful PhD defense of Marius Villiers on May 15th.

• Successful PhD defense of Ronan Gautier on December 4th.

1Here the partiality means that no single quantum measurement is capable of providing the complete information on the state

of the system.

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• Installation of a new experimental laboratory space at ENS Paris with a new dilution cryostat.

• Promotion of Alain Sarlette to DR2.

6 New results

6.1 Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits

Participants:

Ronan Gautier, Mazyar Mirrahimi, Alain Sarlette.

This paper [15], published in PRX Quantum, gathers several different system design possibilities in
order to perform fast operations on cat qubits while strongly reducing the decoherence induced by the
fast actuation on the system. The decoherence is due to the fact that a dissipative element is present on
purpose in order to stabilize the qubit, while simple enough actuation Hamiltonians cannot drive all
necessary system operations without activating this stabilizing dissipation; in this way, fast actuation
would also induce rather fast information loss. One proposed solution, also submitted for patenting, is to
introduce back-action from the output of the main dissipation channel, thus re-injecting the part of the
evacuated entropy which correlates to qubit information which we want to maintain. Other proposed
solutions include the engineering of small nonlinearities in the actuation Hamiltonian, or designing
jump-activated operations. This has been a major part of the thesis of Ronan Gautier, successfully
defended in December 2023.

6.2 Stabilization of approximate GHZ states with quasi-local couplings

Participants:

Vincent Martin, Alain Sarlette.

This work [30], currently under review, comprises essentially 3 contributions. First, we solve the
objective of stabilizing intrinsically long-range entanglement, for which impossibility results have been
known, on a prototypical example. Second, our solution proposes and investigates the use of engineered
reservoirs — thus an autonomous system with steady couplings — whose aim is to mimic the behavior
of automata with little but nonzero memory. We establish the effectiveness of several options and
workings, involving: introducing one auxiliary system per data qubit; adding a third level to the data
qubit for operation purposes ; and inducing waves of effects propagating through the overall system at
stochastic speeds. A third contribution concerns the analysis method, where we bound the Lindblad
master equation evolution by a Markov chain involving hypothetical measurements of the dissipation
channels, and then analyze the associated classical Markov chain.

6.3 Stability and decoherence rates of a GKP qubit protected by dissipation

Participants:

Lev-Arcady Sellem, Rémi Robin, Philippe Campagne-Ibarcq,
Pierre Rouchon.

In this communication at the IFAC WC 2023[20], We analyze an experimentally accessible Lindblad
master equation for a quantum harmonic oscillator. It approximately stabilizes finite-energy periodic
grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to encode and protect a logical
qubit. We give explicit upper bounds for the energy of the solutions of the Lindblad master equation.
Using three periodic observables to define the Bloch sphere coordinates of a logical qubit, we show
that their dynamics is governed by a diffusion partial differential equation on a 2D-torus with a Witten
Laplacian. We show that the evolution of these logical coordinates is exponentially slow even in presence
of small diffusive noise processes along the two quadratures of the phase space. Numerical simulations
indicate similar results for other physically relevant noise processes.

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Inria Annual Report 2023

6.4 Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination

Participants: Masaaki Tokieda, Alain Sarlette, Pierre Rouchon.

This communication at the IFAC WC 2023 [21] adresses quantum adiabatic elimination and complete-
positivity. When a composite Lindblad system consists of weakly coupled sub-systems with fast and slow
timescales, the description of slow dynamics can be simplified by discarding fast degrees of freedom. This
model reduction technique is called adiabatic elimination. While second-order perturbative expansion
with respect to the timescale separation has revealed that the evolution of a reduced state is completely
positive, this paper presents an example exhibiting complete positivity violation in the fourth-order
expansion. Despite the non-uniqueness of slow dynamics parametrization, we prove that complete
positivity cannot be ensured in any parametrization. The violation stems from correlation in the initial
state.

6.5 Correlation functions for realistic continuous quantum measurement

Participants:

Pierre Guilmin, Pierre Rouchon, Antoine Tilloy.

This communication at the IFAC WC 2023 [25] proposes a self-contained and accessible derivation
of an exact formula for the n-point correlation functions of the signal measured when continuously
observing a quantum system. The expression depends on the initial quantum state and on the Stochastic
Master Equation (SME) governing the dynamics. This derivation applies to both jump and diffusive
evolutions and takes into account common imperfections of realistic measurement devices. We show
how these correlations can be efficiently computed numerically for commonly filtered and integrated
signals available in practice.

6.6 Heisenberg formulation of adiabatic elimination for open quantum systems

with two time-scales

Participants:

François-Marie Le Regent, Pierre Rouchon.

This communication at the IEEE CDC 2023 [19],considers an open quantum system governed by a
Gorini, Kossakowski, Sudarshan, Lindblad (GKSL) master equation with two times-scales: a fast one,
exponentially converging towards a linear subspace of quasi-equilibria; a slow one resulting from per-
turbations (small arbitrary decoherence and Hamiltonian dynamics). Usually adiabatic elimination is
performed in the Schrödinger picture. We propose here an Heisenberg formulation where the invariant
operators attached to the fast decay dynamics towards the quasi-equilibria subspace play a key role.
Based on geometric singular perturbations, asympotic expansions of the Heisenberg slow dynamics
and of the fast invariant linear subspaces are proposed. They exploit Carr’s approximation lemma from
center-manifold and bifurcation theory. Second-order expansions are detailed and shown to ensure
preservation, up to second-order terms, of the trace and complete positivity for the slow dynamics on a
slow time-scale. Such expansions can be exploited numerically.

6.7 Adiabatic elimination for composite open quantum systems: reduced model

formulation and numerical simulations

Participants:

François-Marie Le Régent, Pierre Rouchon.

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This preprint under review in Physical Review A [32] proposes a numerical method for simulation of
composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination.
Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly impacted
by some decoherence channels and weakly coupled to the other subsystems. This numerical method
is based on a perturbation analysis with an asymptotic expansion. It exploits the formulation of the
slow dynamics with reduced dimension. It relies on the invariant operators of the local and nominal
dissipative dynamics attached to each subsystem. Second-order expansion can be computed only with
local numerical calculations. It avoids computations on the tensor-product Hilbert space attached to the
full system. This numerical method is particularly well suited for autonomous quantum error correction
schemes. Simulations of such reduced models agree with complete full model simulations for typical
gates acting on one and two cat-qubits (Z, ZZ and CNOT) when the mean photon number of each cat-
qubit is less than 8. For larger mean photon numbers and gates with three cat-qubits (ZZZ and CCNOT),
full model simulations are almost impossible whereas reduced model simulations remain accessible. In
particular, they capture both the dominant phase-flip error-rate and the very small bit-flip error-rate with
its exponential suppression versus the mean photon number.

