# Introduction à l'information quantique

### Fall 2017 INTRIQ meeting, November 9th and 10th

Organizers:

Dr. Jérôme Bourassa, Cégep de Granby

Dr. Olivier Landon-Cardinal, McGill University

90, rue Stanstead, Bromont QC J2L 1K6

Téléphone : 1 800 304 3433

* Note : *The INTRIQ Business meeting (reserved for members) will be held in room "Salle des cantons" on November 9th from 9h30 to 10h30

* Chartered bus Berri-Bromont-Berri *(Departure from gate #3 at Berri on Nov. 9th at 9h00 AM)

**Meeting program**

**Thursday, November 9th**

10h30 - 10h55 Registration

10h55 - 11h00 Opening remarks (Salon A)

11h00 - 12h00 *Gina Passante, Assistant Professor at California State University, Fullerton (Salon A)*

*Research as a guide to improve the teaching and learning of quantum mechanics*

12h00 - 13h30 Lunch (Dining room)

13h30 -14h30 *David Poulin, Professor at Université de Sherbrooke (Salon A)*

*Everything you always wanted to know about theoretical quantum information but were afraid to ask*

14h30 - 15h00 Coffee break (Salon B)

15h00 -15h30 *Edouard Pinsolle, Research Professional at Université de Sherbrooke (Salon A)*

*Third Moment of Current Fluctuations in a Diffusive Conductor*

15h30 - 16h00 J*ean Olivier Simoneau, Doctorate at Université de Sherbrooke (Salon A)*

*Photon statistics of a Josephson parametric amplifier from continuous microwave measurements*

16h00 - 16h30 *Agustin Di Paolo, *Doctorate at Université de Sherbrooke (Salon A)

*Quantum technology efforts across the globe: leveraging its near-term impact*

16h30 - 18h30 *Poster session with refreshments (Salon B)*

19h00 - INTRIQ dinner (Room Knowlton)

**Friday, November 10th**

9h15 - 10h00 *Peter Grüter, Professor at McGill University (Salon A)*

*Attosecond time resolution by AFM*

10h00 - 10h30 *Baptiste Royer, Doctorant at Université de Sherbrooke (Salon A)*

*Itinerant microwave photon detector*

10h30 - 11h00 Coffee break (Salon B)

11h00 - 12h00 *Michael Hilke, Professor at McGill University (Salon A)*

*Introduction to Quantum Machine Learning*

12h00 - 13h30 Lunch (Dining room)

13h30 - 14h30 Nicolas Godbout, Professor at Polytechnique Montréal (Salon A)

*The Micius Satellite Quantum Science Experiments*

14h30 - 15h00 Charles Bédard, Doctorate at Université de Montréal (Salon A)

*Kolmogorov Amplification from Bell Correlation*

15h00 Closing remarks (Salon A)

*INVITED SPEAKERS*

*Assistant Professor Gina Passante**Calilfornia State University, Fullerton*

*Quantum mechanics is a notoriously difficult subject, in part because the physical laws of QM contradict what we see in the classical world, which can make it challenging for students to develop a quantum intuition. My research focuses on investigating what specific ideas or concepts are most difficult for students, to what extent the instructional paradigm affects student learning, and how can we use this information to improve instruction. In this talk I will describe a study into how students think about quantum mechanical superposition, and how targeted instruction improved student understanding. Additionally, we will discuss two different instructional paradigms and preliminary data on how they impact student learning.*

**Research as a guide to improve the teaching and learning of quantum mechanics**

*INTRIQ SPEAKERS*

*Charles Alexandre Bédard*

*Doctorate, Université de Montréal*

*Director: Gilles Brassard*

It was first observed by John Bell that quantum theory predicts correlations between measurement outcomes that lie beyond the explanatory power of local hidden variable theories. These correlations have traditionally been studied extensively in the probabilistic framework. A drawback of this perspective is that one is then forced to use in a single argument the outcomes of mutually-exclusive measurements. One of us has initiated an alternative approach, invoking only data at hand, in order to circumvent this issue. In this factual view, which is based on Kolmogorov complexity, we introduce mechanisms such as complexity amplification. We establish that this functionality is realizable, just as its probabilistic counterpart, hereby underlining that Bell correlations are a precious information-processing resource.

