NEWSLETTER #4 – June 2021



2021 DOCTORAL PROGRAMM CAMPAIGN 

The 2021 Doctoral Program in Quantum Information is now over!
The Quantum Information Center Sorbonne (QICS) awarded two doctoral programs related to quantum information, from both the physics and computer science point of view. 
On May 21st, the 6 projects have been selected by the QICS jury 6 students have been auditioned afterwards.
Go here to get more information


LEARN QUANTUM INFORMATION

Master Quantum Information ; Sorbonne University opens a master program dedicated to Quantum Information in Paris! This program is supported by the Quantum Information Center Sorbonne (QICS), the Computer Science Master Department, and Physics Master Department. Experts from Sorbonne Université labs (LIP6LKBINSPINRIA, etc.) will be part of this program divided into two main specialties the 1st year (computer science and physics) and with a joint course the second year.
To know more about this Master program

Scientific mediation in quantum information ; the objective of this short training course is to give, to PhD students working in one of the thematics of quantum information, the keys to answer easily these questions to the widest possible audience. This training course offers them the opportunity to collaborate all together. Thanks to this transdisciplinarity and cooperation, they also complete their knowledge, transmit it and create new joint projects.
Learn here more information about the training course


SMALL SEMINAR OF THE QICS 
…accessible only to PhD students and post-doc

Our second small seminar, the new monthly event done for them, by them and only between them, will be on July the 7th !

The purpose of this monthly event is to bring together doctoral and post-doctoral students working on diverse and varied thematics of quantum information in order to discover their very wide range, from core thematics to related subjects. Through this interdisciplinarity, they will be able, on the one hand, to complete and share their knowledge, and on the other hand, to bring out collaborations and joint projects.
More information here 

If you are already interested, just send back an email to qics@sorbonne-universite.fr


THEY SPEAK ABOUT US

On May 18th, Sorbonne Université interviewed our colleague Eleni Diamanti regarding Quantum cryptography, the new Paris Center for Quantum Technologies and her role as a woman in science.
Go here to read the complete article

To know more about the QICS, its community, the Co-directors, our ambitions for quantum information in Paris and Sorbonne Université and our goal, go here to listen to Frédéric Grosshans and Nicolas Treps (in French only)


SAVE THE DATE!

The quantum information Center Sorbonne is taking part to The Festives(November 25th to 27th) & Fête de la science (5th to 10th October). Both events, coordinated by Sorbonne Université would be the occasion to present and display the video and game developed by the QICS PhD & Post-doc community.
More information coming soon!


CONTACT
Don’t hesitate to contribute by sending us, at qics@sorbonne-universite.fr, any relevant news or material related to Quantum information. You can also use the mailing list at qics-info@listes.upmc.fr to share important information with the community.

Small seminar #1

The monthly PhD student’s seminar in Quantum information
Accessible only to PhD students and Post-doc


Our first seminar will take place at Jussieu, Pierre & Marie Curie Campus, amphitheater Charpak which is located on the Ground floor / Saint Bernard level of Campus Jussieu. 
From Tower 22 on the Jussieu slab, go down to the SB / RC level. Turn left until the exit of the rotunda. Access to the Charpak amphitheater is through gate 2233-SB-02 on the other side of the internal road.

From 11.45 am to 12.25 pm on Wednesday, the 2nd of June


For this first seminar, our 2 speakers are Federico Centrone, from QI team at Lip6 and Tom Darras, from Quantum Network team at LKB.

Practical quantum e-voting without election authorities:

In this work, Federico Centrone present a quantum protocol that exploits an untrusted multipartite entangled quantum source to carry on an election without relying on election authorities, simultaneous broadcast or computational assumptions, and whose result is publicly verifiable without compromising the robustness of the scheme. The level of security depends directly on the fidelity of the shared multipartite entangled quantum state; however, the protocol can be readily implemented for a few voters with state-of-the-art technology. 
From 11:45 am to 12:05 pm

Hybrid entanglement in heterogeneous quantum networks:

The building of quantum networks is stimulating the development of multiple physical platforms and different types of encodings in a heterogeneous structure allowing full functionality. Central to this endeavour is the capability to distribute and interconnect optical entangled states relying on different discrete and continuous quantum variables. Here, we report an entanglement swapping protocol involving single-photon entanglement and hybrid entanglement between particle- and wave-like optical qubits and demonstrate the creation of hybrid entanglement heralded by a specific Bell-state measurement. This ability opens up the prospect of connecting heterogeneous nodes of a network, with the promise of increased integration and functionalities.
From 12:05 pm to 12.25pm


After the talks and if the weather allows us to do it, we invit you to join us for lunching at the Arènes de lutèce. Just grab a sandwich in your way and meet us here to discuss and share a convivial moment.

NEW ! Small seminars of the #QICS

The Quantum Information Center Sorbonne (QICS) aims at coordinating research, teaching and outreach efforts within the Alliance Sorbonne Université on quantum information — quantum computing and quantum communications —, as well as its impact in other fields. It gathers a large community from computer science to physics, but also mathematics and humanities.
It is within this framework that the QICS proposes to initiate inter-doctoral / post-doctoral seminars of the Alliance Sorbonne Université to allows its members to discover the wide range of research topics related to quantum information. 

Objective: 
The purpose of this monthly event is to bring together doctoral and post-doctoral students working on diverse and varied thematics of quantum information in order to discover their very wide range, from core thematics to related subjects. Through this interdisciplinarity, they will be able, on the one hand, to complete and share their knowledge, and on the other hand, to bring out collaborations and joint projects.
Concretely, our mission is to allow doctoral and post-doctoral students to meet, work together and open the quantum community to other scientific fields. This is why people from other fields of research are welcome, and are invited to present us the existing synergies between their work and quantum information.

