November 11, 2019 10:30 AM

November 12, 2019 3:40 PM
November 11, 2019 10:30 AM

November 12, 2019 3:40 PM
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Hôtel Château Bromont
Hôtel Château Bromont
Opening Remarks
Pr Mathieu Juan, Institut quantique  Université de Sherbrooke
Clasical and quantum computations as tensor networks
Pr Stefanos Kourtis, Institut quantique  Université de Sherbrooke
Classical and quantum computations as tensor networks
Break
Event organized in collaboration with the RQMP and animated by Mrs. Chloé Freslon, founder of URelles
Falisha Karpati, Ph.D.
Think Differently Together: Strengthening research and innovation by embracing cognitive diversity
LouisPhilippe Lamoureux (Slides / Présentation)
Thierry Debuischert, Thales  France (postponed to Monday at 13:15 / reporté à lundi 13h15)
Closing remarks of the day
Opening remark of the day
Thierry Debuischert, Thales  France
Professor Tami PeregBarnea, McGill University
Dynamic topology  quantized conductance and Majoranas on wires
Professor Philippe StJean, Université de Montréal
Topological physics with light and matter: new horizons
Break
Louis Gaudreau, National Research Council Canada (Ottawa)
Entanglement distribution via coherent photontospin conversion in semiconductor quantum dot circuits
Philippe Lamontagne, National Research Council Canada (Montréal)
BlackBox Impossibility in the Common Reference Quantum State Model
Olivier GagnonGordillo, Québec quantique lead
Presentation of the Québec Quantum ecosystem
Institut quantique  Université de Sherbrooke
Classical and quantum computations as tensor networks
Tensor networks are multilinearalgebra data structures that are finding application in diverse fields of science, from quantum manybody physics to artificial intelligence. I will introduce tensor networks and illustrate how they can be used to represent classical and quantum computations. I will then motivate tensor network algorithms that perform or simulate computations in practice and demonstrate their performance on benchmarks of current interest, such as model counting and quantum circuit simulation. I will close with an outline of ongoing work and an outlook on future directions.
Institut quantique  Université de Sherbrooke
Optomechanics with a nonlinear cavity
The possibility to operate massive mechanical oscillators close to or in the quantum regime has become central in fundamental sciences. LIGO is a prime example where quantum states of light are now used to further improve the sensitivity. Concretely, optomechanics relies on the use of photons to control the mechanical motion of a resonator, providing a path toward quantum states of massive objects and for the development of quantum sensors. In order to improve this control many approaches have been explored, some more complicated than others. In particular, in order to cool the mechanical motion a cavity can be used to realise sideband cooling. In general, linear cavities are favoured to allow for large photon number providing stronger cooling. I will show that, surprisingly, nonlinear cavities can be used to achieve very efficient cooling at low powers. Indeed, even in the bad cavity limit, we have been able to cool a mechanical resonator from 4000 thermal phonons down 11 phonons. Currently limited by flux noise, this approach opens promising opportunities to achieve quantum control of massive resonators, an avenue to study foundational questions.
McGill University
Dynamic topology  quantized conductance and Majoranas on wires
This talk will address the issue of outofequilibrium topological systems. While many materials and devices produced in labs today are topological at equilibrium, it is desirable to have a knob to tune or induce topological properties. For example, if we could dynamically turn a superconductor into a topological superconductor we may create the sought after Majorana fermions which are potential building blocks of quantum bits.
In this context we will explore the possibility of perturbing quantum systems using timeperiodic fields (i.e., radiation) and use the Floquet theory to characterize the driven states. We find that in topological systems, beyond the expected splitting of the spectrum into side bands, a change in the topology may occur. In the case of a topological superconductor, the driven system may develop new Majorana modes which do not exist at equilibrium and can be exchanged on a single wire. A protocol for exchanging Majoranas will be presented.
Université de Montréal
Topological physics with light and matter: new horizons
Topology is a branch of mathematics interested in geometric properties that are invariant under continuous deformation, e.g. the number of holes in an object. In the early 1980s it was demonstrated that similar topological properties can be defined for solids presenting appropriate symmetry elements. The discovery of these topological phases of matter has profoundly impacted our understanding of condensed matter, its influence ranging from better explaining the universality of the conductivity plateaus in the quantum Hall effect to developing new platforms for faulttolerant quantum computation[i]. In the late 2000s, Duncan Haldane (colaureate of the Nobel Prize in physics for the discovery of topological phases of matter) demonstrated that this topological physics is not restricted to condensed matter but can also emerge in artificial systems like photonic crystals through a careful engineering of their symmetry properties[ii]. Since then, these photonics platforms have proven to be an amazing resource for pushing the exploration of topological matter beyond what is physically reachable in the solidstate, leading to the emergence of a blooming field called topological photonics[iii].
In this presentation, I will describe recent experimental works based on excitonpolaritons, a hybrid lightmatter quasiparticle, which have opened new horizons in topological photonics[iv]. The main advantages of polaritonic systems arise from their dual nature: their photonic part allows for tailoring welldefined topological properties in lattices of coupled microcavities and makes them inherently nonhermitian; on the other hand, their matter part gives rise to a strong Kerrlike nonlinearity and to lasing[v]. I will then discuss in more details a recent work in which we took profit of these assets to experimentally extract topological invariants  a fundamental quantity in topology  in a polaritonic analog of graphene[vi]. Importantly, this has allowed us to directly probe the topological phase transition occurring in a critically strained lattice  i.e. where Dirac cones have merged  a condition impossible to reach in the solidstate. I will conclude this presentation by discussing how topological protection can provide a powerful asset for generating and stabilizing manybody quantum states of light and matter. Such mesoscopic quantum objects are highly desirable as they would provide an extended playground for quantum simulation, sensing applications or for generating exotic states of light such as manybody entangled states[vii].
[i] M. Z. Hasan and C. L. Kane. Rev. Mod. Phys. 82, 3045 (2010)
[ii] F. D. M. Haldane and S. Raghu. Phys. Rev. Lett. 100, 013904 (2008)
[iii] T. Ozawa et al. Rev. Mod. Phys. 91, 015006 (2019)
[iv] D. D. Solnyshkov, G. Malpuech, P. StJean et al. Opt. Mat. Express 11, 1119 (2021)
[v] I. Carusotto and C. Ciuti. Rev. Mod. Phys. 85, 299 (2013)
[vi] P. StJean et al. Phys. Rev. Lett. 126, 127403 (2021)
[vii] P. Lodahl et al. Nature 541, 473 (2017)
Think Differently Together: Strengthening research and innovation by embracing cognitive diversity
This talk will cover:
Biography
Falisha Karpati, PhD is a neuroscientist turned inclusion consultant. Falisha’s work focuses on using neuroscience to build inclusive environments in academic, research, and scientific organizations. Her approach to inclusion centres on the interconnectedness of cognitive, demographic, and experiential diversity. Prior to starting her consultancy practice, she worked as the Training and Equity Advisor for Healthy Brains, Healthy Lives at McGill University.
Head of Applied Quantum Physics
Thales Research & Technology
Researcher
National Research Council Canada (Ottawa)
In this talk, I will present our proposed long distance entanglement distribution scheme that aims to overcome fundamental limitations present in current optical schemes. By using direct band gap semiconductor quantum dots, efficiency and heralding advantages can be exploited through photontospin conversion. For this reason, materials such as GaAs are superior to Si in this type of applications. I will review current schemes to transfer polarization or timebin encoded photonic qubits to electron spin qubits and will describe adaptations to employ heavy holes which have a number of attractive properties including gfactor tunability. Finally, I will show preliminary results on quantum dot devices using Van der Waals heterostructures which present several potential advantages such as higher confinement energies due to their atomically thin geometry, easier combination with different substrates and the possibility of encoding information in their valley degree of freedom.
Biography
Louis Gaudreau studied physics at Sherbrooke University, followed by a masters and PhD in cosupervision with Andrew Sachrajda at NRC and Alexandre Blais at Sherbrooke. During his graduate studies, Louis studied electrostatic quantum dots and realized for the first time a coupled triple quantum dot system leading to the investigation of the first exchangeonly qubit. During this period he was invited to perform quantum dot experiments in Stefans Ludwig’s group at LMU in Munich. After his PhD, Louis changed fields and studied lightmatter interactions by combining quantum emitters and graphene to create different hybrid systems. These experiments were done during his postdoc at ICFO in Barcelona in the nanooptoelectronics group with Frank Koppens where he was awarded the prestigious MarieCurie fellowship. Finally, since 2015, Louis has worked as research officer at the NRC where he investigates different technologies linked to quantum information.
Researcher
National Research Council Canada (Montréal)
BlackBox Impossibility in the Common Reference Quantum State Model
We explore the cryptographic power endowed by arbitrary shared physical resources. We introduce the Common Reference Quantum State (CRQS) model, where the parties involved share a fresh entangled state at the outset of each protocol execution. This model is a natural generalization of the wellknown Common Reference String (CRS) model but appears to be more powerful. In the twoparty setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once. We formalize this notion as a Weak OneTime Random Oracle (W1TRO), where we only ask of the output to have some randomness when conditioned on the input is still beyond the reach of the CRQS model. We prove that the security of W1TRO cannot be blackbox reduced to any assumption that can be framed as a cryptographic game. Our impossibility result employs the simulation paradigm formalized by Wichs (ITCS ’13) and has implications for other cryptographic tasks.