6.8 Convergence of bipartite open quantum systems stabilized by reservoir engin-

eering

Participants:

Rémi Robin, Pierre Rouchon, Lev-Arcady Sellem.

This preprint [34] considers a generic family of Lindblad master equations modeling bipartite open
quantum systems, where one tries to stabilize a quantum system by carefully designing its interaction with
another, dissipative, quantum system - a strategy known as quantum reservoir engineering. We provide
sufficient conditions for convergence of the considered Lindblad equations; our setting accommodates
the case where steady states are not unique but rather supported on a given subspace of the underlying
Hilbert space. We apply our result to a Lindblad master equation proposed for the stabilization of
so-called cat qubits, a system that received considerable attention in recent years due to its potential
applications in quantum information processing.

6.9 High-sensitivity AC-charge detection with a MHz-frequency fluxonium qubit

Participants:

Angela Riva, Marius Villiers, Alain Sarlette, Zaki Leghtas.

This work [31], provisionally accepted in PRX, is the first step of results in the framework of the
ANR project MecaFlux led by Samuel Deléglise, whose ultimate goal is to stabilize quantum states in a
mechanical oscillator thanks to its coupling to a superconducting circuit in so-called "heavy fluxonium"
configuration. The first step demonstrates the capabilities of such a fluxonium, in terms of actively
cooling it down to the ground state, maintaining qubit-type quantum states, reading out such state. It
also demonstrates experimentally how this circuit does couple to the degree of freedom (MHz charge
fluctuations) where the mechanical oscillator is to be placed; thus we have a fully operational building
block for the overall project, and which may be of independent interest.

6.10 Quantum control of a cat-qubit with bit-flip times exceeding ten seconds

Participants: Ulysse Reglade, Adrien Bocquet, Ronan Gautier, Lev-Arcady Sellem,
Pierre Rouchon, Alain Sarlette, Mazyar Mirrahimi, Philippe Campagne-
Ibarcq, Zaki Leghtas.

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Inria Annual Report 2023

Binary classical information is routinely encoded in the two metastable states of a dynamical system.
Since these states may exhibit macroscopic lifetimes, the encoded information inherits a strong protection
against bit-flips. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a
quantum dynamical system, thereby acquiring bit-flip protection. An outstanding challenge is to gain
quantum control over such a system without breaking its protection. If this challenge is met, significant
shortcuts in hardware overhead are forecast for quantum computing. In this experiment, we implement
a cat-qubit with bit-flip times exceeding ten seconds. This is a four order of magnitude improvement over
previous cat-qubit implementations, and six orders of magnitude enhancement over the single photon
lifetime that compose this dynamical qubit. This was achieved by introducing a quantum tomography
protocol that does not break bit-flip protection. We prepare and image quantum superposition states,
and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these
superpositions while maintaining the bit-flip time above ten seconds. This work demonstrates quantum
operations that preserve macroscopic bit-flip times, a necessary step to scale these dynamical qubits into
fully protected hardware-efficient architectures.
This work has given rise to the preprint [33].

6.11 Observation of Josephson Harmonics in Tunnel Junctions

Participants:

Zaki Leghtas.

Superconducting quantum processors have a long road ahead to reach fault-tolerant quantum
computing. One of the most daunting challenges is taming the numerous microscopic degrees of freedom
ubiquitous in solid-state devices. State-of-the-art technologies, including the world’s largest quantum
processors, employ aluminum oxide (AlOx) tunnel Josephson junctions (JJs) as sources of nonlinearity,
assuming an idealized pure sinφ current-phase relation (CφR). However, this celebrated sinφ CφR is only
expected to occur in the limit of vanishingly low-transparency channels in the AlOx barrier. Here we show
that the standard CφR fails to accurately describe the energy spectra of transmon artificial atoms across
various samples and laboratories. Instead, a mesoscopic model of tunneling through an inhomogeneous
AlOx barrier predicts %-level contributions from higher Josephson harmonics. By including these in the
transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and
measured energy spectra. The reality of Josephson harmonics transforms qubit design and prompts a
reevaluation of models for quantum gates and readout, parametric amplification and mixing, Floquet
qubits, protected Josephson qubits, etc. As an example, we show that engineered Josephson harmonics
can reduce the charge dispersion and the associated errors in transmon qubits by an order of magnitude,
while preserving anharmonicity.

This work has led to the preprint [38].

6.12 Robust suppression of noise propagation in Gottesman-Kitaev-Preskill error

correction

Participants: Christian Siegele, Philippe Campagne Ibarcq.

The recently reported generation and error-correction of GKP qubits in trapped ions and super-
conducting circuits thus holds great promise for the future of quantum computing architectures based
on such encoded qubits. However, these experiments rely on error-syndrome detection via an auxili-
ary physical qubit, whose noise may propagate and corrupt the encoded GKP qubit. In [Siegele, C., &
Campagne-Ibarcq, P. (2023). Robust suppression of noise propagation in Gottesman-Kitaev-Preskill error
correction. Physical Review A, 108(4), 042427.], we propose a simple module composed of two oscillat-
ors and a physical qubit, operated with two experimentally accessible quantum gates and elementary
feedback controls to implement an error-corrected GKP qubit protected from such propagating errors.
In the idealized setting of periodic GKP states, we develop efficient numerical methods to optimize our

Project QUANTIC

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protocol parameters and show that errors of the encoded qubit stemming from flips of the physical
qubit and diffusion of the oscillators state in phase-space may be exponentially suppressed as the noise
strength over individual operations is decreased. Our approach circumvents the main roadblock towards
fault-tolerant quantum computation with GKP qubits.

This work was published in Phys. Rev. A [18].

6.13 A GKP qubit protected by dissipation in a high-impedance superconducting

circuit driven by a microwave frequency comb

Participants:

Lev-Arcady Sellem, Alain Sarlette, Zaki Leghtas, Mazyar Mirrahimi,
Pierre Rouchon, Philippe Campagne-Ibarcq.

In the preprint [35], we propose a novel approach to generate, protect and control GKP qubits.
It employs a microwave frequency comb parametrically modulating a Josephson circuit to enforce a
dissipative dynamics of a high impedance circuit mode, autonomously stabilizing the finite-energy GKP
code. The encoded GKP qubit is robustly protected against all dominant decoherence channels plaguing
superconducting circuits but quasi-particle poisoning. In particular, noise from ancillary modes leveraged
for dissipation engineering does not propagate at the logical level. In a state-of-the-art experimental setup,
we estimate that the encoded qubit lifetime could extend two orders of magnitude beyond the break-even
point, with substantial margin for improvement through progress in fabrication and control electronics.
Qubit initialization, readout and control via Clifford gates can be performed while maintaining the code
stabilization, paving the way toward the assembly of GKP qubits in a fault-tolerant quantum computing
architecture.