Seminars format:
This short and user-friendly event, which encourages interactions and informal moments, is broken down as follow:
– two short presentations, 10 minutes each to describe the project followed by 10 minutes de questions;
– every 1st Wednesday of the month, from 11:45 am to 12:25 pm;  
– using only 10 slides; 
– in an amphitheater of a laboratory;
– followed by a more informal time outside.

How to submit your proposition:
Just by sending your project to qics@sorbonne-universite.fr specifying the following elements:
– name and firstname;
– team and laboratory;
– seminar title and short summary.

Agenda and practical informations:
– the first seminar will takes place on June the 2nd;
– the deadline to send your subject is May the 18th;
– another newsletter announcing the detailed program and location of the event will be sent to you a few days before June the 2nd.

CONTACT

Don’t hesitate to contribute by sending us, at qics@sorbonne-universite.fr, any relevant news or material related to Quantum information. You can also use the mailing list at qics-info@listes.upmc.fr to share important information with the community.

NEWSLETTER #3 – Mars 2021


CHAIRE ANNUELLE DE FRÉDÉRIC MAGNIEZ AU COLLÈGE DE FRANCE

Frédéric Magniez, d’Université de Paris, inaugure sa chaire annuelle au Collège de France, le 1er avril
La leçon inaugurale porte sur les algorithmes quantiques : quand la physique quantique défie la thèse de Church-Turing.
Chaque cours sera accessible au plus grand nombre et accompagné d’un séminaire d’un·e spécialiste sur les dernières avancées du domaine.
Suivez ce lien pour découvrir le programme complet.


PROJETS LAURÉATS DE LA CAMPAGNE DOCTORALE DES INSTITUTS ET INITIATIVES

Dans le cadre des Instituts et Initiatives de l’Alliance Sorbonne Université (ASU), une campagne d’attribution de contrats doctoraux financés par l’Initiative française d’excellence (Idex) a été lancée en janvier 2021. 
Comme pour 2020, le QICS propose deux bourses de thèse. Parmi les nombreux projets reçus, le QICS a choisi de retenir 6 projets dont voici les détails :
Realizing arbitrary quantum operations on a mechanical oscillato
Complex quantum Networks for quantum machine learning protocols
MecaFlux
Peignes de fréquences quantiques pour des protocoles d’information quantique
Quantum Hamiltonian Complexity and Derandomization
Impact of quantum computers on Impagliazzo’s five worlds
Prochaines échéances :
– jusqu’au 3 mai : dépôt des candidatures par les étudiants et étudiantes
– jusqu’au 21 mai : audition des candidats et candidates
– 24 mai : annonce des résultats
Consulter la campagne pour plus d’informations


LES DERNIÈRES INTERVENTIONS DE NOS MEMBRES

C’était le 17 mars, deux membres du QICS participaient à la 1ère édition de l’événement, 100% dédié aux technologies quantiques B2B, Quantum Business Europe.
Nicolas Treps intervenait sur la thématique suivante « Building the future quantum workforce » et Eleni Diamanti proposait une réponse à la question suivante « How is the EU assessing the user needs of a quantum communication infrastructure? »
Suivez ce lien pour revoir leur présentation

« Les exploratrices de l’infiniment petit » décrit ces femmes chercheuses qui non seulement participent mais sont au cœur de la « révolution quantique » en France et en Europe. Dans cet article paru au Point, le 18 mars, vous trouverez les portraits de 10 femmes dont ceux de Eleni Diamanti et Elham Kashefi, toutes deux membres du QICS.


MT180s – FINALE SORBONNE UNIVERSITÉ 2021

Vendredi 19 mars, 18 nouveau.x/nouvelle.s candidat.e.s se présentaient au concours Ma thèse en 180 secondes. Le principe de ce concours : les doctorants, doctorantes, docteures et docteurs, doivent présenter en 3 minutes leur sujet de thèse à un public profane.
Deux membres du QICS ont été sélectionnés pour participer à la finale à Sorbonne Université de #MT180. Félicitations à Thibaut Lacroix qui obtient le 2ème prix du jury et un grand bravo à nos deux candidats pour leur prestation de grande qualité ! 


PRIX LES MARGARET & LES MARGARET JUNIOR 2021

La Pr. Elham Kashefi a reçu, le 8 mars dernier, le prix les Margaret & les Margaret Junior, catégorie «intrapreuneur Europe»
Lancé en 2013 par la JFD, le Prix les Margaret récompense chaque année des femmes entrepreneurs et intrapreneurs en Europe et en Afrique, dont les projets et innovations répondent aux grands enjeux de notre société. 
À travers le Prix les Margaret, la JFD soutient la croissance et le rayonnement international de startups et initiatives en entreprise, portées par des femmes européennes et africaines.
Elham Kashefi, Directrice de Recherches au CNRS/LIP6 et membre du QICS reçoit ce prix en 2021 pour son activité en recherche et la création de la startup VeriQloud Ldt.
Pour en savoir plus, cliquez ici.