**Kolmogorov Amplification from Bell Correlation**

*Agustin Di Paolo **Doctorate, Université de Sherbrooke**Director: Alexandre Blais**Quantum technology efforts across the globe: leveraging its near-term impact*

Recent years have seen a noticeable interest increase in quantum technologies, now materialized in large-scale and worldwide efforts towards strategic use and future commercialization. Moreover, extensive publicity on quantum technologies such as quantum computing, has enhanced their visibility and greatly raised public expectations. In this talk, we contextualize the latest movements in the field to understand their impact on organizations, identifying ways forward towards an effective and long-term collaboration between academic, industrial and media sectors.

*Professor Nicolas Godbout*

Polytechnique Montréal

Tutorial: *The Micius Satellite Quantum Science Experiments*

*Professor Peter GrütterMcGill Univerity*Advancing the time resolution of AFM has been a primary pursuit of multiple research groups [1-3]. In particular, the idea to observe ultrafast events in the femtosecond range combined with nanometer spatial resolution is of great interest. Here the research focus ranges from measuring photocarriers to the molecule motion and beyond [4]. Recently, we demonstrated picosecond time resolution with non contact atomic force microscopy (nc-AFM) and ultrafast laser pulses in low temperature grown GaAs [2].

**Attosecond time resolution by AFM**

Our most recent advances in ultrafast time resolution AFM will be presented. We developed an autocorrelation measurement for ultrashort laser pulses by force detection using nc-AFM. A non-linear crystal is used to generate an electric field which follows the intensity of the impinging ultrashort laser pulse; we directly trace the emitted electric field with attosecond temporal, and nanometer spatial, resolution using our nc-AFM setup. As such, we are able to demonstrate that the lower limit of time resolution in AFM is solely given by the minimal time delay achievable by the optical setup and the thermal noise of the nc-AFM.

[1] M. Takihara, T. Takahashi, T. Ujihara – Appl. Phys. Lett. 93 (2008) 021902.

[2]macher, A. Spielhofer, Y. Miyahara, P. Grutter, Appl. Phys. Lett. 110 (2017) 053111.

Z. Schu[3] G. Shao, M. S. Glaz, F. Ma, H. Ju, D. S. Ginger, ACS Nano, 8 (2014) 10799

[4] M. Peplow, Nature 544 (2017) 408–410.

*Professor Michael Hilke*

McGill University

Tutorial: ** Introduction to Quantum Machine Learning**There has been a lot of talk lately about the importance of Montreal in the context of artificial intelligence and machine learning. combining this with the emergence of quantum technologies, it seems like an opportune moment to learn more about the quantum version of machine learning. I will start with introducing classical machine learning and go through some simple examples, including some details on the coding structure of machine learning. This will serve as a basis to introduce the quantum version of machine learning. This is a much less well defined area with many variants on the degree of "quantumness". I will describe different approaches to quantum machine learning and will give some simple examples and applications, and finish with several open questions.

*Professor David Poulin*

Université de Sherbrooke

Tutorial: *Everything you always wanted to know about theoretical quantum information but were afraid to ask*

I will give a tutorial on a topic in theoretical quantum information chosen by the participants.

*Edouard Pinsolle**Research Professional, Université de SherbrookeSupervisor: Bertrand Reulet*

*Third Moment of Current Fluctuations in a Diffusive Conductor*Over the years the study of current fluctuations in coherent conductors, and in particular their variance (second moment), has given new insights in the properties of quasi-particles, such as the effective charge in fractional quantum Hall effect or more recently the symmetry of the Kondo state in carbon nanotubes. Despite this success there has been only a few attempts to push deeper the study of current fluctuations in mesoscopic conductors by tackling the measurement of higher order moments such as the third one. In this presentation I will show the first measurement of third moment of current fluctuations in a diffusive conductor.

*Baptiste Royer**Doctorate, Université de Sherbrooke*Director: Alexandre Blais

*Itinerant microwave photon detector*The realization of a high-efficiency microwave single photon detector is a long-standing problem in the field of microwave quantum optics. We propose a quantum non-demolition, high-efficiency photon detector that can readily be implemented in present state-of-the-art circuit quantum electrodynamics. This scheme works in a continuous fashion, gaining information about the arrival time of the photon as well as about its presence.

The key insight that allows to circumvent the usual limitations imposed by measurement back-action is the use of long-lived dark states in a small ensemble of inhomogeneous artificial atoms to increase the interaction time between the photon and the measurement device.

Using realistic system parameters, we show that large detection fidelities are possible.