6.14 Robust sparse IQP sampling in constant depth

Participants:

Louis Paletta, Alain Sarlette, Mazyar Mirrahimi.

Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum
advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable
superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is
robust to noise with minimal error correction requirements. We choose a class of sampling problems
with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we
ensure its fault-tolerant implementation by introducing the tetrahelix code. This new code is obtained by
merging several tetrahedral codes (3D color codes) and has the following properties: each sparse IQP
gate admits a transversal implementation, and the depth of the logical circuit can be traded for its width.
Combining those, we obtain a depth-1 implementation of any sparse IQP circuit up to the preparation of
encoded states. This comes at the cost of a space overhead which is only polylogarithmic in the width of
the original circuit. We furthermore show that the state preparation can also be performed in constant
depth with a single step of feed-forward from classical computation. Our construction thus exhibits a
robust superpolynomial quantum advantage for a sampling problem implemented on a constant depth
circuit with a single round of measurement and feed-forward.

This work [23] has been accepted for a plenary presentation at the conference QIP 2024 in Taipei and

is under revision for Quantum.

7 Bilateral contracts and grants with industry

7.1 Bilateral contracts with industry

• New PhD contracts with Alice&Bob for 2 new students: Emilio Rui, Anissa Jacob.

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Inria Annual Report 2023

8 Partnerships and cooperations

8.1 International research visitors

8.1.1 Visits of international scientists

Other international visits to the team

Birgitta Whaley

Status: Professor

Institution of origin: Univ. of Berkeley

Country: USA

Dates: May 5th to June 18th.

Context of the visit: Collaborations with Pierre Rouchon.

Paulo Sérgio Pereira da Silva

Status: Professor

Institution of origin: Univ. of Sao Paolo

Country: Brasil

Dates:

Context of the visit: Collaborations with Pierre Rouchon.

Philippe Lewalle

Status: PhD

Institution of origin: Univ. of Berkeley

Country: USA

Dates: May 4th to June 18th.

Context of the visit: Collaborations with Pierre Rouchon.

Henrik Clausen

Status: PhD

Institution of origin: Aalborg University

Country: Denmark

Dates: Sept 11th to Dec 8th.

Context of the visit: Collaborations with Pierre Rouchon.

Project QUANTIC

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8.2 European initiatives

8.2.1 Horizon Europe

DANCINGFOOL

Participants:

Philippe Campagne Ibarcq, Matthieu Praquin, Vincent Lienhard,
Aron Vanselow.

DANCINGFOOL project on cordis.europa.eu

Title: High-impedance Superconducting Circuits Enabling Fault-tolerant Quantum Computing by Wide-

band Microwave Control

Duration: From December 1, 2022 to November 30, 2027

Partners:

• INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE (INRIA),

France

• ECOLE NORMALE SUPERIEURE (ENS), France

Inria contact: Philippe Campagne-Ibarcq

Coordinator: Philippe Campagne Ibarcq

Summary: A physical system implementing a quantum bit (qubit) is never perfectly isolated from an
uncontrolled environment. The system dynamics is thus noisy, modifying randomly the qubit state.
This phenomenon of decoherence is the main roadblock to build a stable quantum computing
platform. In order to mitigate decoherence, quantum error correction employs only a few code
states within a much larger informational space, so that noise-induced dynamics can be detected
and corrected before the encoded information gets corrupted. Unfortunately, most known proto-
cols require to control dauntingly complex systems, with a degree of coherence currently out of
reach. Our project is to build autonomously error-corrected qubits encoded in high-impedance su-
perconducting circuits. In our protocol, a qubit is encoded in the vast phase-space of the quantum
oscillator implemented by each circuit, in the form of Gottesman-Kitaev-Preskill (GKP) states.
The novelty is that the GKP states are fully stabilized by a modular dissipation, induced by the
coherent tunneling of charges through a stroboscopically biased Josephson junction. The coher-
ence of the encoded qubit is expected to exceed that of existing superconducting qubits by orders
of magnitude. Furthermore, we propose to perform protected logical gates between encoded
qubits by varying adiabatically the parameters of the modular dissipation, paving the way toward
fault-tolerant quantum computing. The major experimental challenge of our protocol resides in
the exquisite level of control needed over a wide band in the microwave range. We propose to
address this challenge by developing novel on-chip filters, tunable couplers and isolators based on
periodically modulated, high-impedance, transmission lines. These on-chip components would
find a wide range of applications in quantum technologies, and favor the advent of large-scale
quantum computing platforms.

QFT.zip

Participants:

Antoine Tilloy, Karanbir Tiwana, Edoardo Lauria.

QFT.zip project on cordis.europa.eu

Title: Compressing many-body quantum states in continuous space-time with tensor networks

Duration: From January 1, 2023 to December 31, 2027

18

Partners:

• ARMINES, France

• INRIA, France

Coordinator: Antoine Tilloy

Inria Annual Report 2023

Summary: Many-body quantum systems with strong correlations are particularly difficult to understand
in the continuum, where non-perturbative techniques are in scarce supply. Direct diagonalization
methods are not available, since the Hilbert space is simply too large to be manageable. This
inhibits progress in high energy physics, nuclear physics, and in the study of exotic topological
phases of matter. On the lattice, tensor network states, a variational class of wavefunctions coming
from quantum information theory, have allowed to compress exponentially large Hilbert spaces
down to a smaller numerically manageable corner. This has allowed substantial theoretical and
numerical advance on the many-body problem on the lattice. This project will develop continuous
tensor network states, a new framework to extend the recent lattice progress to the continuum
and quantum field theory (QFT). The originality of the approach is that it will not rely on any
discretization of space-time. We will work directly in the continuum, without any cutoff. Low
energy states of quantum field theories, which a priori live in a continuously infinite dimensional
Hilbert space, will be compressed down to a finite and small number of parameters. This will
then allow to solve numerically very generic (non-integrable) strongly coupled theories in a fully
non-perturbative manner. Such a compression was long thought to be impossible, in particular
in the relativistic case, but we overcame crucial theoretical hurdles in the past year, making the
proposal particularly timely. We will construct this framework with 3 main applications in mind:
i) non-relativistic problems in 2 space dimensions and more, including e.g. fractional quantum
Hall states, ii) relativistic QFT, starting with 1+1 dimensional toy model and gradually increasing
complexity to get closer to nonabelian gauge theories, iii) critical quantum systems (and classical
statistical mechanics).