LAURÉAT DE L’AAP « SHS ET INFORMATION QUANTIQUE » DU QICS 

Félicitations à Bruno Bachimont du laboratoire Connaissance, Organisation et Systèmes Techniques – COSTECH (SU – UTC, UPR 2223), en collaboration avec Vincent Bontems et Christian de Ronde des laboratoires de recherche sur les sciences de la matière (Larsim-CEA) et la communauté LOGOS (CONICET-Argentine), qui remporte l’appel à projet Sciences humaines et sociales du Centre d’information quantique Sorbonne. 
Le sujet qui a retenu l’attention du jury consiste à « Repenser l’information quantique et l’intrication à la lumière de Simondon »


CONTACT
Si vous souhaitez rejoindre notre communauté, suivre notre actualité, partager des informations ou nous proposer des suggestions, n’hésitez pas à nous adresser un message à qics@sorbonne-universite.fr. Vous pouvez également utiliser la mailing list qics-info@listes.upmc.fr pour partager des informations importantes avec la communauté.

Complex quantum Networks for quantum machine learning protocols

This PhD research project has been submitted for a funding request to “Quantum Information Center Sorbonne (QICS)”. The PhD candidate selected by the project leader will therefore participate in the project selection process (including a file and an interview) to obtain funding.

This project aims at the implementation of quantum enhanced machine learning protocols in a photonics platform. It focuses on the implementation of protocols based on network structures, e.g., quantum reservoir computing, via multimode quantum optics.

The experimental activity concerns the implementation of quantum complex networks by using femtosecond laser sources and parametric processes [1,2]. Such systems can deterministically generate entanglement correlations between quadratures of the electromagnetic field of several spectral-temporal modes that can be exploited in Continuous Variables (CV) quantum information protocols. In most experiments, parametric processes take place in a resonant cavity in order to enhance the non-linear effect [3]. The peculiarity of our approach is the use of non-linear waveguides (in order to reach high enough non-linearity) in a single-pass configuration [4,5], which allows us to preserve the entanglement structure in the laser-pulse basis. This, combined with a fast homodyne detection technique, will allow us to generate very large entangled networks, exploiting both spectral and temporal degrees of freedom. The generated resource will be used for quantum enhanced machine learning.

Machine learning covers a wide range of algorithms and modelling tools with automated data processing capabilities. Here, we consider network-based strategies, like neural networks and reservoir computing. The latter exploits the dynamics of a non-linear system (the reservoir) for information processing of a time dependent input. In the classical case, it has achieved state-of- the-art performance in tasks such as continuous speech recognition and nonlinear time series prediction. The reservoir can have the same architecture as neural networks, but it only needs to train connections leading to the final output layer. In the classical framework it has been implemented in photonics and spintronics hardware.

The quantum implementation of neural networks [6] and, more recently, of reservoir computing [7,8] has been proposed in the CV encoding. In particular it has been proved that Gaussian states provide universal reservoir computing and that quantum Gaussian resources, like squeezed state, provide a larger information capacity than classical states [8]. The proposed PhD project aims at getting the first experimental implementations of quantum reservoir computing. The assessment of the advantage of the quantum setting over the classical one will be studied in collaboration with a theory group based at IFISC (University of Baleares Island).

We will develop tailored protocols based on the experimental resources that, beside the Gaussian large entangled structure, will involve Non-gaussian states derived from single-photon subtraction or addition operations [9,10]. It is in fact known that non-Gaussian probability distributions of quadratures are needed to demonstrate a form of quantum advantage in computation protocols. But it is still unknown the amount of non-Gaussian resources needed for reaching the advantage in different quantum machine learning tasks. The experiment will thus serve as testbed for identifying the resources needed for the Quantum Reservoir Computing to outperform the classical setting.

The project is intended to be inserted in the initiative of the Quantum Information Center Sorbonne (QICS). It in fact covers instances concerning the broad impact of quantum information on machine learning protocols.

The PhD candidate should have a Master diploma in Physics. Familiarity with experimental optics and knowledge of quantum optics and quantum information will be valuable.

Contact to submit your application :
Valentina Parigi, valentina.parigi@lkb.upmc.fr

[1] J. Nokkala, F. Arzani, F. Galve, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps, V. Parigi, “Reconfigurable optical implementation of quantum complex networks”, New J. Phys. 20, 053024 (2018)

[2] F. Sansavini and V. Parigi “Continuous variables graph states shaped as complex networks: optimization and manipulation” Entropy 22, 26 (2020)

[3] Cai, Y. et al. “Multimode entanglement in reconfigurable graph states using optical frequency combs”. Nat. Commun. 8, 15645 (2017).

[4] L. La Volpe, S. De, T. Kouadou, D. Horoshko, M. I. Kolobov, C. Fabre, V. Parigi, and N. Treps, “Multimode single-pass spatio-temporal squeezing” Optics Express Vol. 28, Issue 8, pp. 12385- 12394 (2020)

[5] V. Roman-Rodriguez, B. Brecht, S. Kaali, C. Silberhorn, N. Treps, E. Diamanti, and V. Parigi “Continuous variable multimode quantum states via symmetric group velocity matching”, arXiv:2012.13629

[6] N. Killoran et al. “Continuous-variable quantum neural networks”, Physical Review Research 1, 033063 (2019).

[7] L. C. G. Govia, et al. “Quantum reservoir computing with a single nonlinear oscillator”, Phys. Rev. Research 3, 013077 (2021).