*Jean Olivier Simoneau**Doctorate, Université de SherbrookeDirector: Bertrand Reulet*

*Photon statistics of a Josephson parametric amplifier from continuous microwave measurements*The electric ac current flowing though a mesoscopic device exhibits rich electromagnetic fluctuations.[1] Those fluctuations can either be studied through the lens of charge transport or that of quantum optics. In the quantum optics perspective, it is possible to measure the discrete photon statistics of a microwave signal using the cumulants of its continuous voltage fluctuations.[2] I will present recent results for the photon statistics of a Josephson parametric amplifier, the archetypal source of squeezed states in the microwave domain. The results convincingly agree with an input-output model of the device and measurement setup.

[1] Rolf Landauer. Nature 392, 658-659 (1998)

[2] Virally et al. PRA 93, 043813 (2016)

*POSTER SESSION *

*Alexandre Bédard-ValléeMaster, Université de SherbrookeDirector: Michel Pioro-Ladrière*The use of single-electron transistors to readout spin qubits in quantum dots has been proven to yield excellent sensitivities. Those high sensitivities are what has allowed single-shot readout to be possible. However, SETs come at a high cost. The fact is that the real-estate they occupy is large, sometimes even larger than the space occupied by the quantum dots. This poses significant challenges to the scalability of the quantum dot devices. In this work, we present the base idea for an alternative approach based on quantum capacitance measurement by an external capacitance bridge that would allow the devices to do away with SETs altogether. Some preliminary results using a cryogenic bridge prototype and using a SET as a quantum dot will be shown. As of now, the sensitivity of the prototype is still too low to see Coulomb blockade, but accumulation effects in a SET cooled to cryogenic temperatures were still clearly visible, which shows that the technique we propose could work.

**Developing a cryogenic C-V measurement technique with the goal of it being used for the readout of spin qubits in quantum dots**

*Simon Bernard**Doctorate, McGill University**Director: Jack Sankey**Design considerations for high-reflectivity SiN photonic crystal membranes, and progress toward optical control of mechanical geometry*

Photonic crystal membranes exhibit a resonantly enhanced reflectivity. Many applications require this resonance to occur at a pre-specified wavelength, imposing stringent geometrical tolerances. Here we tune a freestanding photonic crystal reflector resonance to within 0.15 nm (0.04 linewidths) of 1550 nm using iterative hydrofluoric acid etches, and present a series of simulations for creating reflectors robust against beam collimation [1]. Furthermore, we report progress toward creating a tunable, localized mechanical mode in a phononic crystal using radiation pressure from light [2]. Specifically, we describe fabrication techniques producing consistently 100 nm to 300 nm thick stoichiometric SiN freestanding crystals with an area as large as 20 mm^2, up to 2750 crystal unit cells, and tethers as narrow as ~ 1 um. We interferometrically measure Brownian motion of these crystals and identify a phononic bandgap required for laser-induced localization experiments (with a ratio of gap width to band edge frequency as high as 0.8), consistent with COMSOL simulations. We expect a localization length of ~ 1 unit cell for our optimal devices.

[1] S. Bernard et al., Optics letters 41 (24), 5624-5627 (2016)

[2] A. Z. Barasheed et al., Phys. Rev. A 93, 053811 (2016)

*Vincent Dumont**Doctorate, McGill University**Director: Jack Sankey**Ultra-short Half-Cavities for Optomechanical Applications*

In the field of optomechanics, we are interested in studying the coupling of light to a mechanical resonator. In a typical experiment, the position of a mechanical oscillator modulates the optical resonant frequency (dispersive coupling) of a Fabry-Perot optical cavity. In this case, it is advantageous to create optical cavitites that are as small as possible to increase the coupling between light and the motion of mechanical resonators (i.e., small cavities lead to more photon bounces per second on the mechanical resonator). Alternatively, the position of the mechanical element can also modulate the input coupling rate to the cavity (dissipative coupling). We report progress towards creating a micron-scale half-cavity formed by a flat mirror and a ~90 nm thick SiN membrane mechanical resonator. By integrating this small half-cavity in a conventional Fabry-Perot optical resonator, we demonstrate dissipative coupling. This approach to create small cavitites could be used to reduce the dimension of free-space optical cavities down to dimensions comparable to a laser wavelength, yielding an optomechanical coupling rate orders of magnitude higher than with current macroscopic free space systems. It could also enable ground-state cooling of the mechanical oscillator in the "bad cavity" limit.

*Felix Fehse**Doctoreate, McGill University**Director: Bill Coish**Improving preparation and readout fidelity of spin-qubits in gated quantum dots*

The possibility to construct a working quantum computer depends on the frequency of errors that occur during operation. If the frequency is low enough – estimates for error-correction thresholds typically suggest an operation fidelity of more than 99 % – quantum error-correction algorithms can counteract these errors. However, these algorithms heavily depend on the readout process of qubits, so that the readout fidelity must be typically on the order of 99.9 % or better.