8.2.2 H2020 projects

ERC Starting Grant ECLIPSE

• Program: H2020

• Type: ERC

• Project acronym: ECLIPSE

• Project title: Exotic superconducting circuits to probe and protect quantum states of light and

matter

• Duration: 2019-2024

• Coordinator: Zaki Leghtas, Mines Paristech

• Abstract: Quantum systems can occupy peculiar states, such as superposition or entangled states.
These states are intrinsically fragile and eventually get wiped out by inevitable interactions with the
environment. Protecting quantum states against decoherence is a formidable and fundamental
problem in physics, which is pivotal for the future of quantum computing. The theory of quantum
error correction provides a solution, but its current envisioned implementations require daunting
resources: a single bit of information is protected by encoding it across tens of thousands of physical
qubits. This project intend to encode quantum information in an entirely new type of qubit with
two key specificities. First, it will be encoded in a single superconducting circuit resonator whose
infinite dimensional Hilbert space can replace large registers of physical qubits. Second, this qubit
will be rf-powered, continuously exchanging photons with a reservoir. This approach challenges
the intuition that a qubit must be isolated from its environment. Instead, the reservoir acts as a
feedback loop which continuously and autonomously corrects against errors. This correction takes

Project QUANTIC

19

place at the level of the quantum hardware, and reduces the need for error syndrome measurements
which are resource intensive. The circuits I will develop manipulate quantum states of light, whose
utility transcends the long term goal of quantum computing, and can readily be used to probe
fundamental properties of matter. In mesoscopic physics where a large number of particles exhibit
collective quantum phenomena, the measurement tools to characterize subtle quantum effects
are often lacking. Here, the project proposes to measure the spin entanglement of a single Cooper
pair, by coupling a superconductor to a circuit composed of microwave resonators and a carbon
nanotube. The spin entanglement can be swapped into microwave photons, which can be detected
by deploying the arsenal of quantum limited microwave measurement devices.

ERC Advanced Grant Q-Feedback

• Program: H2020

• Type: ERC

• Project acronym: Q-Feedback

• Project title: Quantum feedback Engineering

• Duration: 2020-2025

• Coordinator: Pierre Rouchon, Mines Paristech

• Abstract : Quantum technologies, such as quantum computers and simulators, have the potential
of revolutionizing our computational speed, communication security and measurement preci-
sion.The power of the quantum relies on two key but fragile resources: quantum coherence and
entanglement. This promising field is facing a major open question: how to design machines
which exploit quantum properties on a large scale, and efficiently protect them fromexternal
perturbations (decoherence), which tend to suppress the quantum advantage?

Making a system robust and stable to the influence of external perturbations is one of the core
problems in control engineering. The goal of this project is to address the above question from
the angle of control systems. The fundamental and scientific ambition is to elaborate theoretical
control methods to analyse and design feedback schemes for protecting and stabilizing quantum
information. Q-Feedback develops mathematical methods to harness the inherently stochastic
aspects of quantum measurements. Relying on the development of original mathematical per-
turbation techniques specific to open quantum systems, Q-Feedback proposes a new hierarchical
strategy for quantum feedback modeling, design and analysis.

The building block of a quantum machine is the quantum bit (qubit), a system which can adopt two
quantum states. Despite major progress, qubits remain fragile and lose their quantum properties
before a meaningful task can be accomplished. For this reason, a qubit must be both protected
against external perturbations, and manipulated to perform a task. Today, no such qubit has been
built. In collaboration with experimentalists, the practical ambition is to design, relying on the
control tools developed here, qubits readily integrable in a quantum processing unit. The physical
platform will be Josephson superconducting circuits. Q-Feedback is expected to demonstrate the
crucial role of control engineering in emerging quantum technologies.

Quantera Grant QuCos

• Program: H2020

• Type: Quantera

• Project acronym: QuCos

• Project title: Quantum Computation with Schrödinger cat states

• Duration: 2019-2023

• Coordinator: Gerhard Kirchmair, University of Innsbruck, Austria.

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Inria Annual Report 2023

• Inria contacts: Zaki Leghtas and Mazyar Mirrahimi

• Other partners: ENS Lyon (France), Karlsruhe Institut of Technology (Germany), Quantum Ma-
chines (Israel), National Institute for Research and Development of Isotopic and Molecular Techno-
logies, Romania.

• Abstract: This project seeks to establish a radically new, alternative approach to realizing the
fundamental building blocks of quantum computers with superconducting qubits. In the next 3
years, we plan to employ only a handful of realistic components to realize robust error-corrected
logical quantum bits. We aim to demonstrate the same level of protection provided by a few
hundreds of qubits (with properties beyond the state of the art) in today’s mainstream approach of
the so-called surface code architecture. Our alternative approach is known as cat codes, because
it employs multiple interconnected high coherence cavity modes with non-linear dissipation,
to encode a qubit in superpositions of Schrödinger cat states. Our project combines realizing
the quantum processor architecture as well as the control system and the protocols that drive it,
building towards a full-stack error-corrected quantum computer. The partners in our collaboration
form a strong synergetic group that has the full range of expertise needed to design and realize these
systems, and to obtain these challenging goals. Furthermore, all partners of our project, including
both industry and academia, have worked together and published works in the fields of quantum
computing and quantum information processing. We aim to implement error protected qubits,
fault tolerant operations, and demonstrate the scalability of this approach by realizing a repetition
code. Our project will enable quantum experiments towards the ambitious and well-defined goal
of constructing a logical qubit, on which we can perform gates, and most importantly, quantum
error-correction (QEC).

8.3 National initiatives

• PEPR NISQ2LSQ: Quantic is a PI and the coordinator of WP1 of this PEPR project which started
in 2022. The goal is to accelerate French research on the topic of bosonic and LDPC codes for
preparing the ground for hardware-efficient and fault-tolerant quantum computation.

• PEPR RobustSuperQ: Quantic is a PI and the coordinator of WP1 of this PEPR project which started
in 2022. The goal is to accelerate French research on the topic of high quality, noise resilient,
superconducting qubits.

• 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 Mecaflux: Alain Sarlette is a PI of this ANR Grant that started in 2022 and runs for 4
years. 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. The PhD thesis of
Angela Riva is funded on this ANR.

• ANR project OCTAVES: Mazyar Mirrahimi is a PI of this ANR Grant that started in 2022 and will
run for 4 years. 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). The PhD thesis of Linda Greggio is funded on this ANR.