[8] J. Nokkala, R. Martínez-Peña, G. L. Giorgi, V. Parigi, M. C. Soriano, R. Zambrini, “Gaussian states provide universal and versatile quantum reservoir computing” arXiv:2006.04821

[9] M Walschaers, V Parigi, N Treps, “Practical Framework for Conditional Non-Gaussian Quantum State Preparation” PRX Quantum 1 (2), 020305 (2020)

[10] V Parigi, A Zavatta, M Kim, M Bellini “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field” Science 317 (5846), 1890-1893 (2007)

MecaFlux

This PhD research project has been submitted for a funding request to “Quantum Information Center Sorbonne (QICS)”. The PhD candidate selected by the project leader will therefore participate in the project selection process (including a file and an interview) to obtain funding.

Objectives: This thesis experimental project aims at demonstrating strong resonant coupling between a long-lived quantum memory in the form of a nano-mechanical resonator, and a qubit. This strongly interacting quantum system will be used to demonstrate an original qubit-assisted cooling scheme, the generation of arbitrary phononic states such as Fock states or Schrödinger cat states, and to perform experimental tests of gravitational collapse models.

Motivation: Controlling the quantum state of a mechanical system is a long-standing scientific goal, with profound implications in both fundamental physics and engineering of hardware for quantum computation and quantum information. From a fundamental perspective, massive mechanical resonators placed in a quantum superposition are promising candidates to study potential deviations from quantum physics induced by gravitational decoherence [1]. On the other hand, mechanical resonators are a unique resource for quantum engineering as they can store fragile quantum states in long-lived mechanical oscillations [2]. Moreover, mechanical resonators could play an important role as quantum transducers, connecting otherwise incompatible quantum systems [3], for example superconducting circuits and optical photons [4], or for sensing spins in a solid state matrix [5]. The field of quantum optomechanics addresses this challenge by coupling a mechanical resonator to a high-frequency microwave or optical cavity. A decade-long quest for low- mass and low dissipation mechanical resonators has led to a new generation of optomechanical systems, where quantum radiation pressure strongly dominates over thermal noise [6]. This has enabled a number of breakthroughs, such as ground-state cooling [7], or the optomechanical generation of squeezed states [8]. However, the standard optomechanical framework suffers a major deficiency: the mechanical and electromagnetic modes are coupled via a linear effective interaction. Their dynamics can thus be entirely captured by a semi-classical model, where the system is described at all times by a positive Wigner function embodying a classical probability distribution in phase space.

State of the art: The most direct approach to go beyond this linear regime is to exploit the resonant coupling between a mechanical mode and a superconducting qubit to control the mechanical quantum state [2, 9–11]. However, in spite of recent breakthroughs, such as the demonstration of multi-phonon Fock states [2], it is restricted to GHz resonators, with short coherence times. Extending such schemes to MHz mechanical resonators would open intriguing perspectives, as ultra- coherent mechanical systems recently developed in the optomechanics community have demonstrated unprecedented force sensitivities [12], and lifetimes in the minute range [13–15].
The main difficulty stems from the large frequency difference between the mechanical resonator and the superconducting circuit, typically operating at GHz frequency. Many routes have been pioneered, but none of them proved fully satisfying: either the qubit coherence properties are poor [16], or the fidelity of the mechanical mode state is very small [17].

Approach followed in this thesis project: We propose a resolutely new approach that will enable full quantum control of a mechanical resonator operating in the 3-30 MHz range and with a lifetime >10 s. This parameter regime makes it an appealing candidate for quantum sensing, quantum information storage, and experimental tests of quantum gravity. We will overcome the frequency gap between this mechanical object and superconducting quantum circuits by coupling the former to a strongly non-linear circuit: the fluxonium qubit [19]. At a particular bias point, this circuit presents a low-frequency qubit manifold which is protected simultaneously against flux noise and energy relaxation. This new qubit paradigm has recently outperformed the transmon architecture [20], which constitutes the current quantum computing standard. Eventhough the qubit manifold lies well below the frequency range accessible with standard microwave components, the rich level structure of higher qubit excited states allows for its efficient readout, reset, and manipulation. Opportunely, the frequency of the qubit manifold in the heavy fluxonium regime [20, 21] naturally matches the mechanical resonance frequency of the ultracoherent mechanical membranes envisioned here. The large capacitive shunt of the heavy fluxonium is also perfectly compatible with a capacitive coupling scheme.

Mechanical resonator implementation: The mechanical resonator which is at the heart of this project is a softly-clamped [14] silicon-nitride membrane developed at LKB [15] with an ultra-low dissipation rate of Γ<(30 /s) [22]. The mechanical modes are well localized within the defects of a phononic bandgap that is directly etched in the 100-nm thick Si3N4 membrane, and can be engineered to present an anti-symmetric vibration pattern. We have recently demonstrated that the membrane could serve as the electrode of a planar capacitor by depositing a metallic pad on the mechanical antinode [22].

Qubit implementation: The fluxonium qubit is composed of a Josephson junction (JJ) shunted by an extremely large inductance. This inductance cancels charge carrier noise across the JJ, and together with a large capacitive shunt and the JJ, result in a system with transitions in the MHz range with very good coherence properties. The large inductance will be implemented with on arrays of JJs [19].

PhD candidate work: The PhD candidate would first have to estimate the coupling between the qubit and the mechanical mode. As the qubit transition has a low frequency, prior to any protocol implementation, the qubit needs to be actively set in its ground state. For this purpose, GHz-range transitions to higher qubit excited states can be used to evacuate the system’s entropy into an effective zero-temperature bath [20]. Then he will investigate and implement qubit-assisted cooling, to set the mechanical mode in its ground state. Finally, he will use these higher frequency qubit transitions to prove readout of the dressed qubit-resonator system [20]. An additional scientific aim will be the quantum manipulation of the membrane and perform tests of gravitational collapse models.