Although the currently achieved gate-operational fidelity is already at >99.9 % [1], the fidelity of qubit state preparation and readout for single electron-spins in gated quantum-dots lies at just about 80 % [2] which is too low for realistic applications. Since this technology is a promising platform for scalable quantum-computers, our goal is to achieve ideally a fidelity of higher than 99.9 %. In that case, a real working quantum computer comes into close reach.

We develop an optimal pulse-shape of the given tuning-parameter for minimal conversion-errors and at the same time maximal stability to noise in the experimental setup.

[1] J. Yoneda, K. Taked, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Hondea, T. Kodera, S. Oda, Y. Hoshi, N. Usami, K. M. Itoh, S. Tarucha, “A >99.9%-fidelity quantum-dot spin qubit with coherence limited by charge noise”, arXiv:1708.01454, 4. Aug 2017

[2] T. F. Watson, S. G. J. Philips, E. Kawakami, D. R. Ward, P. Scarlino,, M. Veldhorst, D. E. Savage, M. G. Lagally, Mark Friesen, S. N. Coppersmith, M. A. Eriksson, L. M. K. Vandershypen, “A programmable two-qubit quantum processor in silicon”, arXiv:1708.04214, 14th Aug. 2017

*Pierre Février**Postdoc, Université de Sherbrooke**Director: Bertrand Reulet**Quantum current fluctuations in a tunnel junction at optical frequency*

We report the measurement of emission noise by a planar metallic tunnel junction driven far from its equilibrium state. To investigate this regime, we bias the junction at voltage V>1Volt, and measure the emitted photons at optical frequency (f < eV/h ∼ 10^{14}Hz). This emission results from the scattering of surface-plasmon-polaritons, generated by high frequency current fluctuations inside the junction due to tunneling electrons (shot-noise). This allows noise measurement at timescales smaller than the RC time of the junction. We show that the emitted photon power P_{f}(V) at frequency f, which is proportionnal to the current spectral density S_{II}(f,V), isn't given by the usual fluctuation-relation which have been previously demonstrated in the GHz range for metallic and supraconductive linear tunnel junction. Our results are in agreement with a prediction based on the Landauer-Büttiker scattering approach accounting for the energy/voltage dependence of the transmission of the tunnel barrier. With a quantitative calculation of the emission efficiency, we demonstrate that the photon emission results from current fluctuations inside the barrier.

*Yannik Fontana*

*Postdoc, McGill University*

*Director: Lilian Childress*

*Toward a Tunable Coupling of Optical Micro-cavities and Color Centers in Diamond*Defect centers in diamond are attractive solid-state candidates for quantum optics experiments. The “flagship” nitrogen vacancy center (NV-) is a robust spin-qubit platform [1,2]. Unfortunately, ~ 97% of the photons emitted by an NV- are useless for spin-photon entanglement protocols.We present our on-going effort to couple NV- and germanium-vacancy (GeV) centers embedded in ultralow-loss diamond membranes to a fully tunable optical micro-cavity directly interfaced with an optical fiber. The required passive and active cavity stabilisation mechanisms will be discussed, as well as our state-of-the-art results for the finesse of a cavity loaded with a diamond membrane. We expect that at cryogenic temperatures both NV- and GeV decay rates and fraction of “useful” photons will be enhanced, scaling up with the cavity finesse [3]. In addition, GeV centers could also be used to improve the “Indistinguishability x Photon rate” figure of merit for room temperature photon sources.

[1] E. Hogan et al., Nature 466 (2010)

[2] N. Kalb et al., Science 356 (2017)

[3] D. Riedel et al., PRX 7 (2017)

*Louis Haeberlé**Master, Université de Sherbrooke**Director: Michel Pioro-Ladrière**Frequency-tunable microwave cavity with uniform field for coherent control of large spin ensembles*

Electron spin resonance (ESR) is a conventional technique for reading and manipulating spin qubits. Many experimental realizations of ESR readout and control use some form of resonant cavity, but most cavity resonator designs are not quickly frequency-tunable over a wide frequency range and have a non-uniform microwave field. Uniformity of the microwave field is essential for coherent control of large spin ensembles; using large spin ensembles is desirable because the sensitivity of spin state measurement increases as the square root of the ensemble size. We present an alternative cavity resonator design optimized for ESR experiments. The cavity design provides an uniform field over macroscopic volumes (several mm³) and is dynamically frequency-tunable over a large bandwidth by piezoelectric modulation of a flexible copper diaphragm capacitor. This enables applications for quantum sensing technology and general ESR spectroscopy.