 There is no universal implementation of the FiatShamir transform whose security can be blackbox reduced to a cryptographic game assumption. This extends the impossibility result of Bitansky et al. (TCC ’13) to the CRQS model.
 We impose severe limitations on constructions of quantum lightning (Zhandry, Eurocrypt ’19). If a scheme allows n lightning states’ serial numbers (of length m such that n > m) to be combined in such a way that the outcome has entropy, then it implies W1TRO, and thus cannot be blackbox reduced to a cryptographic game assumption.
Senior Product Manager
Aspen Technology
Biography
Montrealbased quantum physicist, senior product manager, and full stack developer with strong experience building awardwinning hardware and software products. Currently Senior Product Manager at Aspen Technology leading connectivity and AI inference at the Edge. Prior to Aspen Technology, I worked at MachineToMachine Intelligence (M2Mi) a leader in IoT Security and Management located at NASA Ames research center in the heart of Silicon Valley.
Prior to M2Mi, built SQR Technologies a belgian quantum based, hardware security startup that pioneered distributed quantum key generation. Acquired by IDQ (Switzerland). Awarded a Ph.D. in Physics (Quantum Cryptography) from the University of Brussels. Research interests include: quantum cloning, experimental quantum cryptography, quantum noise reduction, and quantum random number generation.
10h30  10h55 Inscription
10h55  11h00 Mots d'ouverture (Salon A)
11h00  11h45 Pr Frédéric Dupuis, Université de Montréal
Purely quantum polar codes
11h45  12h05 Marco David, Student, McGill University
QED. The Quest to Formally Verify Mathematics
12h05  13h30 Dîner (Salle 4 Canards)
13h30  14h15 Dr. Louis Gaudreau, National Research Council (NRC)  Ottawa
Entanglement distribution via coherent photontospin conversion in
semiconductor quantum dot circuits
14h15  14h45 Dr. Joel Griesmar, Université de Sherbrooke
A mesoscopic spectrometer based on the Josephson effect
14h45  15h15 Pause café (Salon B)
15h15  15h45 Dr Stephane Virally, Polytechnique Montréal
Quantum optics in the time domain
15h45  16h25 Industry & Startups in quantum technologies
Dr Félix Beaudoin, Les Technologies Nanoacademic Inc
(www.nanoacademic.com)
Dr David RoyGuay, SB Quantum (www.sbquantum.com)
Pr David Poulin, Microsoft
16h25  17h00 Equity, diversity & inclusion (Résumé et photos de l'atelier)
17h00  Session d'affiches et rafraichissements (Salon B)
19h30  INTRIQ dinner (Knowlton room)
8h30  9h00 Pr Anne Broadbent, Université d'Ottawa
Quantum encryption with certified deletion
9h00  10h00 Dr Tomas JochymO'Connor, IBM  Yorktown Heights, New York
Disjointness in stabilizer codes
10h00  10h30 Pause café(Salon B)
10h30  11h30 Pr Signe Seidelin, Institut NEEL CNRS/UGA
RareEarth Doped Crystals for straincoupled optomechanics
11h30  12h00 Dr Erika Janitz, McGill University
CavityEnhanced Photon Emission from a Single Germanium
Vacancy Center in a Diamond Membrane
12h00  13h30 Dîner (Salle 4 Canards)
13h30  14h00 Pr Jérôme Bourassa, Cégep de Granby
Quantum illumination : exploiting quantum correlations when
entanglement is lost
14h00  14h30 Dr Thomas Baker, Université de Sherbrooke
Modeling superconducting circuits with a tensor network
14h30  15h00 Dr Anirban Chowdhury, Université de Sherbrooke
Simulating thermal physics on quantum computers
15h00  15h30 Questions et réponses
15h30  15h40 Mots de clôture
Institut NEEL CNRS/UGA
RareEarth Doped Crystals for straincoupled optomechanics
A challenge of modern physics is to investigate the quantum behavior of a bulk material object  for instance a mechanical oscillator  placed in a nonclassical state. One major difficulty relies in interacting with the mechanical object without perturbing with its quantum behavior. An approach consists of exploiting a hybrid quantum system consisting of a mechanical oscillator coupled to an atomlike object, and interact via the atomlike object. A particularly appealing coupling mechanism between resonator and “atom” is based on material strain. Here, the oscillator is a bulk object containing an embedded artificial atom (dopant, quantum dot, ...) which is sensitive to mechanical strain of the surrounding material. Vibrations of the oscillator result in a timevarying strain field that modulates the energy levels of the embedded structure. We have suggested to use rareearth doped crystals for straincoupled systems [1] and proposed a mechanism to cool down the resonator [2]. In this talk, I will report on our progress towards realizing experimentally these protocols. We are using an yttrium silicate (Y2SiO5) crystal containing triply charged europium ions (Eu3+), which are optically active. The reason behind this choice stems from the extraordinary coherence properties of this dopant, combined with its high strainsensitivity: the Eu3+ in an Y2SiO5 matrix has an optical transition with the narrowest linewidth known for a solidstate emitter, and the transition is directly sensitive to strain. We have successfully fabricated mechanical resonators, designed and set up the experiment, and achieved a signaltonoise ratio compatible with the planned measurements, as well as measured the strain sensitivity of europium ions in bulk Y2SiO5 crystals.
[1] K. Mølmer, Y. Le Coq and S. Seidelin, Dispersive coupling between light and a rareearth ion doped mechanical resonator, Phys. Rev. A 94, 053804 (2016)
[2] S. Seidelin, Y. Le Coq and K. Mølmer, Rapid cooling of a straincoupled oscillator by an optical phaseshift measurement, Phys. Rev. A 100, 013828 (2019)
IBM  Yorktown Heights, New York
Disjointness in stabilizer codes
The disjointness for stabilizer codes in quantum error correction is an algebraic quantity tied to the structure of the stabilizer generators of a code. It can be used to characterize the properties of different classes of logical gates, placing bounds on the level of the Clifford hierarchy attainable by constant depth circuits. This talk will introduce the notion of disjointness, highlight its usefulness with several examples, and posit open questions for which the disjointness may be useful in addressing.
Université de Montréal
Purely quantum polar codes
We provide a purely quantum version of polar codes, achieving the coherent information of any quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where random twoqubit Clifford gates are used to combine two singlequbit channels. The inputs to the synthesized bad channels are frozen by sharing EPR pairs between the sender and the receiver, so our scheme is entanglement assisted. We further show that a Pauli channel polarizes if and only if a specific classical channel over four symbol input set polarizes. We exploit this equivalence to prove fast polarization for Pauli channels, and to devise an efficient successive cancellation based decoding algorithm for such channels. This is joint work with Ashutosh Goswami, Mehdi Mhalla and Valentin Savin.
National Research Council (NRC)  Ottawa
Entanglement distribution via coherent photontospin conversion in semiconductor quantum dot circuits
In this talk, I will present our proposed long distance entanglement distribution scheme that aims to overcome fundamental limitations present in current optical schemes. By using direct band gap semiconductor quantum dots, efficiency and heralding advantages can be exploited through photontospin conversion. For this reason, materials such as GaAs are superior to Si in this type of applications. I will review current schemes to transfer polarization or timebin encoded photonic qubits to electron spin qubits and will describe adaptations to employ heavy holes which have a number of attractive properties including gfactor tunability. Finally, I will show preliminary results on quantum dot devices using Van der Waals heterostructures which present several potential advantages such as higher confinement energies due to their atomically thin geometry, easier combination with different substrates and the possibility of encoding information in their valley degree of freedom.
Université de Sherbrooke
Modeling superconducting circuits with a tensor network
We introduce a tensor network method tailored for the simulation of largescale superconducting circuits. We leverage information unavailable to other stateoftheart simulation methods to produce firstprinciples coherencetime estimates for the fluxonium qubit. In particular, we study the charge dispersion of this qubit due to coherent quantum phase slip processes as a function of the arrayjunction impedance, and we provide direct numerical evidence of the validity of an effective theory introduced in [V. E. Manucharyan et. al, PRB 85, 024521 (2012)]. We can analyze circuits in terms of entanglement, which can signal how protected quantum information is in circuits and motivate better ways of encoding it. Measurements of the energy participation ratio of circuit components indicates how the qubit transitions are affected by dissipation channels and circuitelement disorder.
Cégep de Granby
Quantum illumination : exploiting quantum correlations when entanglement is lost
sTwomode squeezed states quantum states of light where photons in a pair of distinct beams are entangled together. These EPRstates of light are an excellent resource for quantum sensing and quantum communications protocols. Excess noise in a lossy transmission channel however breaks the entanglement and prohibits secure quantum communication between parties. In spite of this, the quantum correlations in the final state are resilient to environment noise and remain larger than what is classically allowed. Consequently, illuminating a distant object with quantum entangled light, or quantum illumination, has been shown to lead to quantum enhancements in remote sensing detection capabilities and resilience to adversary noise. Quantum illumination could provide invaluable performance enhancements of observations made in noisy environments, from biological samples in the optical range to satellite surveillance in the microwaves. In this talk, I will introduce the concept of quantum illumination, present an overview of different detection schemes and discuss their capabilities and limitations. With a particular focus on microwave technology, I will present the requirements and progress towards building microwave quantumenhanced radar system.