The PhD candidate will develop skills in: finite element analysis (both in the mechanical and electromagnetic domains), microfabrication in clean rooms of the Paris area, optical characterization of silicon nitride resonators and microwave experiments in a cryogenic environnement. He will work in close collaboration with the Quantic team of LPENS (Zaki Legthas), the teams of Emmanuel Flurin and Hélène Lesueur at CEA, and the Alice&Bob spinoff of ENS.

PhD advisors: Antoine Heidmann (DR), head of the Quantum Optomechanics group at LKB, will be the PhD director. Samuel Deléglise (CR) would be the co-director, and Thibaut Jacqmin (MCF) would be the second co-director. Antoine Heidmann pioneered the field of optomechanics twenty years ago, and will be the reference for optomechanics. Samuel Deléglise has a strong experience in CQED and optomechanics. The last five years he started to perform experiments with superconducting circuits and built many strong collaborations with groups specialized in that field. These collaborations lead to important scientific results [18]. He also originated CryoParis the « Plateforme cryogénique de Sorbonne Université » where the experiments performed during this thesis will be implemented. This platform has now a fully equipped Bluefors dilution cryostat. Thibaut Jacqmin has been working in close collaboration with Samuel Deléglise for the past six years. He has a strong experience in clean room micro-fabrication, optical characterization of mechanical samples and FEA simulations. He contributed to the state of the art phononic crystal resonators that were recently demonstrated in the group and that will be at the heart of this project.

Owing to their extreme aspect ratio and large tensile stress, ultracoherent membranes are very delicate objects that require precise control at every step of the microfabrication process. LKB is one of a handful labs in the world able to interface such systems with superconducting circuits. Moreover, our consortium gathers some of the best experts in high-impedance circuits (LPENS, Zaki Legthas) and hyperinductances (CEA, Emmanuel Flurin, Hélène Lesueur). Finally, we have unrestricted access to cutting-edge superconducting deposition equipment that will enable us to achieve state-of-the-art dissipation in these hyperinductances.

Contact to submit your application :
Antoine Heidmann, antoine.heidmann@lkb.upmc.fr
Samuel Deléglise, samuel.deleglise@lkb.upmc.fr

The publications authored by the advisors and related to the project are [15, 18, 22, 23].

[1] M. Carlesso et al., NJP 20, 083022 (2018)
[2] Y. Chu et al., Nature 563, 666 (2018)
[3] M. Wallquist et al., Physica Scripta T137, 014001 (2009) [4] R. W. Andrews et al., Nature Physics 10, 321 (2014)
[5] D. Rugar et al., Nature 430, 329 (2004)
[6] M. Rossi et al., Nature 563, 53 (2018)
[7] E. Verhagen et al., Nature 482, 63 (2012)
[8] D. Mason et al., Nature Physics 15, 745 (2019)
[9] A. D. O’Connell et al., Nature 464, 697 (2010)
[10] Y. Chu et al., Science 358, 199 (2017)
[11] P. Arrangoiz-Arriola et al., Nature 571, 537 (2019)
[12] D. Hälg et al., Phys. Rev. Applied 15, L021001
[13] A. H. Ghadimi et al., Science 360, 764 (2018)
[14] Y. Tsaturyan et al., Nature Nanotech.12, 776 (2017) [15] E. Ivanov et al., Appl. Phys. Lett. 117, 254102 (2020) [16] J. J. Viennot et al., Phys. Rev. Lett.121, 183601 (2018) [17] A. P. Reed et al., Nature Physics 13, 1163 (2017)
[18] R. Lescanne et al., Phys. Rev. X10, 021038 (2020)
[19] V. E. Manucharyan et al., Science 326, 113 (2009)
[20] H. Zhang et al., Phys. Rev. X 11, 011010
[21] N. Earnest et al., Phys. Rev. Lett.120, 150504 (2018) [22] T. Capelle, PhD thesis, Sorbonne Université (2020) [23] T. Capelle et al., Phys. Rev. Applied 13, 034022 (2020)

Peignes de fréquences quantiques pour des protocoles d’information quantique

This PhD research project has been submitted for a funding request to “Quantum Information Center Sorbonne (QICS)”. The PhD candidate selected by the project leader will therefore participate in the project selection process (including a file and an interview) to obtain funding.

Quantum frequency combs for quantum information protocols

Light offers a vast potential in the development of modern quantum technologies due to its intrinsic resilience to decoherence effects. One avenue for employing light to process quantum information focuses on the continuous variable regime, where the observables of interest are the quadratures of the electric field. They have proven their worth as a platform for creating huge entangled states (entangling up to one million optical modes). Additionally, this entanglement can be created in a deterministic fashion and easily manipulated with standard techniques in optics [1,2].

To reach a quantum advantage, and perform a task that cannot be efficiently simulated with a classical device, we require more than just entanglement. The additional ingredient is non-Gaussian statistics in the outcomes of the quadrature measurements. More specifically, we must create quantum states with a negative Wigner function. At LKB, we have recently developed a mode- tunable photon subtractor as a device for creating such states [3,4]. As such, we now have the possibility to produce large entangled states and to render them non-Gaussian. This opens up a whole new realm of research, where a vast amount of questions on the interplay between entanglement and non-Gaussian effects remain unanswered [4,5].

The experiment consists in manipulating the spectral modes of a frequency comb to engineer entangled Gaussian states, and use photon-subtraction through mode-dependent sum-frequency to induce non-Gaussian features in these states. We implement experimental techniques from optical cavities, non-linear optics, ultra-short optical pulses manipulation and highly sensitive and multiplexed detection.