*Pavithran Iyer**Doctorate, Université de Sherbrooke**Director: David Poulin**Critical parameters for quantum error correction*

In this work, we present a numerical study to determine the parameters of a single qubit CPTP map that are critical to the estimate of the logical error rate, for a quantum error correction scheme. In particular, our study shows that metrics to quantify the amount of noise in a quantum channel, such as Diamond norm, entanglement fidelity, etc., cannot provide tight bounds on the logical error rate of a quantum error correction scheme. Alternatively we use machine learning techniques to propose a new definition of a physical noise strength for a quantum channel, that provides, in some cases, a more accurate estimate of the logical error rate than previously known metrics.

*Mathieu Lachapelle**Master, Université de Sherbrooke**Director: Alexandre Blais**Longitudinal Coupling for Fast QND Measurement: Numerical Study*

Dispersive qubit readout in circuit QED relies on transverse coupling to a microwave resonator. This type of coupling, however, leads to mixing between qubit and resonator eigenstates. In turn, this leads to Purcell decay and to a breakdown of the quantum non-demolition (QND) aspect of the measurement associated with the critical number photons. An alternative approach avoiding these two issues is longitudinal qubit-resonator coupling [1,2,3]. In our research, we consider circuit realizations of this idea and perform realistic numerical simulations of the longitudinal measurement. We show that the measurement remains QND at higher power than can be expected under transverse coupling. Moreover, comparing transverse and longitudinal qubit readouts, we show that the latter leads to fast and high-fidelity QND measurements.

[1] Nicolas Didier, Jérôme Bourassa, and Alexandre Blais, Phys. Rev. Lett. 115, 203601, (2015)

[2] P.-M. Billangeon, J. S. Tsai, and Y. Nakamura, Phys. Rev. B 91, 094517, (2015)

[3] Susanne Richer and David DiVincenzo, Phys. Rev. B 93, 134501, (2016)

* Maxime Lapointe-Major**Master, Université de Sherbrooke**Director: Michel Pioro-Ladrière**Automated tuning of a quantum dot to the single electron regime*

In this work, we perform automated tuning of a quantum dot to an operational target for any device equipped and measured using a SET. We first extract the position of electron occupancy transitions in a noisy and featureful signal using the phase of the signal, which is computed using a Hilbert transform. From the transition points, we are able to reconstruct transition lines on a two-dimensional stability diagram using image recognition tools. The decision making procedure must be adapted to the gate architecture.

*Pericles PhilippopoulosDoctorate, McGill University*

*Director: Bill Coish*

*Accurate hyperne tensors for electrons and holes in Si and GaAs*Knowing (and controlling) hyperfine interactions in semiconductor nanostructures is important for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory calculations and k.p corrections, we have found accurate hyperfine tensors for electrons and holes in GaAs and Si. Our results indicate significant corrections to previous theoretical estimates for the hyperfine coupling of electrons in GaAs and Si, but are consistent with earlier experimental measurements on Knight shifts and Korringa relaxation. In addition, we make new predictions for the hyperfine tensors of both heavy and light holes in the valence band. These calculations are consistent with T_2* times very recently measured for heavy holes in Si quantum dots [1], and with recent measurements on hole spins in InGaAs quantum dots showing an Ising-like hyperfine coupling [2].

[1] Maurand et al., arXiv:1605.07599 (2016)

[2] Prechtel et al., Nat. Mat. 15, 981 (2016)

*Adrian SolyomMärta Tschudin*

*Master, McGill University*

*Director: Lilian Childress*

*Coupling Nitrogen-Vacancy Spins to a Nanomagnet's Ferromagnetic Modes*The nitrogen-vacancy (NV) center in diamond is a solid state spin system with long coherence times, with promising applications in quantum information and precision sensing. Optical readout of the spin state allows for the detection of magnetic fields, in principle localized at the nano-scale. Thus far we have fabricated Py/Pt nanowires on single-crystal diamond having a layer of NV centers implanted 70nm below the surface. Using the injected spin-transfer torque from the platinum layer, we can efficiently drive ferromagnetic resonance in the wires, and detect the response via its anisotropic magnetoresistance. Efforts toward observing spatially- and spectrally-resolved stray fields using nearby NVs have allowed for detection of the nanomagnet's parametrically driving mode, which may allow for novel ways of controlling NV centers. Finally, we discuss preliminary relaxometry measurements of the coupled NV when only DC currents are applied to gain insight into the magnon mode occupation of the device.