Université d'Ottawa
Quantum encryption with certified deletion
Given a ciphertext, is it possible to prove the deletion of the underlying plaintext? Since classical ciphertexts can be copied, clearly, such feat is impossible using classical information alone. In stark contrast to this, we show that quantum encodings allow such certified deletion. More precisely, we show that it is possible to encrypt classical data into a quantum ciphertext such that the recipient of the ciphertext can produce a classical string which proves to the originator that the recipient has relinquished any chance of recovering the plaintext, should the decryption key be revealed. Our scheme is feasible with current quantum technology: the honest parties only require quantum devices for singlequbit preparation and measurements, and is robust against noise in these devices. Furthermore, we provide an analysis that is suitable in the finitekey regime.
https://arxiv.org/abs/1910.03551
Université de Sherbrooke
Simulating thermal physics on quantum computers
Simulating systems in thermal equilibrium and computing their properties are important problems in physics. These are also however known to be computationally hard problems, especially for quantum systems. I will talk about quantum algorithms that can, under certain conditions, provide advantages in sampling from thermal Gibbs states and computing partition functions of quantum Hamiltonians. A key idea in our algorithms is to approximate an imaginarytime evolution as a linear combination of (unitary) realtime evolutions. This linear combination can then be easily implemented on a usual gatemodel quantum computer. I will also discuss how this approximation can be used to compute the partition function on a restricted model of computation that uses only one pure qubit.
Undergrad student
Director : Bill Coish
McGill University
QED. The Quest to Formally Verify Mathematics
Formal correctness and formal truth are of great value. Through formal verification, one can ensure that the autopilot software of commercial airplanes does not endanger its passengers, and correctness proofs are already standard practice in the industry. Typically, this is done through a precise mathematical formulation of the algorithm and deductive reasoning about its properties, which is then machinechecked. Yet, mathematicians themselves have not developed any interest in carrying out formal verifications. Although mathematics prides itself as the most fundamental of sciences, almost all proofs are conventionally written with many abstractions and omissions. This leads to an astonishingly high number of significant errors in published mathematical literature. Building on the deep dilemma between what a proof is and what it should be, this talk explores the field of formal verification and interactive theorem proving with particular emphasis on mathematics, and also gives an outlook over applications to quantum algorithms.
Université de Sherbrooke
A mesoscopic spectrometer based on the Josephson effect
A key element of mesoscopic topological systems, such as hybrid semiconductorsuperconductor circuits, are Andreev Bound States, single quasiparticles localized at superconducting weak links. The characteristic transition energy of these states is twice the superconducting gap (90 GHz in aluminum). Conventional microwave techniques allow probing these states but only in a limited bandwidth. We propose a new broadband spectrometer operating at frequencies up to 180 GHz based on the Josephson effect which converts a DC voltage to microwave oscillations at a frequency proportional to this voltage. Using a symmetrical SQUID biased at half a flux quantum allows decoupling the spectrometer from environmental modes. In addition, careful design of the biasing circuit reduces the number of remaining modes and damps them. The fabricated mesoscopic spectrometer has a linewidth of 2 MHz, a bandwidth of 180 GHz and a minimal theoretical sensitivity of 5 kHz.
McGill University
CavityEnhanced Photon Emission from a Single GermaniumVacancy Center in a Diamond Membrane
Atomiclike defects in diamond provide a promising lightmatter interface for quantum information applications. Looking at alternatives to the wellstudied nitrogenvacancy (NV) center, we examine interactions between a defect with superior optical properties, the germaniumvacancy (GeV), and an open microcavity. We demonstrate roomtemperature coupling between a single emitter in a diamond membrane and a finesse 11,000 fiber cavity, evidenced by a 8fold increase in the spectral density of emission. The experimental advancements in this work set the stage for future cryogenic experiments, where for the existing system we predict a factor of 7 increase in the GeV spontaneous emission rate.
Polytechnique Montréal
Quantum optics in the time domain
Quantization of the electromagnetic (EM) field is carried in two steps: first quantization selects discrete modes, and second quantization promotes the classical amplitude of these modes to quantum operators. In quantum optics textbooks, the first step is always carried in the frequency domain (i.e. monochromatic modes are selected). This is very useful in many situations where the signal is indeed quasimonochromatic. However, the description is inadequate for the fewcycle, broadband signals that can be found e.g. in ultrafast optics and in many experiments in the microwave domain. We thus show how it is possible to carry a full quantization of the EM with the first step in time rather than frequency [1]. This procedure yields interesting consequences such as the existence of a dual of the Hamiltonian in the time domain and of a noncausal relationship between the EM field transporting the probability amplitude for the energy and the “photonics field”, which transports the probability amplitude for photon clicks on a broadband detector.
[1] Virally, S. and Reulet, B., “Unidimensional time domain quantum optics”, PRA 100, 023833 (2019)
Doctorate, McGill University
Director : Jack Sankey
Progress toward optical control of mechanical geometry
We report experimental progress toward achieving our group's recent proposal [1] to gain an unprecedented level of optomechanical control over the shape and mass of a mechanical mode, using an optical spring to perturb a single lattice site of a phononic crystal, thereby smoothly localizing the spatial distribution of oscillating mass from the centimeter scale to the micron scale. Such control over shape and mass has never been demonstrated, and represents an entirely unexplored avenue in the field. Thus far, we have reliably fabricated the requisite (delicate!) mechanical structures, and observed the characteristic "phononic bandgap" (a necessary ingredient for localization). We have assembled a rigid, vibrationisolated fiberfiber cavity with a phononic crystal in the middle to measure these effects. We show preliminary attempts at locking this cavity on resonance and obtaining the crystal Brownian motion from the error signal. Finally, we present a technique to decrease the finesse of a fibermirror in a controllable manner by smoothly etching away the bilayers forming the distributed Bragg reflector. We etch six bilayers, and subsequently measure finesse after each bilayer is removed. We find that the measured finesse agrees remarkably well with a 1D transfer matrix model. Achieving a specific finesse value for our fibermirrors is necessary so that our cavity will generate a strong optical spring whilst displaying a sufficiently large decay rate, therefore minimizing antidamping of the phononic crystal and facilitating cavity locking.
[1] A. Z. Barasheed et al., Phys. Rev. A 93, 053811 (2016)
Research professionnal
Institut Quantique
Suspended NbN superconducting resonator for reducing intrinsic losses
Superconducting coplanar waveguide (CPW) microwave resonators are crucial elements in Photon detectors, Quantumlimited parametric amplifiers, Narrowband filters, Readout, interconnect in quantum processors and Hybrid devices, connecting solidstate spins with superconducting circuits [13]. In the quantum regime, the dominant loss mechanism for highQ superconducting resonators can be attributed to parasitic twolevel systems (TLSs) in the dielectrics. Interface TLSs are common by products of the fabrication process, often introduced by impurities associated with Si surfaces [3]. To reduce intrinsic losses, we employ isotropic deep reactiveion etching (DRIE) of Si substrate to create suspended NbN superconducting resonators (SSR).
In this study, thin films of niobium (Nb) and niobium nitride (NbN) are deposited on Si substrate by a DC magnetron sputtering system. The influence of the N2/Ar gas ratio, the deposition current, the substrate bias potential on the superconducting critical temperature of the films are investigated. Plasma etching of Nb and NbN thin films in a SF6 and Cl2BCl3 gas plasma is studied using inductively coupled plasma (icp) reactor. Parametric studies on the effects of total gas flow rate and chamber pressure on the edge angles and etch rates are reported. Finally, suspended NbN superconducting resonator is fabricated and will be tested. This could be applied to the fabrication of superconducting qubits in integrated circuits, offering a path towards longer qubit coherence times.
[1] Landig et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018)
[2] Tosi et al. Silicon quantum processor with robust longdistance qubit couplings. Nat Commun 8, 450 (2017)
[3] Bruno et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates, Appl. Phys. Lett. 106, 182601 (2015)
Master, Université de Sherbrooke
Director : Alexandre Blais
Variational Quantum Algorithms for the FermiHubbard model
Noisy intermediatescale quantum computation has the potential to be useful for the simulation of quantum materials. A prominent simulation approach is using variational quantum algorithms (VQAs), which have some resilience to noise and can handle limited qubit connectivity. Here, we aim to simulate the FermiHubbardmodel ground state by means of a VQA. We investigate a number of possibilities for engineering the variational statepreparation circuit, and benchmark these in presence of realistic noise. We find that Hamiltonianinspired variational forms have better performance over a hardwareefficient approach. This work is progress towards the simulation of highTc superconductivity on a quantum device.
Intern, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Experimental Study of single hole EDSR with strong spinorbit coupling in a gated GaAs/AlGaAs Double Quantum Dot
Master, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Fabrication and irradiation effects of fieldinduced shallow twodimensional electron gas in dopantetched modulationdoped GaAs/AlGaAs heterostructures
Collaboration with Takafumi Fujita, Yasushi Kanai, Kazuhiko Matsumoto, Yuji Sakai, Haruki Kiyama, Julian Ritzmann, Arne Ludwig, Andreas D. Wieck, and Akira Oiwa (Osaka University, Ruhr University Bochm).: Electron spin qubits based on GaAs/AlGaAs gatedefined quantum dots (QDs) formed in a twodimensional electron gas (2DEG) are strong candidates for a single photon and single electron spin quantum interface. However, suppression of the irreversible response of photon irradiation in conventional doped GaAs/AlGaAs gatedefined QDs is indispensable for performing stable and continual manipulation of a single electron spin generated by a single photon. It is one of the most promising solution to utilize QDs formed in a fieldinduced 2DEG on undoped heterostructures since these problems are caused by Si dopants. On the other hand, it is necessary in conventional undoped structures to optimize complicated etching and deposition processes for fabrication of Ohmic contacts to avoid creating a discontinuous 2DEG and undesired leakage paths to the top gates. Here, we show the fabrication and irradiation effects of an improved fieldinduced 2DEG structure in dopantetched modulationdoped GaAs/AlGaAs heterostructures taking advantage of a conventional doped structure to simplify ohmic contact fabrication. We successfully induce a 2DEG and evaluate the effects of the light irradiation on the transport properties while an electric current decays with time. This work may provide an additional way to realize undoped GaAs gatedefined QDs for robust quantum interface against photon irradiation.