Gradually, more and more non-Gaussian elements will be added to the experimental setup. On the level of state engineering, we will aim at the subtraction of multiple tailored photons. On the detection stage, we will incorporate photon-number detection schemes, mesoscopic detectors and double homodyne detection.

All of these elements will make the experiment a platform for quantum information protocols. On the one hand, it will be possible to explore non-Gaussian quantum steering and to implement elaborated tests of required quantum properties, necessary for any quantum advantage. This will be done in collaboration with the QI group at LIP6 [6]. Then, we will study how to implement elementary quantum protocols, for instance linked to error correction.

Contact to submit your application :
Nicolas Treps, nicolas.treps@upmc.fr

[1] J. Roslund, R. M. de Araujo, S. Jiang, C. Fabre, N. Treps, Nature Photonics 8, 109 (2014).

[2] Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, N. Treps, Nature Communication 8, 15645

(2017).
[3] Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, N. Treps, Phys. Rev. X, 7, 031012 (2017).


[4] Y.-S. Ra, A Dufour, M. Walschaers, C. Jacquard, T. Michel, C. Fabre, N. Treps, Nature Physics 11, 1 (2019).


[5] M. Walschaers and N. Treps, Phys Rev Lett 124, 150501 (2020).

[6] U. Chabaud, G. Roeland, M. Walschaers, F. Grosshans, V. Parigi, D. Markham, and N. Treps, ArXiv:2011.04320 [Quant-Ph] (2020).

Realizing arbitrary quantum operations on a mechanical oscillator

This PhD research project has been submitted for a funding request to “Quantum Information Center Sorbonne (QICS)”. The PhD candidate selected by the project leader will therefore participate in the project selection process (including a file and an interview) to obtain funding.

Abstract:

Quantum optomechanics and electromechanics is a fast growing field with promising applications in quantum information. Recently non-classical mechanical states have been realized. However, full control of a quantum mechanical mode, which is necessary for successful quantum information processing based on electromechanical systems, has yet to be demonstrated. This project aims to develop a novel quantum electromechanical device capable of obtaining full quantum control of a macroscopic mechanical resonator by integrating a phononic microcavity with a superconducting transmon qubit. We expect to achieve a very strong qubit-phonon coupling coefficient that will allow the realization of any quantum unitary operation on the phononic mode. This will have important applications in quantum information and quantum sensing. In addition this project opens the route to test the relevance of the quantum mechanics to the macroscopic world.

Objectives:

Quantum information processing with electromechanical devices requires full control over a non- classical mechanical state.

Although non-classical mechanical states have been recently demonstrated full control over these quantum mechanical states has yet to be achieved.

This project aims to develop a novel quantum electromechanical device, capable of obtaining full quantum control of a macroscopic mechanical resonator, based on a phononic cavity strongly coupled with a superconducting qubit.

This has the potential to pave the way towards successful quantum information processing based on electromechanical systems.

The main objectives of this project are to:
Integrate a phononic micropillar cavity with a transmon superconducting qubit.

Prepare arbitrary superpositions of phonon number states of the mechanical mode (including Fock and Schrodinger cat states).

Realize arbitrary quantum unitary operations on the mechanical mode.
This project will be done in collaboration with Benjamin Huard and Audrey Bienfait from ENS Lyon

Contact to submit your application :
Valia Voliotis, valia.voliotis@insp.jussieu.fr
Daniel Garcia Sanchez, daniel.garcia-sanchez@insp.upmc.fr

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Impact of quantum computers on Impagliazzo’s five worlds

This PhD research project has been submitted for a funding request to “Quantum Information Center Sorbonne (QICS)”. The PhD candidate selected by the project leader will therefore participate in the project selection process (including a file and an interview) to obtain funding.

Since its early stages, quantum computing has had drastic consequences to cryptography. In the one hand, (full-scalable) quantum computers could be used to break widely used cryptosystems, given the celebrated Shor’s algorithm for factoring. On the other hand, quantum resources have also been used to realize cryptographic tasks that are otherwise impossible, for example quantum money (e.g. Wiesner’80), sharing private keys (e.g. Bennet and Brassard’84) or generating certifiable randomness (e.g. Colbeck’09). We remark that all of these primitives can be constructed in the quantum world unconditionally, meaning that we do not need to impose any computational assumption on the adversaries.

These results raise an ambitious possibility for the field of cryptography, namely the possibility of realizing every cryptographic primitive unconditionally with quantum resources.
Unfortunately, this was shown impossible, we know today several primitives that are not realizable even with quantum resources unconditionally (Mayers’97, Lo and Chau’97). Therefore, in order to be able to implement cryptographic protocols of interest, even in a quantum world, we must rely on computational assumptions.

We have seen that these computational assumptions come in two flavours. First, we see constructions based on the hardness of specific problems, such as factoring, lattices problems, etc. As spotted by Shor’s algorithm, the downside of this approach is that we are walking on thin ice by relying on particular assumptions and this brings us to the second, and more general, way of constructing cryptographic schemes. This second perspective in cryptography is to rely on the hardness of abstract problems with special properties. For example, we know how to construct some protocols based on the existence of one-way functions (OWF), which are functions that are easy to compute and hard to invert. We remark that these protocols work for any OWF that you might implement.