8.4 Regional initiatives

• Alain Sarlette is a member of the steering committee of DIM Quantip.

Project QUANTIC

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9 Dissemination

9.1 Promoting scientific activities

9.1.1 Scientific events: selection

Reviewer

• Pierre Rouchon was a referee for IEEE and IFAC conferences.

• Alain Sarlette was a referee for IEEE and IFAC conferences.

9.1.2 Journal

Member of the editorial boards

• Pierre Rouchon is a member of the editorial board of Annual Reviews in Control.

Reviewer - reviewing activities

• Philippe Campagne Ibarcq was a referee for PRL, PRX, Nature Physics.

• Zaki Leghtas was a referee for PRL and Nature Communications.

• Mazyar Mirrahimi was a referee for PRL and npj Quantum Information.

• Tudor-Alexandru Petrescu was a referee for Physical Review and Quantum.

• Pierre Rouchon was a referee for Journal of differential equation, PRX.

• Alain Sarlette was a referee for IEEE Transactions, PRL, PRX Quantum, PRA.

• Antoine Tilloy was a referee for PRL, PRX, Physics Letters A, and Foundations of Physics.

9.1.3 Invited talks

• Philippe Campagne Ibarcq: BBQ conference in Boulder, Colorado, on bosonic error correction.

• Philippe Campagne Ibarcq: Erlangen University (remote).

• Philippe Campagne Ibarcq: Chalmers University.

• Zaki Leghtas: Hebrew University of Jerusalem. Invited by Alex Retzker (2023).

• Zaki Leghtas: Weizmann Instiute. Invited by Fabien Lafont and Serge Rosenblum (2023).

• Zaki Leghtas: Institut Néel. Invited by Jérémie Viennot (2023).

• Zaki Leghtas: C2N. Invited by Rebeca Ribeiro-Palau (2023)

• Zaki Leghtas: Les Houches. France. Invited by Benjamin Sacépé (2023)

• Mazyar Mirrahimi: BBQ conference in Boulder, Colorado, on bosonic error correction.

• Mazyar Mirrahimi: ENS-Mitsubishi Heavy Industry meeting.

• Mazyar Mirrahimi: University of Glasgow Centre for Quantum Technology (remote) invited by

Kaveh Delfanazari.

• Mazyar Mirrahimi: Workshop "Feedback control of Quantum Machines", Okinawa Institute for

Science and Technology, Japan.

• Mazyar Mirrahimi: Conference "Quantum PhotoniX", Jinhua, China.

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Inria Annual Report 2023

• Tudor-Alexandru Petrescu: APS March Meeting 2023 in New Orleans

• Tudor-Alexandru Petrescu: MPQ

• Tudor-Alexandru Petrescu: Université Paris-Cité

• Tudor-Alexandru Petrescu: Institut Néel, Grenoble

• Pierre Rouchon: Feedback and autonomous Quantum Error Correction (QEC). Innovations in

Nonlinear Control 13-17 February 2023, IIT Bombay.

• Pierre Rouchon: Feedback and quantum error corrections: Séminaire de Mathématiques Appli-

quées, Collège de France, 9 juin 2023.

• Pierre Rouchon: Feedback et correction d’erreurs quantiques: Stratégie Nationale Quantique

Journée du 30 mars 2023, Paris; Académie des Technologies, 21 novembre 2023, Paris.

• Antoine Tilloy: IFT Madrid.

• Antoine Tilloy: Capital Fund Management.

• Antoine Tilloy: "Entangle This 5" conference in Benasque.

• Antoine Tilloy: Maspin event in Besançon.

9.1.4 Leadership within the scientific community

• Alain Sarlette is a board member of the new DIM "QUANTIP" (Quantum Technologies in Paris

Region), which has been launched in 2022.

• Mazyar Mirrahimi is leader for WP1 of the PEPR NISQ2LSQ.

• Zaki Leghtas is co-leader for WP1 of the PEPR RobustSuperQ.

9.1.5 Scientific expertise

• Pierre Rouchon was a member of ANR Comité d’Evaluation Scientifique on Quantum Technologies

(CS 47).

• Philippe Campagne-Ibarcq, Zaki Leghtas and Mazyar Mirrahimi are members of the scientific

board of the Startup Alice and Bob.

9.1.6 Research administration

• Alain Sarlette has been a member of the selection committees at inria Paris (invited professors, PhD

and postdoc grants).

• Philippe Campagne-Ibarcq has been a member of the selection committee at Inria Paris-Saclay for

Junior Researcher (CRCN) positions.

• Mazyar Mirrahimi has been a member of the selection committee at Inria Paris for Junior Researcher

(CRCN) positions.

Project QUANTIC

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9.2 Teaching - Supervision - Juries

9.2.1 Teaching

• Mazyar Mirrahimi: Quantum Feedback at Ecole Polytechnique (60 hours), Ecole Polytechnique

bachelor program thesis instructor (20 hours).

• Alexandru Petrescu and Pierre Rouchon give the M1 course (Mathematical method for quantum

engineering) of the new PSL Master Quantum Engineering.

• Alexandru Petrescu and Pierre Rouchon give the M2 course (dynamics and control of open quantum

systems) of the PSL Master Quantum Engineering.

• Philippe Campagne-Ibarcq : 12h of préceptorat at ESPCI.

• Alex Petrescu Automatics at Mines ParisTech (12 hours).

• Pierre Rouchon is a member of the steering commitee of PSL master of Quantum Engineering with

ENS-Paris.

• Pierre Rouchon is in charge of the "Mathematics and Automatics" specialty within the ISMME-621

doctoral school.

• Antoine Tilloy: Mines Paris, TDs of Optimisation, TDs of Introduction to quantum mechanics.

• Alain Sarlette and Antoine Tilly: M1 Course (Introduction to quantum computing) of the new PSL

Master Quantum Engineering, 20 hours.

• Alain Sarlette: Robotics at Ghent university (24 hours).

• Alain Sarlette : M2 Course (Quantum Information Theory) of the new PSL Master Quantum Engin-

eering, 10 hours.

9.2.2 Supervision

PhD defended in 2023 Marius Villiers. Enhancing qubit-photon interactions with anti-squeezing. Su-

pervision Zaki Leghtas.

PhD defended in 2023 Camille Berdou. Cat-qubit: macroscopic bit-flip times. Supervision of Zaki

Leghtas.

PhD defended in 2023 Christian Siegele. Quantum error correction with grid states of light. Supervision

of Philippe Campagne-Ibarcq and Mazyar Mirrahimi.

PhD defended in 2023 Ronan Gautier. Efficient protection and fast gates in bosonic quantum codes.