Doctorate, Université de Sherbrooke
Director : Michel PioroLadrière
28nm UTBB FDSOI technology for Siliconbased quantum dots and cryoCMOS electronics
Although remarkable progress has been made over the last few years in the field of Siliconbased spin qubits hosted in small scale conventional CMOS technologies, coupling several qubits together for the needs of largescale logical operations remains a challenge. Utilizing state of the art mass production process methods from the field of microelectronics seems to be a very promising candidate to solve this problem. Another problem that needs to be tackled concerns the control electronics for the qubits. Indeed, in the case where more than a thousand qubits will need to be controlled, the heat and noise produced by standard electronics will rapidly be a major issue.
Our goal towards a compact quantum processor is to develop a Siliconbased electron or hole spin qubit architecture fabricated via industrial techniques, with onchip embedded control achieved by cointegrating classical electronics at cryogenic temperatures. In this poster, we present our progress on both the qubit architecture and the cryogenic electronics. Our qubit device is designed and fabricated using exclusively CMOS industrial manufacturing techniques, based on STMicroelectronics’ 28nm fully depleted silicononinsulator (FDSOI) planar ultrathin body and BOX (UTBB) technology. We report our progress on both single and multiple quantum dot systems in 1D (array) and 2D (matrix) architectures.We also propose a design for cryogenic CMOS electronics for manipulation and readout of many qubits, in order to perform logical operations for the needs of largescale quantum computing. FDSOI is a promising technology for cryoCMOS implementation, as it has already been demonstrated to operate down to 4K. We studied the performance of ring oscillators, consisting of 28nm FDSOI NMOS and PMOS transistors, designed to generate 6 to 10 GHz microwave signals.Our ring oscillator is coupled to a frequency divider, enabling onchip downconversion, allowing readout with conventional electronics measurement setup in the MHz regime.
Master, McGill University
Director : Claude Crépeau
General Strategy for Bit Commitment Scheme from Pseudo Telepathy Games
Quantum information processing contributed greatly to the rapid advancement of modern cryptography with it being the intersection of mathematics, physics and computer science. Communication tasks that are previously impossible to realize classically can be accomplished with the use of quantum entanglement. Pseudotelepathy game is an application of this where a game exhibits pseudotelepathy with the existence of a quantum winning strategy and the lack of its classical counterpart. After the examination of known pseudotelepathy games, a general strategy for devising a bit commitment scheme using pseudotelepathy games is presented. Due to the nature of the game, the bit commitment schemes derived from the games are unconditionally secure classically, but can be cheated by quantum players.
Director : Jack Sankey
Master : McGill University
Mechanical Motion Driven by Quantum Radiation Pressure Noise
We present progress towards observing mechanical motion of a trampoline driven by quantum radiation pressure noise (QRPN). Lasers have quantum fluctuations which are caused by fluctuations in photons emission, also called shot noise, and our goal is to measure the effect of theses fluctuations "kicking" a trampoline mechanical resonator. To do so, we will place the trampoline inside a short (~10 microns) fiberfiber cavity in a vacuum chamber at room temperature and shine laserlight in it. The trampoline will be driven by radiation pressure caused by the shot noise of the laser inside the cavity. The trampoline possesses great mechanical properties (high quality factor and low force noise) and the short cavity allows high decay rate without compromising the finesse, which enables us to have the trampoline's motion dominated by QRPN instead of thermal noise. We currently have characterized the mechanical properties of the trampoline, which has high mechanical quality factor (> 20 million), and we have proven that we are able to get shot noise predominated laser by squashing its classical noise. The future work will be focused on increasing the bandwidth of the shot noise predominated frequency range of the laser, and assembling the chamber and cavity.
Doctorate, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Formation of quantum dots on (110) GaAs substrate
Collaboration with Rio Fukai, Yuji Sakai, Takafumi Fujita, Haruki Kiyama, Takashi Nakajima, Julian Ritzmann, Arne Ludwig, Andreas D. Wieck, Seigo Tarucha, and Akira Oiwa (Osaka University, Ruhr University Bochm, RIKEN, and University of Tokyo).: Gatedefined semiconductor devices provide a platform which enable us to perform various quantum transport experiments. Electron spins in gatedefined GaAs quantum dots (QDs) have been extensively studied for integrated and stable quantum bits. In those experiments, epitaxial layers grown on the (001) plane are generally used. In a (110) GaAs quantum well (QW), we expect more efficient photonelectron spin quantum state conversion by exciting heavyhole Zeeman levels under inplane magnetic field. However, experimental works on the electricallydefined low dimensional systems on the (110) substrate have been hardly done. From the Hall bar measurements, the mobility and electron density of a QW grown on (110) substrate were estimated as 7×104 cm2/Vs and 9×1010 cm2, respectively at a temperature of 1.5 K. Subsequently, we fabricated gatedefined lateral QDs and measured them using a dilution refrigerator. We clearly observe Coulomb oscillations in the fewelectron regime by monitoring a nearby charge sensor current. We expect that the (110) GaAs QDs will provide a new platform for studying photonspin coupling.
Intern, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Single Hole Energy Spectrum in a GaAs/AlGaAs DQD with Strong SpinOrbit Interaction and DotSpecific gfactors
Doctorate, Polytechnique Montréal
Director : Sébastien Francoeur
ExcitonPolaritons as a tool to control the emission characteristics of excitons and trions bound to Te2 in ZnSe
Te2 molecules in ZnSe form a quantum defect that offers advantageous characteristics, including a high optical uniformity due to its atomic nature and a strong optical dipole moment matching those from semiconductor nanostructures, for the development of efficient spinphoton interfaces for applications in quantum optics, communications and networks.
In this work, we demonstrate that excitonspolaritons generated in the ZnSe host material can be used to deterministically control the emission characteristics of excitons and trions bound to a single Te2 molecule. In particular, the emission efficiency is increased by two orders of magnitude, indicating a very efficient coupling between free excitons and Te2 bound states. Scanning the freeexciton band with a narrowfrequency tunable laser over the free exciton spectral region reveals strong inphase oscillations with a period of about 1 meV in the bound exciton emission intensity, emission energy, and emission linewidth. These modulations are explained by the strong coupling naturally occurring in ZnSe between photons and freeexcitons, or excitonpolaritons.
This type of cooperative process whereby a host excitation is used to control the behavior of a single emitter has never been reported before. It allows deterministically controlling the emission properties and enables the development of new coherent control schemes.
Master, Polytechnique Montréal
Director : Sébastien Francoeur
Optical stabilization of the spectral wandering of an exciton bound to a Te isoelectronic center in ZnSe
We report on the stabilization of the electrostatic environment of a single emitter bound to a Te isoelectronic center in ZnSe resulting in an increased coherence time T2. Nonresonant excitation is used to reduce charge fluctuations in the vicinity of the emitter. Ultraweak nonresonant excitation powers allow for radiative recombination of holes trapped in the vicinity of the emitter thus lowering the redshift of the resonance energy induced by DC Stark effect. The PLE spectrum is the result of the superposition of nonresolved Lorentzian lines each corresponding to a certain charge distribution. With higher nonresonant excitation powers we reach saturation and populate the trap states with excitons, thus inducing another redshift through the HeitlerLondon interaction.
Master, McGill University
Director : Lilian Childress
Towards Coupling Color Centers in Diamond to Fiber Microcavities
Color centers in diamond are attractive spinphoton interfaces for future quantum technologies. The “flagship” nitrogen vacancy center (NV) is a proven platform but suffers from a low emission probability (~3%) of photons into the zerophonon line (ZPL), which is necessary for remote entanglement protocols [1,2]. One potential workaround leverages resonant coupling to an optical cavity to enhance the emission efficiency [3]. In addition, germanium vacancy (GeV) centers can be used for their higher photon emission rate into the ZPL and lower inhomogenous broadening [4]. We present our ongoing effort to couple NV and GeV centers to a fiberbased microcavity configured as a scanning microscope. The high cavity finesses (> 30k) obtained using ultralowloss diamond membranes pave the road to the observation of Purcell enhancement of individual spin transitions but also set stringent requirements regarding cavity stabilisation.