Of course, we still have the problem to show that these generic objects such as OWFs exist and to structure this, Impagliazzo proposed five possible “worlds” in which we might be living:
• Algorithmica: P = NP or something « morally equivalent » like fast probabilistic algorithms for NP.
• Heuristica: NP problems are hard in the worst case but easy on average.
• Pessiland: NP problems are hard on average but no one-way functions exist. We can easily create hard NP problems, but not hard NP problems where we know the solution.
• Minicrypt: One-way functions exist
• Cryptomania: Public-key cryptography (PKE) is possible, i.e. parties can exchange secrets over open channels.

Recently, a sixth world was later added with stronger cryptographic primitives than PKE.
• Obfutopia: Obfuscation of programs is possible
The first three worlds are not so interesting for cryptography (using our current security notions), since they actually say that cryptography is not possible. Then, there has been a lot of study on trying to understand which primitives are possible in Minicrypt, Cryptomania and Obfutopia. More concretely, there has been a lot of study on the (im)possibilities of implementation of cryptographic primitives with minimal set of assumptions.

Recently, Grilo et al.’20 and Bartusek et al.’20 have independently proved that oblivious transfer can be built from OWF in the quantum world, which was an open problem since the protocol proposal of Bennet et al ‘96.(Roughly, in oblivious transfer, Alice has two messages m0 and m1 and Bob has a bit b. At the end of the protocol, Alice does not learn b and Bob learns mb, but not mb). These results are another example where quantum resources can help us implement cryptographic primitives from weaker assumptions, since there are strong indications that OT cannot be built from OWF in the classical world.

PhD project

The main goal in our project is to explore novel consequences that quantum computing could bring to Impagliazzo’s 5 worlds, specially its impact on cryptography. Despite the impressive success of quantum computation/cryptography, we remark that progress on this line has been very limited. Examples of questions that could be explored by the PhD candidate are:

Constant-round ZK proofs from OWF: There is strong evidence that zero-knowledge proofs (a fundamental cryptographic primitive) cannot be implemented in constant-round classically in the plain mode, i.e. without any trusted help (Katz’08). However, these no-go results rely on complexity theoretical assumptions that do not quantize. Thus, a natural open question that could be explore in this PhD project is the (in)feasibility of constant-round quantum zero-knowledge proofs (ideally from one-way functions). This could clarify which type of advantage quantum resources can provide on the construction of cryptographic primitives.

Role of quantum obfuscation in quantum cryptography: In the classical world, the concept of indistinguishable obfuscation (iO), which asks that the ofuscation of two programs with the same functionality cannot be distinguished, has been shown to be a very strong primitive that can enable the implementation of several cryptographic primitives which are not known to exist otherwise. To stress its usefulness, iO is frequently called « crypto-complete » in the classical scenario. Such a strong functionality comes of course with a cost: for decades the existence of secure iO schemes was elusive, until a very recent result of Jain, Lin and Sahai, which constructs iO from well-founded cryptographic assumptions.

The study of obfuscation in the quantum setting, specially its consequences, has been very limited. In particular, a direction that could be pursued in this PhD project would be to study the feasibility of strong quantum functionalities from quantum iO.

Lower bounds on quantum cryptographic protocols. Shoup’97 showed that in a « generic group » model, it is impossible to solve the discrete logarithm problem (or Diffie-Hellman) of a group of prime order p using O(sqrt(p)) group operations. Shor’s polynomial algorithm for discrete-log directly implies that such a lower bound does not hold in the quantum setting. One potential direction for this PhD project would be to study if such lower bounds on the computational complexity for quantum algorithms can be proven for other generic mathematical structures, for example the Couveignes hard homogeneous spaces (based on group actions) underlying the cryptographic constructions based on elliptic curves isogenies, a cryptographic assumption that has resisted to quantum attacks (so far).

Pertinence of the project 

This PhD concerns topics in the theoretical aspects (post-)quantum cryptography, a very important subject within the scope of QICS. The different background of both PhD supervisors (cryptography for D. Vergnaud and quantum computing for A. Grilo) combine in a very natural way to supervise this project.

Contact to submit your application :
Damien Vergnaud, damien.vergnaud@lip6.fr
Alex Bredariol Grilo, Alex.Bredariol-Grilo@lip6.fr

We list now some publications from the supervisors that are relevant for this proposal:

Grilo, Lin, Song, and Vaikuntanathan. Oblivious Transfer is in MiniQCrypt. Accepted at Eurocrypt 2021 and plenary talk at QIP 2021.

Alagic, Childs, Grilo and Hung. Non-interactive Classical Verification of Quantum Computation. TCC 2020 and contributed talk at QIP 2021.

Broadbent and Grilo. QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge, FOCS 2020 and plenary talk at QIP 2021

Quantum Hamiltonian Complexity and Derandomization

This PhD research project has been submitted for a funding request to “Quantum Information Center Sorbonne (QICS)”. The PhD candidate selected by the project leader will therefore participate in the project selection process (including a file and an interview) to obtain funding.

The main goal of this PhD project is to study the problems that lie in the intersection of quatum Hamiltonian complexity and (classical) derandomization. These are two important topics in the field of Computational Complexity theory of independent interest.

On the one hand, the derandomization problem asks if randomness increases the computational power of polynomial-time computation. More specifically, we are interested in the non- deterministic version of the derandomization conjecture, which roughly says that every problem whose solution can be verified by randomized algorithms can also be verified by deterministic ones. In technical terms, this is stated as NP = MA, where NP is the class of problems with efficient deterministic verification and MA is its randomized analog. It is widely believed that derandomization is possible,and this is supported by plausible assumptions (e.g. the existence of pseudorandom generators, etc.), but proving even weaker versions of this conjecture has been an active area of research.