Supervision of Alain Sarlette.

PhD in progress Alvise Borgognoni. Non-local quantum dynamics. Supervision of Zaki Leghtas.

PhD in progress Ulysse Réglade. 3D cat-qubit. Supervision of Zaki Leghtas and Raphaël Lescanne.

PhD in progress Adrien Bocquet. Cat-qubit: quantum coherence and macroscopic bit-flip times. Super-

vision of Zaki Leghtas and Raphaël Lescanne.

PhD in progress Erwan Roverch’. Protected qubits. Supervision of Zaki Leghtas.

PhD in progress Angela Riva. Dynamics and control of a mechanical quantum oscillator quasi-resonantly

coupled to a Heavy Fluxonium qubit. Supervision of Alain Sarlette.

PhD in progress Aron Vanselow. Autonomous stabilization of GKP grid states in high impedance circuits.

Supervision of Philippe Campagne-Ibarcq and Mazyar Mirrahimi.

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Inria Annual Report 2023

PhD in progress François-Marie Le Régent. Quantum computing architecture with cat-qubits. Supervi-

sion of Mazyar Mirrahimi and Jérémie Guillaud

PhD in progress Lev-Arcady Sellem. Mathematical methods for simulation and control of open quantum

systems. Supervision of Claude Le Bris and Pierre Rouchon.

PhD in progress Thiziei Aissaoui. On-chip biasing of superconducting circuits. Supervision of Alain

Sarlette and Anil Murani.

PhD in progress Matthieu Praquin, Reconfigurable microwave photonics crystals based on granular

superconductors. Supervision of Philippe Campagne-Ibarcq and Zaki Leghtas.

PhD in progress Linda Greggio. Strong drive effects in quantum superconducting circuits. Supervision

of Alexandru Petrescu and Mazyar Mirrahimi.

PhD in progress Diego Ruiz. Scaling up a bosonic quantum processor. Supervision of Mazyar Mirrahimi

and Jérémie Guillaud.

PhD in progress Louis Paletta. Autonomous quantum error correction with cat qubits. Supervision of

Mazyar Mirrahimi, Anthony Leverrier, Christophe Vuillot and Alain Sarlette.

PhD in progress Pierre Guilmin. Quantum estimation and control of cat-qubit. Supervision of Pierre

Rouchon and Antoine Tilloy.

PhD in progress Leon Carde. Control and fast preparation of cat qubits, supervision of Joachim Cohen,

Alexandru Petrescu, Pierre Rouchon.

PhD in progress Karanbir Singh Tiwana. Tensor networks for quantum field theory. Supervision of

Antoine Tilloy.

PhD in progress Emilio Rui. Cifre with Alice and Bob, Tensor network simulations for superconducting

quantum circuit design. Supervision of Alexandru Petrescu and Pierre Rouchon.

PhD in progress Brieuc Beauseigneur. Supported by ERC Q-Feedback, Design and characterization
of high-impedance superconducting circuits for autonomous error-correction. Supervision of
Philippe Campagne-Ibarcq and Pierre Rouchon.

PhD in progress Anissa Jacob. Parametric pumping of Josephson circuits for quantum error-correction.

Supervision of Philippe Campagne-Ibarcq and Anil Murani (Alice and Bob).

9.2.3 Juries

• Zaki Leghtas has been referee for the HDR of Jean-Damien Pillet.

• Mazyar Mirrahimi has been the jury president for the PhD defense of Valentin Heyraud at Univ.

Paris Cité.

• Mazyar Mirrahimi was a jury member for the PhD defense of Leo Balembois at Univ. Paris Saclay.

• Alexandru Petrescu was external reader for the PhD thesis of Xu Xiao at Yale University.

• Pierre Rouchon was referee of the "mémoire d’habilitation de François Ollivier" on Effective Formal

Resolution of Systems of Algebraic Differential Equations at Université Paris-Saclay.

• Pierre Rouchon was member of the jury of the "mémoire d’habilitation de Amaury Hayat" on

Stabilization of 1D evolution systems at Université Paris-Dauphine.

• Antoine Tilloy was in the PhD committee of Manuel Campos, UNIVERSIDAD AUTÓNOMA DE

MADRID.

Project QUANTIC

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9.3 Popularization

9.3.1 Interventions

• Alain Sarlette participated in an afternoon roundtable discussion on "quantum computing" at

EFREI, Villejuif.

10 Scientific production

10.1 Major publications

[1]

S. Apers and A. Sarlette. ‘Quantum Fast-Forwarding: Markov chains and graph property testing’.
In: Quantum Information & Computation (Apr. 2019). URL: https://hal.inria.fr/hal-0239
4399.

[2] P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys-Geller, N. E. Frattini, V. V. Sivak, P. Reinhold,
S. Puri, S. Shankar, R. J. Schoelkopf, L. Frunzio, M. Mirrahimi and M. H. Devoret. ‘Quantum error
correction of a qubit encoded in grid states of an oscillator’. In: Nature 584 (Aug. 2020). Text
and figures edited for clarity. The claims of the paper remain the same. Author list fixed. URL:
https://hal.inria.fr/hal-03084673.

[3]

J. Guillaud and M. Mirrahimi. ‘Repetition Cat Qubits for Fault-Tolerant Quantum Computation’.
In: Physical Review X (Dec. 2019). https://arxiv.org/abs/1904.09474 - 22 pages, 11 figures.
DOI: 10.1103/PhysRevX.9.041053. URL: https://hal.inria.fr/hal-02413978.

[4] Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlastakis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar,
M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi and M. H. Devoret. ‘Confining
the state of light to a quantum manifold by engineered two-photon loss’. In: Science 347.6224 (Feb.
2015), pp. 853–857. DOI: 10.1126/science.aaa2085. URL: https://hal.inria.fr/hal-012
40210.

[5] R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi
and Z. Leghtas. ‘Exponential suppression of bit-flips in a qubit encoded in an oscillator’. In: Nature
Physics (Mar. 2020). DOI: 10.1038/s41567-020-0824-x. URL: https://hal.archives-ouver
tes.fr/hal-02526631.

[6] M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang and M. H. Devoret.
‘Dynamically protected cat-qubits: a new paradigm for universal quantum computation’. In: New
Journal of Physics 16.4 (Apr. 2014), p. 045014.

[7] N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. Girvin,
L. Jiang, M. Mirrahimi, M. H. Devoret and R. J. Schoelkopf. ‘Extending the lifetime of a quantum
bit with error correction in superconducting circuits’. In: Nature 536 (2016), p. 5.