[1] E. Hogan et al., Nature 466 (2010)
[2] N. Kalb et al., Science 356 (2017)
[3] D. Riedel et al., PRX 7 (2017)
[4] P. Siyushev el a., PRB 96 (2017)
Doctorate, Université de Sherbrooke
Director : Eva DupontFerrier
Highresolution cryogenic capacitance measurements of FDSOI structures using a capacitance bridge
As CMOS structures are envisioned to host silicon spin qubits and for cointegrating quantum systems with control electronics, the cryogenic behaviour of such structures must be investigated. Capacitancevoltage (CV) measurements are widely used to determine semiconductor parameters. Performing highresolution CV measurements at cryogenic temperatures is necessary to characterize CMOS structures and can set a path towards charge readout of quantum dots based on capacitance change. However, in nanoscale devices the capacitance to be measured is often reduced to hundreds of attofarads. Moreover, the wiring of dilution fridges introduces lengths of cables that have a parasitic capacitance on the order of nanofarads, hindering such measurements. Here we present a highly sensitive capacitance bridge circuit designed to perform measurements inside a dilution refrigerator with attofarad resolution. We demonstrate the utility of our circuit by performing split CV measurements on 28 nm Fully Depleted Silicon on Insulator (FDSOI) nanostructures at 20 mK. Preliminary results also show that Coulomb blockade is observable using this method; a first step towards charge readout using a capacitance bridge.
Master, Université de Sherbrooke
Director : Michel PioroLadrière
Fast tuning of quantum dots using FPGAs
Spin qubits are a promising architecture for quantum computers due to their long coherence time and compatibility with industrial fabrication techniques. However, scalability issues arise when trying to create a system with many qubits. The more qubits there are, the more time it takes to initialize the system in the desired configuration and the more equipment is needed to control each quantum dot. Therefore, a scalable qubit control system addressing both these issues is presented. By using a Field Programmable Gate Array (FPGA) based system, it is possible to greatly accelerate device characterization while being relatively compact. The FPGA system can be several orders of magnitude faster than typical apparatus allowing for realtime measurements.
Undergrade student, Université de Sherbrooke
Director : Eva DupontFerrier
Silicon Donor SpinPhoton Coupling
Thanks to their record coherence time and their ability to be controlled precisely, donor spin qubit in silicon are very promising candidates for longlived quantum information storage in the solid state. In particular, it has been showed recently that spin states can be electrically controlled through electric dipole degrees of freedom: this new “allelectrical” architecture is called flipflop qubit.
On the other hand, superconducting resonators are inherently lowdissipative systems making them ideal ingredient for long distance coupling of two qubits. In addition, the fact that they can be fabricated using integratedcircuit processing techniques makes them attractive for scaling to a large number of qubits.
Combining these two entities into a hybrid system would bring best of both worlds: a long lasting quantum memory encoded in the spin state and scalable platform for electrical manipulation and long distance coupling using superconducting circuits. The goal of this project is to study and optimize the coupling of a single spin in silicon and a microwave photon in an NbN superconducting 2D resonator. A special effort is made to keep the design as minimalist as possible to settle the quantum device scalability challenge.
Doctorate, McGill University
Director : Lilian Childress
Probing a Spin Transfer Controlled Nanomagnet with a Single Nitrogen Vacancy in Diamond
We apply spintransfer (ST) torques to magnetic nanowires to efficiently tune the damping of the ferromagnetic dynamics, which we measure via local strayfield readout using a single nitrogen vacancy center in diamond. By reducing the nanowire’s geometry, we can increase the frequency separation of the standing spinwave modes until they are resolvable, which would allow for the detection of modedependent ST effects; however doing so requires new techniques for patterning these increasingly small devices onto diamond. In this poster, we present preliminary data characterizing an argonmilling subtractive process for patterning nanomagnetic structures onto diamond, and discuss the ramifications for NV readout.
Doctorate, Université de Sherbrooke
Directors : Bertrand Reulet & Guillaume Gervais, McGill University
Quantized Microwave Faraday rotation
We report the first quantitative measurement of microwave Faraday rotation originating from the cyclotron motion of electrons in a lowdimensional semiconductor heterostructure. As with the Hall effect, a continuous classical Faraday effect is observed as well as a quantized Faraday effect.The high electron mobility of our GaAs/AlGaAs hetero structure enables a large singlepass Faraday rotation of θF≈45°( ≈0.8 rad) to be achieved at a modest magnetic field of B≈100 mT. In the quantum regime, the Faraday rotation θFis naturally quantized in units of the fine structure constant α≈ 1/137, giving a geometric prescription for the fine structure constant. Electromagnetic confinement leads to Faraday rotation that is quantized in units of an effective α*, whose value is on the order of its free space value
Master, McGill University
Director : Lilian Childress
Towards Coupling Color Centers in Diamond to Fiber Microcavities
Color centers in diamond are attractive spinphoton interfaces for future quantum technologies. The “flagship” nitrogen vacancy center (NV) is a proven platform but suffers from a low emission probability (~3%) of photons into the zerophonon line (ZPL), which is necessary for remote entanglement protocols [1,2]. One potential workaround leverages resonant coupling to an optical cavity to enhance the emission efficiency [3]. In addition, germanium vacancy (GeV) centers can be used for their higher photon emission rate into the ZPL and lower inhomogenous broadening [4]. We present our ongoing effort to couple NV and GeV centers to a fiberbased microcavity configured as a scanning microscope. The high cavity finesses (> 30k) obtained using ultralowloss diamond membranes pave the road to the observation of Purcell enhancement of individual spin transitions but also set stringent requirements regarding cavity stabilisation.
[1] E. Hogan et al., Nature 466 (2010)
[2] N. Kalb et al., Science 356 (2017)
[3] D. Riedel et al., PRX 7 (2017)
[4] P. Siyushev el a., PRB 96 (2017)
10h30  10h55 Registration
10h55  11h00 Opening remarks (Salon A)
11h00  11h45 Pr Frédéric Dupuis, Université de Montréal
Purely quantum polar codes
11h45  12h05 Marco David, Student, McGill University
QED. The Quest to Formally Verify Mathematics
12h05  13h30 Lunch (Dining room  4 Canards)
13h30  14h15 Dr. Louis Gaudreau, National Research Council (NRC)  Ottawa
Entanglement distribution via coherent photontospin conversion in
semiconductor quantum dot circuits
14h15  14h45 Dr. Joel Griesmar, Université de Sherbrooke
A mesoscopic spectrometer based on the Josephson effect
14h45  15h15 Coffee break (Salon B)
15h15  15h45 Dr Stephane Virally, Polytechnique Montréal
Quantum optics in the time domain
15h45  16h25 Industry & Startups in quantum technologies
Dr Félix Beaudoin, Les Technologies Nanoacademic Inc
(www.nanoacademic.com)
Dr David RoyGuay, SB Quantum (www.sbquantum.com)
Pr David Poulin, Microsoft
16h25  17h00 Equity, diversity & inclusion (minutes and photos of the workshop)
17h00  Poster session with refreshments (Salon B)
19h30  INTRIQ dinner (Knowlton room)
November 12th
08h30  9h00 Pr Anne Broadbent, Université d'Ottawa
Quantum encryption with certified deletion
9h00  10h00 Dr Tomas JochymO'Connor, IBM  Yorktown Heights, New York
Disjointness in stabilizer codes
10h00  10h30 Coffee break (Salon B)
10h30  11h30 Pr Signe Seidelin, Institut NEEL CNRS/UGA
RareEarth Doped Crystals for straincoupled optomechanics
11h30  12h00 Dr Erika Janitz, McGill University
CavityEnhanced Photon Emission from a Single Germanium
Vacancy Center in a Diamond Membrane
12h00  13h30 Lunch (Dining room  4 Canards)
13h30  14h00 Pr Jérôme Bourassa, Cégep de Granby
Quantum illumination : exploiting quantum correlations when
entanglement is lost
14h00  14h30 Dr Thomas Baker, Université de Sherbrooke
Modeling superconducting circuits with a tensor network
14h30  15h00 Dr Anirban Chowdhury, Université de Sherbrooke
Simulating thermal physics on quantum computers
15h00  15h30 Questions and answers
15h30  15h40 Closing remarks
Institut NEEL CNRS/UGA
RareEarth Doped Crystals for straincoupled optomechanics
A challenge of modern physics is to investigate the quantum behavior of a bulk material object  for instance a mechanical oscillator  placed in a nonclassical state. One major difficulty relies in interacting with the mechanical object without perturbing with its quantum behavior. An approach consists of exploiting a hybrid quantum system consisting of a mechanical oscillator coupled to an atomlike object, and interact via the atomlike object. A particularly appealing coupling mechanism between resonator and “atom” is based on material strain. Here, the oscillator is a bulk object containing an embedded artificial atom (dopant, quantum dot, ...) which is sensitive to mechanical strain of the surrounding material. Vibrations of the oscillator result in a timevarying strain field that modulates the energy levels of the embedded structure. We have suggested to use rareearth doped crystals for straincoupled systems [1] and proposed a mechanism to cool down the resonator [2]. In this talk, I will report on our progress towards realizing experimentally these protocols. We are using an yttrium silicate (Y2SiO5) crystal containing triply charged europium ions (Eu3+), which are optically active. The reason behind this choice stems from the extraordinary coherence properties of this dopant, combined with its high strainsensitivity: the Eu3+ in an Y2SiO5 matrix has an optical transition with the narrowest linewidth known for a solidstate emitter, and the transition is directly sensitive to strain. We have successfully fabricated mechanical resonators, designed and set up the experiment, and achieved a signaltonoise ratio compatible with the planned measurements, as well as measured the strain sensitivity of europium ions in bulk Y2SiO5 crystals.