On the other hand, Hamiltonian complexity lies in the heart of quantum complexity theory due to its relevance for physics and computer science. The central problem here is the following: given as input a local Hamiltonian H that describes the evolution of an n-particle quantum system, find an approximation of the ground-energy of H, which is the value of energy corresponding to the ground- state of H. The importance of this problem was put in evidence by Kitaev, who showed in 1999 that the approximation of the ground-energy of a Hamiltonian, up to an inverse polynomial additive error, is QMA-complete, where QMA is the quantum analog of NP. The quantum PCP conjecture states that approximating the ground-energy of a Hamiltonian up to a constant additive error remains QMA-complete. This conjecture has important consequences to complexity theory and condensed matter physics, e.g. it implies the existence of families of quantum systems with highly entangled states even at « room temperature ».

The surprising relation between derandomization and Hamitlonian complexity was proved by Aharonov and Grilo – one of the co-advisors in this project – (FOCS’19). More concretly, they show that proving the quantum PCP conjecture for a restricted family of quantum Hamiltonians, named Stoquastic Hamiltonians, is actually equivalent to the MA vs. NP questions. For the best of our knowledge, this is the very first approach to prove derandomization statements from results in quantum computing.

It is worthy to mention that stoquastic Hamiltonians arise naturally in quantum physics, and since they do not suffer of what is called the sign problem, they are more amenable to be tackled by classical techniques. Moreover, stoquastic Hamiltonians have practical importance, since, for example, they describe some non-universal quantum computers that were developed in practice, like D-Wave devices.

PhD project

The goal is to strengthen the connection between derandomization and Hamiltonian complexity that was initiated by Grilo and Aharonov.

More concretely, our plan is to try tackle intermediate steps towards a quantum PCP theorem for stoquastic Hamiltoanians. Attacking these « simpler » problems would not only provide valuable insights towards the stoquastic PCP conjecture, but it could also elucidate critical difficulties for the general version of these problems, which remain open.

We now describe some specific problems that could be explore by the PhD candidate:

Low-energy state generation: An important question in Hamiltonian complexity is the efficiency of creating low-energy states of Hamiltonians. Notice that there is always an efficient circuit that constructs the ground-state of classical Hamiltonians (but, finding such a circuit is a hard task since the problem is NP-complete). Quantumly, it is not expected that the ground-state of local Hamiltonians can be efficiently created since this contradicts some believed complexity theoretical assumptions, namely QCMA being different of QMA. However, it is unclear if this (conditional) impossibility also holds for low-energy states of the Hamiltonian. In this context, the No Low-energy Trivial States conjecture (NLTS) was proposed to study « toy » versions of this question. NLTS states that there is a family of Hamiltonians for which constant-depth quantum circuits cannot construct states with low energy. While this statement is reasonable, being even implied by the quantum PCP conjecture, it has been answered only partially and in restricted settings. In this project, we want to study the NLTS conjecture but restricted to stoquastic Hamiltonians. In particular, our goal is to use tools developed in Aharonov and Grilo, together with techniques related to Markov chains, quantum walks, and derandomization, to possibly disprove a stoquastic version of the NLTS conjecture.

Classical simulation of the evolution of stoquastic Hamiltonians. Adiabatic quantum computation is a computational model described by the evolution of quantum systems. Formally, it is defined by two Hamiltonians: the first one has an easy-to-prepare ground-state, whereas the second one encodes the computational problem that we want to solve. The computation is performed by slowly transitioning from the ground-state of the initial Hamiltonian into the ground-state of the final one, which would give us the answer for our computational problem. This model of computation was proposed hoping that it would lead to faster algorithms for combinatorial optimization problems and for this purpose it was used in the (non-universal) D-Wave’s machine. In particular, D-Wave’s devices implement the adiabatic evolution of stoquastic Hamiltonians. Bravyi and Terhal (SICOMP 2009) proved an efficient classical simulation of the adiabatic evolution of a natural subfamily of stoquastic Hamiltonians, namely frustration-free ones. On the other hand, in a recent results by Gilyén, Hastings and Vazirani (STOC 2021) gives some indication that the adiabatic evolution of stoquastic Hamiltonians is strictly more powerful than classical computation, by proving an oracle separation between them. In this project, we want to explore some of the graph-theoretical tools from Aharonov and Grilo, together with new combinatorial techniques from Hodge theory and derandomization to find larger families of Hamiltonians that can be classically simulated. This could be used to achieve further advances on the question « how quantum is the D-Wave machine? ». Moreover, another question in this direction is extending the oracle separation of Hasting to the non-deterministic setting, clarifying the landscape of the complexity of stoquastic Hamiltonians. Pertinence of the project

This PhD project has the potential to achieve important advances in our understanding of the computational power of sub-families of quantum Hamiltonians, which clearly lies in the scope of QICS.

Contact to submit your application :
Damian Markham, damian.markham@lip6.fr
Alex Bredariol Grilo, Alex.Bredariol-Grilo@lip6.fr

We list now some publications from the supervisors that are relevant for this proposal:

Antonio, Markham, Anders, Trade-off between computation time and Hamiltonian degree in adiabatic graph state quantum computation, NJP 16, 113070 (2014)

Aharonov, Grilo, and Liu. StoqMA vs. MA: the power of error reduction. Under submission. Aharonov and Grilo. Two Combinatorial MA-Complete Problems. ITCS 2021
Aharonov and Grilo. Stoquastic PCP vs. Randomness. FOCS 2019 and plenary talk at QIP 2020.