[8] A. Sarlette, J.-M. Raimond, M. Brune and P. Rouchon. ‘Stabilization of nonclassical states of the
radiation field in a cavity by reservoir engineering’. In: Phys. Rev. Lett. 107 (2011). 010402.

[9] C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi,
H. Amini, M. Brune, J.-M. Raimond and S. Haroche. ‘Real-time quantum feedback prepares and
stabilizes photon number states’. In: Nature 477 (2011), pp. 73–77.

[10] W. C. Smith, M. Villiers, A. Marquet, J. Palomo, M. Delbecq, T. Kontos, P. Campagne-Ibarcq,
B. Douçot and Z. Leghtas. ‘Magnifying quantum phase fluctuations with Cooper-pair pairing’.
In: Physical Review X 12.2 (Apr. 2022), p. 021002. DOI: 10.1103/PhysRevX.12.021002. URL:
https://hal.inria.fr/hal-03084684.

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Inria Annual Report 2023

10.2 Publications of the year

International journals

[11] C. Berdou, A. Murani, U. Reglade, W. C. Smith, M. Villiers, J. Palomo, M. Rosticher, A. Denis, P.
Morfin, M. Delbecq, T. Kontos, N. Pankratova, F. Rautschke, T. Peronnin, L.-A. Sellem, P. Rouchon, A.
Sarlette, M. Mirrahimi, P. Campagne-Ibarcq, S. Jezouin, R. Lescanne and Z. Leghtas. ‘One hundred
second bit-flip time in a two-photon dissipative oscillator’. In: PRX Quantum 4.2 (2023), p. 020350.
DOI: 10.1103/PRXQuantum.4.020350. URL: https://hal.science/hal-03662636.

[12]

J. Cohen, A. Petrescu, R. Shillito and A. Blais. ‘Reminiscence of classical chaos in driven transmons’.
In: PRX Quantum 4.2 (2023), p. 020312. DOI: 10.1103/PRXQuantum.4.020312. URL: https://h
al.science/hal-03758792.

[13] L. C. Contamin, T. Cubaynes, W. Legrand, M. Marga ´nska, M. Villiers, M. Desjardins, V. Vinel, Z.
Leghtas, S. Rohart, A. Cottet, A. Thiaville, M. Dartiailh, M. R. Delbecq and T. Kontos. ‘Inhomo-
geneous magnetic fields interacting with spinful states in a double quantum dot: Evidence for
a staggered spin-orbit interaction’. In: Physical Review B 107.8 (15th Feb. 2023), p. 085152. DOI:
10.1103/PhysRevB.107.085152. URL: https://hal.science/hal-04094062.

[14] A. Gasull, A. Tilloy, J. I. Cirac and G. Sierra. ‘Symmetries and field tensor network states’. In:
Physical Review B 107.15 (3rd Apr. 2023), p. 155102. DOI: 10.1103/PhysRevB.107.155102. URL:
https://minesparis-psl.hal.science/hal-03858060.

[15] R. Gautier, M. Mirrahimi and A. Sarlette. ‘Designing High-Fidelity Zeno Gates for Dissipative Cat
Qubits’. In: PRX Quantum 4.4 (25th Oct. 2023), p. 040316. DOI: 10.1103/PRXQuantum.4.040316.
URL: https://inria.hal.science/hal-04378911.

[16] F.-M. L. Régent, C. Berdou, Z. Leghtas, J. Guillaud and M. Mirrahimi. ‘High-performance repetition
cat code using fast noisy operations’. In: Quantum 7 (6th Dec. 2023), p. 1198. DOI: 10.22331/q-2
023-12-06-1198. URL: https://inria.hal.science/hal-03918298.

[17] D. Ruiz, R. Gautier, J. Guillaud and M. Mirrahimi. ‘Two-photon driven Kerr quantum oscillator
with multiple spectral degeneracies’. In: Physical Review A 107.4 (6th Apr. 2023), p. 042407. DOI:
10.1103/PhysRevA.107.042407. URL: https://inria.hal.science/hal-03918293.

[18] C. Siegele and P. Campagne-Ibarcq. ‘Robust suppression of noise propagation in GKP error-
correction’. In: Phys.Rev.A 108.4 (2023), p. 042427. DOI: 10.1103/PhysRevA.108.042427. URL:
https://hal.science/hal-04017937.

International peer-reviewed conferences

[19] F.-M. L. Régent and P. Rouchon. ‘Heisenberg formulation of adiabatic elimination for open
quantum systems with two time-scales’. In: 62nd IEEE Conference on Decision and Control.
Singapore, Singapore, 2023. URL: https://inria.hal.science/hal-04379140.

[20] L.-A. Sellem, R. Robin, P. Campagne-Ibarcq and P. Rouchon. ‘Stability and decoherence rates of a
GKP qubit protected by dissipation’. In: 22nd World Congress of the International Federation of
Automatic Control. IFAC 2023 - 22nd World Congress of the International Federation of Automatic
Control. Yokohama, Japan, 7th Apr. 2023. DOI: 10.48550/arXiv.2304.03806. URL: https://in
ria.hal.science/hal-04071008.

[21] M. Tokieda, C. Elouard, A. Sarlette and P. Rouchon. ‘Complete Positivity Violation in Higher-order
Quantum Adiabatic Elimination’. In: IFAC-PapersOnLine. IFAC 2023 - 22nd World Congress of the
International Federation of Automatic Control. Vol. 56. 2. Yokohama, Japan, 2023, pp. 1333–1338.
DOI: 10.1016/j.ifacol.2023.10.1779. URL: https://inria.hal.science/hal-0437908
0.

Conferences without proceedings

[22] L. Paletta, A. Leverrier, A. Sarlette, M. Mirrahimi and C. Vuillot. ‘Robust sparse IQP sampling in
constant depth’. In: QIP2024. Taipei, Taiwan, 20th July 2023. URL: https://hal.science/hal-
04320801.

Project QUANTIC

27

[23] L. Paletta, A. Leverrier, A. Sarlette, M. Mirrahimi and C. Vuillot. ‘Robust sparse IQP sampling in
constant depth’. In: QIP2024 The international conference on Quantum Information Processing.
Taipei, Taiwan, 20th July 2023. URL: https://hal.science/hal-04312163.

Scientific book chapters

[24]

J. Guillaud, J. Cohen and M. Mirrahimi. ‘Quantum computation with cat qubits’. In: SciPost Physics
Lecture Notes. 2019-07: Quantum Information Machines Collection in the Les Houches Summer
School Lecture Notes Series. 16th June 2023, p. 72. DOI: 10.21468/SciPostPhysLectNotes.72.
URL: https://inria.hal.science/hal-03918283.