[1] K. Mølmer, Y. Le Coq and S. Seidelin, Dispersive coupling between light and a rareearth ion doped mechanical resonator, Phys. Rev. A 94, 053804 (2016)
[2] S. Seidelin, Y. Le Coq and K. Mølmer, Rapid cooling of a straincoupled oscillator by an optical phaseshift measurement, Phys. Rev. A 100, 013828 (2019)
IBM  Yorktown Heights, New York
Disjointness in stabilizer codes
The disjointness for stabilizer codes in quantum error correction is an algebraic quantity tied to the structure of the stabilizer generators of a code. It can be used to characterize the properties of different classes of logical gates, placing bounds on the level of the Clifford hierarchy attainable by constant depth circuits. This talk will introduce the notion of disjointness, highlight its usefulness with several examples, and posit open questions for which the disjointness may be useful in addressing.
Université de Montréal
Purely quantum polar codes
We provide a purely quantum version of polar codes, achieving the coherent information of any quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where random twoqubit Clifford gates are used to combine two singlequbit channels. The inputs to the synthesized bad channels are frozen by sharing EPR pairs between the sender and the receiver, so our scheme is entanglement assisted. We further show that a Pauli channel polarizes if and only if a specific classical channel over four symbol input set polarizes. We exploit this equivalence to prove fast polarization for Pauli channels, and to devise an efficient successive cancellation based decoding algorithm for such channels. This is joint work with Ashutosh Goswami, Mehdi Mhalla and Valentin Savin.
National Research Council (NRC)  Ottawa
Entanglement distribution via coherent photontospin conversion in semiconductor quantum dot circuits
In this talk, I will present our proposed long distance entanglement distribution scheme that aims to overcome fundamental limitations present in current optical schemes. By using direct band gap semiconductor quantum dots, efficiency and heralding advantages can be exploited through photontospin conversion. For this reason, materials such as GaAs are superior to Si in this type of applications. I will review current schemes to transfer polarization or timebin encoded photonic qubits to electron spin qubits and will describe adaptations to employ heavy holes which have a number of attractive properties including gfactor tunability. Finally, I will show preliminary results on quantum dot devices using Van der Waals heterostructures which present several potential advantages such as higher confinement energies due to their atomically thin geometry, easier combination with different substrates and the possibility of encoding information in their valley degree of freedom.
Université de Sherbrooke
Modeling superconducting circuits with a tensor network
We introduce a tensor network method tailored for the simulation of largescale superconducting circuits. We leverage information unavailable to other stateoftheart simulation methods to produce firstprinciples coherencetime estimates for the fluxonium qubit. In particular, we study the charge dispersion of this qubit due to coherent quantum phase slip processes as a function of the arrayjunction impedance, and we provide direct numerical evidence of the validity of an effective theory introduced in [V. E. Manucharyan et. al, PRB 85, 024521 (2012)]. We can analyze circuits in terms of entanglement, which can signal how protected quantum information is in circuits and motivate better ways of encoding it. Measurements of the energy participation ratio of circuit components indicates how the qubit transitions are affected by dissipation channels and circuitelement disorder.
Cégep de Granby
Quantum illumination : exploiting quantum correlations when entanglement is lost
sTwomode squeezed states quantum states of light where photons in a pair of distinct beams are entangled together. These EPRstates of light are an excellent resource for quantum sensing and quantum communications protocols. Excess noise in a lossy transmission channel however breaks the entanglement and prohibits secure quantum communication between parties. In spite of this, the quantum correlations in the final state are resilient to environment noise and remain larger than what is classically allowed. Consequently, illuminating a distant object with quantum entangled light, or quantum illumination, has been shown to lead to quantum enhancements in remote sensing detection capabilities and resilience to adversary noise. Quantum illumination could provide invaluable performance enhancements of observations made in noisy environments, from biological samples in the optical range to satellite surveillance in the microwaves. In this talk, I will introduce the concept of quantum illumination, present an overview of different detection schemes and discuss their capabilities and limitations. With a particular focus on microwave technology, I will present the requirements and progress towards building microwave quantumenhanced radar system.
Université d'Ottawa
Quantum encryption with certified deletion
Given a ciphertext, is it possible to prove the deletion of the underlying plaintext? Since classical ciphertexts can be copied, clearly, such feat is impossible using classical information alone. In stark contrast to this, we show that quantum encodings allow such certified deletion. More precisely, we show that it is possible to encrypt classical data into a quantum ciphertext such that the recipient of the ciphertext can produce a classical string which proves to the originator that the recipient has relinquished any chance of recovering the plaintext, should the decryption key be revealed. Our scheme is feasible with current quantum technology: the honest parties only require quantum devices for singlequbit preparation and measurements, and is robust against noise in these devices. Furthermore, we provide an analysis that is suitable in the finitekey regime.
https://arxiv.org/abs/1910.03551
Université de Sherbrooke
Simulating thermal physics on quantum computers
Simulating systems in thermal equilibrium and computing their properties are important problems in physics. These are also however known to be computationally hard problems, especially for quantum systems. I will talk about quantum algorithms that can, under certain conditions, provide advantages in sampling from thermal Gibbs states and computing partition functions of quantum Hamiltonians. A key idea in our algorithms is to approximate an imaginarytime evolution as a linear combination of (unitary) realtime evolutions. This linear combination can then be easily implemented on a usual gatemodel quantum computer. I will also discuss how this approximation can be used to compute the partition function on a restricted model of computation that uses only one pure qubit.
Undergrad student
Director : Bill Coish
McGill University
QED. The Quest to Formally Verify Mathematics
Formal correctness and formal truth are of great value. Through formal verification, one can ensure that the autopilot software of commercial airplanes does not endanger its passengers, and correctness proofs are already standard practice in the industry. Typically, this is done through a precise mathematical formulation of the algorithm and deductive reasoning about its properties, which is then machinechecked. Yet, mathematicians themselves have not developed any interest in carrying out formal verifications. Although mathematics prides itself as the most fundamental of sciences, almost all proofs are conventionally written with many abstractions and omissions. This leads to an astonishingly high number of significant errors in published mathematical literature. Building on the deep dilemma between what a proof is and what it should be, this talk explores the field of formal verification and interactive theorem proving with particular emphasis on mathematics, and also gives an outlook over applications to quantum algorithms.
Université de Sherbrooke
A mesoscopic spectrometer based on the Josephson effect
A key element of mesoscopic topological systems, such as hybrid semiconductorsuperconductor circuits, are Andreev Bound States, single quasiparticles localized at superconducting weak links. The characteristic transition energy of these states is twice the superconducting gap (90 GHz in aluminum). Conventional microwave techniques allow probing these states but only in a limited bandwidth. We propose a new broadband spectrometer operating at frequencies up to 180 GHz based on the Josephson effect which converts a DC voltage to microwave oscillations at a frequency proportional to this voltage. Using a symmetrical SQUID biased at half a flux quantum allows decoupling the spectrometer from environmental modes. In addition, careful design of the biasing circuit reduces the number of remaining modes and damps them. The fabricated mesoscopic spectrometer has a linewidth of 2 MHz, a bandwidth of 180 GHz and a minimal theoretical sensitivity of 5 kHz.
McGill University
CavityEnhanced Photon Emission from a Single GermaniumVacancy Center in a Diamond Membrane
Atomiclike defects in diamond provide a promising lightmatter interface for quantum information applications. Looking at alternatives to the wellstudied nitrogenvacancy (NV) center, we examine interactions between a defect with superior optical properties, the germaniumvacancy (GeV), and an open microcavity. We demonstrate roomtemperature coupling between a single emitter in a diamond membrane and a finesse 11,000 fiber cavity, evidenced by a 8fold increase in the spectral density of emission. The experimental advancements in this work set the stage for future cryogenic experiments, where for the existing system we predict a factor of 7 increase in the GeV spontaneous emission rate.
Polytechnique Montréal
Quantum optics in the time domain
Quantization of the electromagnetic (EM) field is carried in two steps: first quantization selects discrete modes, and second quantization promotes the classical amplitude of these modes to quantum operators. In quantum optics textbooks, the first step is always carried in the frequency domain (i.e. monochromatic modes are selected). This is very useful in many situations where the signal is indeed quasimonochromatic. However, the description is inadequate for the fewcycle, broadband signals that can be found e.g. in ultrafast optics and in many experiments in the microwave domain. We thus show how it is possible to carry a full quantization of the EM with the first step in time rather than frequency [1]. This procedure yields interesting consequences such as the existence of a dual of the Hamiltonian in the time domain and of a noncausal relationship between the EM field transporting the probability amplitude for the energy and the “photonics field”, which transports the probability amplitude for photon clicks on a broadband detector.
[1] Virally, S. and Reulet, B., “Unidimensional time domain quantum optics”, PRA 100, 023833 (2019)
Doctorate, McGill University
Director : Jack Sankey
Progress toward optical control of mechanical geometry
We report experimental progress toward achieving our group's recent proposal [1] to gain an unprecedented level of optomechanical control over the shape and mass of a mechanical mode, using an optical spring to perturb a single lattice site of a phononic crystal, thereby smoothly localizing the spatial distribution of oscillating mass from the centimeter scale to the micron scale. Such control over shape and mass has never been demonstrated, and represents an entirely unexplored avenue in the field. Thus far, we have reliably fabricated the requisite (delicate!) mechanical structures, and observed the characteristic "phononic bandgap" (a necessary ingredient for localization). We have assembled a rigid, vibrationisolated fiberfiber cavity with a phononic crystal in the middle to measure these effects. We show preliminary attempts at locking this cavity on resonance and obtaining the crystal Brownian motion from the error signal. Finally, we present a technique to decrease the finesse of a fibermirror in a controllable manner by smoothly etching away the bilayers forming the distributed Bragg reflector. We etch six bilayers, and subsequently measure finesse after each bilayer is removed. We find that the measured finesse agrees remarkably well with a 1D transfer matrix model. Achieving a specific finesse value for our fibermirrors is necessary so that our cavity will generate a strong optical spring whilst displaying a sufficiently large decay rate, therefore minimizing antidamping of the phononic crystal and facilitating cavity locking.
[1] A. Z. Barasheed et al., Phys. Rev. A 93, 053811 (2016)
Research professionnal
Institut Quantique
Suspended NbN superconducting resonator for reducing intrinsic losses
Superconducting coplanar waveguide (CPW) microwave resonators are crucial elements in Photon detectors, Quantumlimited parametric amplifiers, Narrowband filters, Readout, interconnect in quantum processors and Hybrid devices, connecting solidstate spins with superconducting circuits [13]. In the quantum regime, the dominant loss mechanism for highQ superconducting resonators can be attributed to parasitic twolevel systems (TLSs) in the dielectrics. Interface TLSs are common by products of the fabrication process, often introduced by impurities associated with Si surfaces [3]. To reduce intrinsic losses, we employ isotropic deep reactiveion etching (DRIE) of Si substrate to create suspended NbN superconducting resonators (SSR).
In this study, thin films of niobium (Nb) and niobium nitride (NbN) are deposited on Si substrate by a DC magnetron sputtering system. The influence of the N2/Ar gas ratio, the deposition current, the substrate bias potential on the superconducting critical temperature of the films are investigated. Plasma etching of Nb and NbN thin films in a SF6 and Cl2BCl3 gas plasma is studied using inductively coupled plasma (icp) reactor. Parametric studies on the effects of total gas flow rate and chamber pressure on the edge angles and etch rates are reported. Finally, suspended NbN superconducting resonator is fabricated and will be tested. This could be applied to the fabrication of superconducting qubits in integrated circuits, offering a path towards longer qubit coherence times.
[1] Landig et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018)
[2] Tosi et al. Silicon quantum processor with robust longdistance qubit couplings. Nat Commun 8, 450 (2017)
[3] Bruno et al. Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates, Appl. Phys. Lett. 106, 182601 (2015)
Master, Université de Sherbrooke
Director : Alexandre Blais
Variational Quantum Algorithms for the FermiHubbard model
Noisy intermediatescale quantum computation has the potential to be useful for the simulation of quantum materials. A prominent simulation approach is using variational quantum algorithms (VQAs), which have some resilience to noise and can handle limited qubit connectivity. Here, we aim to simulate the FermiHubbardmodel ground state by means of a VQA. We investigate a number of possibilities for engineering the variational statepreparation circuit, and benchmark these in presence of realistic noise. We find that Hamiltonianinspired variational forms have better performance over a hardwareefficient approach. This work is progress towards the simulation of highTc superconductivity on a quantum device.
Intern, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Experimental Study of single hole EDSR with strong spinorbit coupling in a gated GaAs/AlGaAs Double Quantum Dot
Master, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Fabrication and irradiation effects of fieldinduced shallow twodimensional electron gas in dopantetched modulationdoped GaAs/AlGaAs heterostructures
Collaboration with Takafumi Fujita, Yasushi Kanai, Kazuhiko Matsumoto, Yuji Sakai, Haruki Kiyama, Julian Ritzmann, Arne Ludwig, Andreas D. Wieck, and Akira Oiwa (Osaka University, Ruhr University Bochm).: Electron spin qubits based on GaAs/AlGaAs gatedefined quantum dots (QDs) formed in a twodimensional electron gas (2DEG) are strong candidates for a single photon and single electron spin quantum interface. However, suppression of the irreversible response of photon irradiation in conventional doped GaAs/AlGaAs gatedefined QDs is indispensable for performing stable and continual manipulation of a single electron spin generated by a single photon. It is one of the most promising solution to utilize QDs formed in a fieldinduced 2DEG on undoped heterostructures since these problems are caused by Si dopants. On the other hand, it is necessary in conventional undoped structures to optimize complicated etching and deposition processes for fabrication of Ohmic contacts to avoid creating a discontinuous 2DEG and undesired leakage paths to the top gates. Here, we show the fabrication and irradiation effects of an improved fieldinduced 2DEG structure in dopantetched modulationdoped GaAs/AlGaAs heterostructures taking advantage of a conventional doped structure to simplify ohmic contact fabrication. We successfully induce a 2DEG and evaluate the effects of the light irradiation on the transport properties while an electric current decays with time. This work may provide an additional way to realize undoped GaAs gatedefined QDs for robust quantum interface against photon irradiation.
Doctorate, Université de Sherbrooke
Director : Michel PioroLadrière
28nm UTBB FDSOI technology for Siliconbased quantum dots and cryoCMOS electronics
Although remarkable progress has been made over the last few years in the field of Siliconbased spin qubits hosted in small scale conventional CMOS technologies, coupling several qubits together for the needs of largescale logical operations remains a challenge. Utilizing state of the art mass production process methods from the field of microelectronics seems to be a very promising candidate to solve this problem. Another problem that needs to be tackled concerns the control electronics for the qubits. Indeed, in the case where more than a thousand qubits will need to be controlled, the heat and noise produced by standard electronics will rapidly be a major issue.
Our goal towards a compact quantum processor is to develop a Siliconbased electron or hole spin qubit architecture fabricated via industrial techniques, with onchip embedded control achieved by cointegrating classical electronics at cryogenic temperatures. In this poster, we present our progress on both the qubit architecture and the cryogenic electronics. Our qubit device is designed and fabricated using exclusively CMOS industrial manufacturing techniques, based on STMicroelectronics’ 28nm fully depleted silicononinsulator (FDSOI) planar ultrathin body and BOX (UTBB) technology. We report our progress on both single and multiple quantum dot systems in 1D (array) and 2D (matrix) architectures.We also propose a design for cryogenic CMOS electronics for manipulation and readout of many qubits, in order to perform logical operations for the needs of largescale quantum computing. FDSOI is a promising technology for cryoCMOS implementation, as it has already been demonstrated to operate down to 4K. We studied the performance of ring oscillators, consisting of 28nm FDSOI NMOS and PMOS transistors, designed to generate 6 to 10 GHz microwave signals.Our ring oscillator is coupled to a frequency divider, enabling onchip downconversion, allowing readout with conventional electronics measurement setup in the MHz regime.
Master, McGill University
Director : Claude Crépeau
General Strategy for Bit Commitment Scheme from Pseudo Telepathy Games
Quantum information processing contributed greatly to the rapid advancement of modern cryptography with it being the intersection of mathematics, physics and computer science. Communication tasks that are previously impossible to realize classically can be accomplished with the use of quantum entanglement. Pseudotelepathy game is an application of this where a game exhibits pseudotelepathy with the existence of a quantum winning strategy and the lack of its classical counterpart. After the examination of known pseudotelepathy games, a general strategy for devising a bit commitment scheme using pseudotelepathy games is presented. Due to the nature of the game, the bit commitment schemes derived from the games are unconditionally secure classically, but can be cheated by quantum players.
Director : Jack Sankey
Master : McGill University
Mechanical Motion Driven by Quantum Radiation Pressure Noise
We present progress towards observing mechanical motion of a trampoline driven by quantum radiation pressure noise (QRPN). Lasers have quantum fluctuations which are caused by fluctuations in photons emission, also called shot noise, and our goal is to measure the effect of theses fluctuations "kicking" a trampoline mechanical resonator. To do so, we will place the trampoline inside a short (~10 microns) fiberfiber cavity in a vacuum chamber at room temperature and shine laserlight in it. The trampoline will be driven by radiation pressure caused by the shot noise of the laser inside the cavity. The trampoline possesses great mechanical properties (high quality factor and low force noise) and the short cavity allows high decay rate without compromising the finesse, which enables us to have the trampoline's motion dominated by QRPN instead of thermal noise. We currently have characterized the mechanical properties of the trampoline, which has high mechanical quality factor (> 20 million), and we have proven that we are able to get shot noise predominated laser by squashing its classical noise. The future work will be focused on increasing the bandwidth of the shot noise predominated frequency range of the laser, and assembling the chamber and cavity.
Doctorate, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Formation of quantum dots on (110) GaAs substrate
Collaboration with Rio Fukai, Yuji Sakai, Takafumi Fujita, Haruki Kiyama, Takashi Nakajima, Julian Ritzmann, Arne Ludwig, Andreas D. Wieck, Seigo Tarucha, and Akira Oiwa (Osaka University, Ruhr University Bochm, RIKEN, and University of Tokyo).: Gatedefined semiconductor devices provide a platform which enable us to perform various quantum transport experiments. Electron spins in gatedefined GaAs quantum dots (QDs) have been extensively studied for integrated and stable quantum bits. In those experiments, epitaxial layers grown on the (001) plane are generally used. In a (110) GaAs quantum well (QW), we expect more efficient photonelectron spin quantum state conversion by exciting heavyhole Zeeman levels under inplane magnetic field. However, experimental works on the electricallydefined low dimensional systems on the (110) substrate have been hardly done. From the Hall bar measurements, the mobility and electron density of a QW grown on (110) substrate were estimated as 7×104 cm2/Vs and 9×1010 cm2, respectively at a temperature of 1.5 K. Subsequently, we fabricated gatedefined lateral QDs and measured them using a dilution refrigerator. We clearly observe Coulomb oscillations in the fewelectron regime by monitoring a nearby charge sensor current. We expect that the (110) GaAs QDs will provide a new platform for studying photonspin coupling.