Edition (books, proceedings, special issue of a journal)

[25] P. Guilmin, P. Rouchon and A. Tilloy, eds. Correlation functions for realistic continuous quantum
measurement. IFAC-PapersOnLine. Vol. 56. 2. 22nd Nov. 2023, pp. 5164–5170. DOI: 10.1016/j.if
acol.2023.10.110. URL: https://hal.science/hal-03882949.

Doctoral dissertations and habilitation theses

[26] C. Berdou. ‘Macroscopic bit-flip times in two-photon dissipative oscillator’. Université Paris
sciences et lettres, 14th Mar. 2023. URL: https://pastel.hal.science/tel-04235044.

[27] R. Gautier. ‘High-Fidelity Control and Stabilization of Cat Qubits’. Inria Paris, 4th Dec. 2023. URL:

https://hal.science/tel-04362128.

[28] C. Siegele. ‘Robust suppression of back-propagating noise in GKP error syndrome measurements’.
ENS Paris - Ecole Normale Supérieure de Paris, 24th Feb. 2023. URL: https://theses.hal.scie
nce/tel-04385083.

[29] M. Villiers. ‘Dynamically Enhancing Qubit-Photon Interactions with Anti-Squeezing’. Sorbonne

Université, 15th May 2023. URL: https://hal.science/tel-04209718.

Reports & preprints

[30] V. Martin and A. Sarlette. Stabilization of approximate GHZ state with quasi-local couplings.

22nd June 2023. URL: https://hal.science/hal-04137276.

[31] B.-L. Najera-Santos, R. Rousseau, K. Gerashchenko, H. Patange, A. Riva, M. Villiers, T. Briant, P.-F.
Cohadon, A. Heidmann, J. Palomo, M. Rosticher, H. Le Sueur, A. Sarlette, W. C. Smith, Z. Leghtas,
E. Flurin, T. Jacqmin and S. Deléglise. High-sensitivity AC-charge detection with a MHz-frequency
fluxonium qubit. 24th July 2023. URL: https://hal.science/hal-04169999.

[32] F.-M. L. Régent and P. Rouchon. Adiabatic elimination for composite open quantum systems:
reduced model formulation and numerical simulations. 8th Jan. 2024. URL: https://inria.hal
.science/hal-04379147.

[33] U. Réglade, A. Bocquet, R. Gautier, A. Marquet, E. Albertinale, N. Pankratova, M. Hallén, F.
Rautschke, L.-A. Sellem, P. Rouchon, A. Sarlette, M. Mirrahimi, P. Campagne-Ibarcq, R. Lescanne,
S. Jezouin and Z. Leghtas. Quantum control of a cat-qubit with bit-flip times exceeding ten seconds.
13th July 2023. URL: https://hal.science/hal-04189479.

[34] R. Robin, P. Rouchon and L.-A. Sellem. Convergence of bipartite open quantum systems stabilized

by reservoir engineering. 16th Nov. 2023. URL: https://inria.hal.science/hal-04379101.

[35] L.-A. Sellem, A. Sarlette, Z. Leghtas, M. Mirrahimi, P. Rouchon and P. Campagne-Ibarcq. A GKP
qubit protected by dissipation in a high-impedance superconducting circuit driven by a microwave
frequency comb. 3rd Apr. 2023. DOI: 10.48550/arXiv.2304.01425. URL: https://inria.hal
.science/hal-04070996.

[36] W. C. Smith, A. Borgognoni, M. Villiers, E. Roverc’H, J. Palomo, M. Delbecq, T. Kontos, P. Campagne-
Ibarcq, B. Douçot and Z. Leghtas. Spectral signature of high-order photon processes mediated by
Cooper-pair pairing. 22nd Dec. 2023. URL: https://hal.science/hal-04387016.

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[37] M. Villiers, W. C. Smith, A. Petrescu, A. Borgognoni, M. Delbecq, A. Sarlette, M. Mirrahimi, P.
Campagne-Ibarcq, T. Kontos and Z. Leghtas. Dynamically enhancing qubit-oscillator interactions
with anti-squeezing. 2nd Jan. 2023. URL: https://inria.hal.science/hal-03918303.

[38] D. Willsch, D. Rieger, P. Winkel, M. Willsch, C. Dickel, J. Krause, Y. Ando, R. Lescanne, Z. Leghtas,
N. T. Bronn, P. Deb, O. Lanes, Z. K. Minev, B. Dennig, S. Geisert, S. Günzler, S. Ihssen, P. Paluch,
T. Reisinger, R. Hanna, J. H. Bae, P. Schüffelgen, D. Grützmacher, L. Buimaga-Iarinca, C. Morari, W.
Wernsdorfer, D. P. Divincenzo, K. Michielsen, G. Catelani and I. M. Pop. Observation of Josephson
Harmonics in Tunnel Junctions. 23rd Aug. 2023. URL: https://hal.science/hal-04387195.

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<scratchpad>
- Main topic: Research Centre - QUANTIC Project
- Key points:
  - QUANTIC team's research focuses on quantum systems engineering, applied mathematics, and control theory.
  - The team explores various topics, including hardware-efficient quantum information processing, reservoir engineering, and stabilization of quantum systems.
  - They also investigate application domains, such as quantum engineering, quantum information processing, and quantum computing.
  - The team has published several papers on their research, including those on bosonic error correction, cat qubits, and quantum feedback.
- Structure: The document is divided into sections, including activity report, project-team, research program, and application domains.
- Potential artifacts to ignore: Web-related elements, such as links and HTML tags.
</scratchpad>

<final_summary>
The QUANTIC project is a research centre that focuses on quantum systems engineering, applied mathematics, and control theory. The team explores various topics, including hardware-efficient quantum information processing, reservoir engineering, and stabilization of quantum systems. They have published several papers on their research, including those on bosonic error correction, cat qubits, and quantum feedback. The team's research aims to develop quantum devices ensuring robust processing of quantum information and to explore application domains, such as quantum engineering and quantum computing. Their work has the potential to contribute to the development of fault-tolerant quantum computing architectures.
The QUANTIC project is a research centre that focuses on quantum systems engineering, applied mathematics, and control theory. The team explores various topics, including hardware-efficient quantum information processing, reservoir engineering, and stabilization of quantum systems. They have published several papers on their research, including those on bosonic error correction, cat qubits, and quantum feedback. The team's research aims to develop quantum devices ensuring robust processing of quantum information and to explore application domains, such as quantum engineering and quantum computing. Their work has the potential to contribute to the development of fault-tolerant quantum computing architectures.