Intern, National Research Council (NRC)  Ottawa
Director : Andrew Sachrajda
Single Hole Energy Spectrum in a GaAs/AlGaAs DQD with Strong SpinOrbit Interaction and DotSpecific gfactors
Doctorate, Polytechnique Montréal
Director : Sébastien Francoeur
ExcitonPolaritons as a tool to control the emission characteristics of excitons and trions bound to Te2 in ZnSe
Te2 molecules in ZnSe form a quantum defect that offers advantageous characteristics, including a high optical uniformity due to its atomic nature and a strong optical dipole moment matching those from semiconductor nanostructures, for the development of efficient spinphoton interfaces for applications in quantum optics, communications and networks.
In this work, we demonstrate that excitonspolaritons generated in the ZnSe host material can be used to deterministically control the emission characteristics of excitons and trions bound to a single Te2 molecule. In particular, the emission efficiency is increased by two orders of magnitude, indicating a very efficient coupling between free excitons and Te2 bound states. Scanning the freeexciton band with a narrowfrequency tunable laser over the free exciton spectral region reveals strong inphase oscillations with a period of about 1 meV in the bound exciton emission intensity, emission energy, and emission linewidth. These modulations are explained by the strong coupling naturally occurring in ZnSe between photons and freeexcitons, or excitonpolaritons.
This type of cooperative process whereby a host excitation is used to control the behavior of a single emitter has never been reported before. It allows deterministically controlling the emission properties and enables the development of new coherent control schemes.
Master, Polytechnique Montréal
Director : Sébastien Francoeur
Optical stabilization of the spectral wandering of an exciton bound to a Te isoelectronic center in ZnSe
We report on the stabilization of the electrostatic environment of a single emitter bound to a Te isoelectronic center in ZnSe resulting in an increased coherence time T2. Nonresonant excitation is used to reduce charge fluctuations in the vicinity of the emitter. Ultraweak nonresonant excitation powers allow for radiative recombination of holes trapped in the vicinity of the emitter thus lowering the redshift of the resonance energy induced by DC Stark effect. The PLE spectrum is the result of the superposition of nonresolved Lorentzian lines each corresponding to a certain charge distribution. With higher nonresonant excitation powers we reach saturation and populate the trap states with excitons, thus inducing another redshift through the HeitlerLondon interaction.
Master, McGill University
Director : Lilian Childress
Towards Coupling Color Centers in Diamond to Fiber Microcavities
Color centers in diamond are attractive spinphoton interfaces for future quantum technologies. The “flagship” nitrogen vacancy center (NV) is a proven platform but suffers from a low emission probability (~3%) of photons into the zerophonon line (ZPL), which is necessary for remote entanglement protocols [1,2]. One potential workaround leverages resonant coupling to an optical cavity to enhance the emission efficiency [3]. In addition, germanium vacancy (GeV) centers can be used for their higher photon emission rate into the ZPL and lower inhomogenous broadening [4]. We present our ongoing effort to couple NV and GeV centers to a fiberbased microcavity configured as a scanning microscope. The high cavity finesses (> 30k) obtained using ultralowloss diamond membranes pave the road to the observation of Purcell enhancement of individual spin transitions but also set stringent requirements regarding cavity stabilisation.
[1] E. Hogan et al., Nature 466 (2010)
[2] N. Kalb et al., Science 356 (2017)
[3] D. Riedel et al., PRX 7 (2017)
[4] P. Siyushev el a., PRB 96 (2017)
Doctorate, Université de Sherbrooke
Director : Eva DupontFerrier
Highresolution cryogenic capacitance measurements of FDSOI structures using a capacitance bridge
As CMOS structures are envisioned to host silicon spin qubits and for cointegrating quantum systems with control electronics, the cryogenic behaviour of such structures must be investigated. Capacitancevoltage (CV) measurements are widely used to determine semiconductor parameters. Performing highresolution CV measurements at cryogenic temperatures is necessary to characterize CMOS structures and can set a path towards charge readout of quantum dots based on capacitance change. However, in nanoscale devices the capacitance to be measured is often reduced to hundreds of attofarads. Moreover, the wiring of dilution fridges introduces lengths of cables that have a parasitic capacitance on the order of nanofarads, hindering such measurements. Here we present a highly sensitive capacitance bridge circuit designed to perform measurements inside a dilution refrigerator with attofarad resolution. We demonstrate the utility of our circuit by performing split CV measurements on 28 nm Fully Depleted Silicon on Insulator (FDSOI) nanostructures at 20 mK. Preliminary results also show that Coulomb blockade is observable using this method; a first step towards charge readout using a capacitance bridge.
Master, Université de Sherbrooke
Director : Michel PioroLadrière
Fast tuning of quantum dots using FPGAs
Spin qubits are a promising architecture for quantum computers due to their long coherence time and compatibility with industrial fabrication techniques. However, scalability issues arise when trying to create a system with many qubits. The more qubits there are, the more time it takes to initialize the system in the desired configuration and the more equipment is needed to control each quantum dot. Therefore, a scalable qubit control system addressing both these issues is presented. By using a Field Programmable Gate Array (FPGA) based system, it is possible to greatly accelerate device characterization while being relatively compact. The FPGA system can be several orders of magnitude faster than typical apparatus allowing for realtime measurements.
Undergrade student, Université de Sherbrooke
Director : Eva DupontFerrier
Silicon Donor SpinPhoton Coupling
Thanks to their record coherence time and their ability to be controlled precisely, donor spin qubit in silicon are very promising candidates for longlived quantum information storage in the solid state. In particular, it has been showed recently that spin states can be electrically controlled through electric dipole degrees of freedom: this new “allelectrical” architecture is called flipflop qubit.
On the other hand, superconducting resonators are inherently lowdissipative systems making them ideal ingredient for long distance coupling of two qubits. In addition, the fact that they can be fabricated using integratedcircuit processing techniques makes them attractive for scaling to a large number of qubits.
Combining these two entities into a hybrid system would bring best of both worlds: a long lasting quantum memory encoded in the spin state and scalable platform for electrical manipulation and long distance coupling using superconducting circuits. The goal of this project is to study and optimize the coupling of a single spin in silicon and a microwave photon in an NbN superconducting 2D resonator. A special effort is made to keep the design as minimalist as possible to settle the quantum device scalability challenge.
Doctorate, McGill University
Director : Lilian Childress
Probing a Spin Transfer Controlled Nanomagnet with a Single Nitrogen Vacancy in Diamond
We apply spintransfer (ST) torques to magnetic nanowires to efficiently tune the damping of the ferromagnetic dynamics, which we measure via local strayfield readout using a single nitrogen vacancy center in diamond. By reducing the nanowire’s geometry, we can increase the frequency separation of the standing spinwave modes until they are resolvable, which would allow for the detection of modedependent ST effects; however doing so requires new techniques for patterning these increasingly small devices onto diamond. In this poster, we present preliminary data characterizing an argonmilling subtractive process for patterning nanomagnetic structures onto diamond, and discuss the ramifications for NV readout.
Doctorate, Université de Sherbrooke
Directors : Bertrand Reulet & Guillaume Gervais, McGill University
Quantized Microwave Faraday rotation
We report the first quantitative measurement of microwave Faraday rotation originating from the cyclotron motion of electrons in a lowdimensional semiconductor heterostructure. As with the Hall effect, a continuous classical Faraday effect is observed as well as a quantized Faraday effect.The high electron mobility of our GaAs/AlGaAs hetero structure enables a large singlepass Faraday rotation of θF≈45°( ≈0.8 rad) to be achieved at a modest magnetic field of B≈100 mT. In the quantum regime, the Faraday rotation θFis naturally quantized in units of the fine structure constant α≈ 1/137, giving a geometric prescription for the fine structure constant. Electromagnetic confinement leads to Faraday rotation that is quantized in units of an effective α*, whose value is on the order of its free space value
Master, McGill University
Director : Lilian Childress
Towards Coupling Color Centers in Diamond to Fiber Microcavities
Color centers in diamond are attractive spinphoton interfaces for future quantum technologies. The “flagship” nitrogen vacancy center (NV) is a proven platform but suffers from a low emission probability (~3%) of photons into the zerophonon line (ZPL), which is necessary for remote entanglement protocols [1,2]. One potential workaround leverages resonant coupling to an optical cavity to enhance the emission efficiency [3]. In addition, germanium vacancy (GeV) centers can be used for their higher photon emission rate into the ZPL and lower inhomogenous broadening [4]. We present our ongoing effort to couple NV and GeV centers to a fiberbased microcavity configured as a scanning microscope. The high cavity finesses (> 30k) obtained using ultralowloss diamond membranes pave the road to the observation of Purcell enhancement of individual spin transitions but also set stringent requirements regarding cavity stabilisation.
[1] E. Hogan et al., Nature 466 (2010)
[2] N. Kalb et al., Science 356 (2017)
[3] D. Riedel et al., PRX 7 (2017)
[4] P. Siyushev el a., PRB 96 (2017)