# Programmation de la recherche

### Spring 2018 INTRIQ meeting

*Spring 2018 INTRIQ meeting, May 15 & 16th*

At Hotel Château Bromont

Organizers:

Pr Bertrand Reulet, Université de Sherbrooke

Pr Glen B. Evenbly, Université de Sherbrooke

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 May 15th from 9h30 to 10h30

* Meeting program *

*May 15th*

10h30 - 10h55 Registration

10h55 - 11h00 Opening remarks (Salon A)

11h00 - 12h00 *Max Hofheinz, Professor at Université de Sherbrooke *(Salon A)

*Quantum microwave devices based on inelastic Cooper-pair tunneling*

12h00 - 13h30 Lunch (Dining room - 4 Canards)

13h30 - 14h30 *John Mattsson, Ericsson Research *(Salon A)

*Post-Quantum Cryptography in Practice*

14h30 - 15h00 *Michael Hilke, Professor at McGill University*(Salon A)

*Decoherence in qutrits (3-qubit systems)*

15h00 - 15h30 *Sergei Studenikin, Researcher at National Research Council Canada *(Salon A)

*Hole spin qubits in laterla GaAs/AlGaAs double quantum dots*

15h30 - 16h00 Coffee break (Salon B)

16h00 - 17h00 *Eva Dupont-Ferrier, Professor at Université de Sherbrooke* (Salon A)

*Quantum information with dopants in silicon*

17h00 - Poster sesson with refreshments (Salon B)

19h30 - INTRIQ dinner (Salon C)

*May 16th*

9h00 - 10h00 Dr *Miles Stoudenmire, Center for Computational Quantum Physics* (Salon A)

*Classical and Quantum Machine Learning with Tensor Networks (pdf)*

10h00 - 11h00 Coffee break (Salon B)

11h00 - 12h00 *Dr Dave Touchette, Institute for Quantum Computing *(Salon A)

*Interactive Quantum Information Theory*

12h00 - 13h45 Lunch (Dining room - 4 Canards)

13h45 - 14h45 *William Witczak-Krempa, Professor at Université de Montréal* (Salon A)

*Understanding exotic magnetism through quantum entanglement (pdf)*

14h45 - 15h15 Olivier Landon-Cardinal, Postdoc at McGill University

*Quantitative Tomography for Continuous Variable Quantum Systems*

15h15 - 15h45 Charles Bédard, Doctorate at Université de Montréal

*An Algorithmic Approach to Quantify Emergence (pdf)*

15h45 - 15h50 Closing remarks

*INVITED SPEAKERS*

*John Mattsson*

*Ericsson Research*

The last 5 years, the use of cryptography has exploded and the use of cryptography for authentication, confidentiality, and integrity protection is required even in constrained IoT environments. The use of cryptography everywhere has been enabled by new faster algorithms and security protocols combined with faster hardware. Unfortunately, a large enough quantum computer running Shor’s algorithm would practically break all commonly used public key algorithms such as RSA and ECC. Such algorithms are typically used for authentication and key exchange. NIST has just initiated PQC standardization with the goal of standardizing new asymmetric algorithms replacing RSA and ECC. The new algorithms are based on mathematical problems not affected by Shor’s algorithm (e.g. lattices, codes, multivariate, isogenies). Grover’s algorithms could theoretically break some symmetric algorithms, but it is unknown if it will ever be relevant for practical cryptanalysis. QKD, which only provides unauthenticated key exchange, will likely continue to be a niche product as post-quantum cryptography running on classical computers are likely to provide excellent security to a much lower cost. In this talk we describe the current use cases of cryptography and the effects of quantum computer would affect these, the current status and challenges with post-quantum cryptography running on classical computers and the role of quantum cryptography.

**Post-Quantum Cryptography in Practice**

*Pr William Witczak-Krempa*

*Université de Montréal*

*Understanding exotic magnetism through quantum entanglement (pdf)*I’ll present 2 spin models that host unusual emergent excitations. First, the 1d Motzkin spin chain introduced by Shor et al has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale Density Matrix Renormalization Group (DMRG) simulations, we find that that there are 2 low-energy excitations with distinct and non-trivial dispersion relations. Various correlation functions and entanglement properties will be discussed. Second, I’ll discuss the Heisenberg model on the frustrated kagome lattice, which is one of the most studied and experimentally relevant models for a quantum spin liquid. Despite years of study, its solution remains under debate. Using DMRG on this model, we uncover universal features of neutral Dirac fermions in the entanglement entropy. We infer that these are the fractionalized excitations of the kagome quantum spin liquid. Such methods can be used to study other quantum states of matter, such as systems poised near a quantum critical phase transition.

*Pr Eva Dupont-Ferrier*

*Université de Sherbrooke*

Dopants in silicon are promising candidates for quantum information processing. They form an extremely compact and reproducible quantum system in which the nuclear spin can be used to store quantum information, while the electron spin serves as a means of interfacing nuclear spin with other quantum systems. The nuclear spin in purified silicon has set the record for coherence times in solid state qubits. Spin readout and manipulation for both electron and nuclear spins have been demonstrated, with fidelities beyond the threshold for quantum error correction protocols. But high coherence times come in pair with strong isolation from the environment, i.e. spins of dopants are difficult to address and couple together which prevents realization of two qubits gates.

**Quantum information with dopants in silicon**I will show how integration of dopants in transistors form state of the art CMOS technology could help solve this problem. We use a split-gate transistor to electrically control two dopants connected in series and perform coherent charge exchange between them. For longer range coupling between dopants, a possibility is to use magnetic coupling of the dopants’ spins to superconducting circuits. I will show the first steps in that direction, namely the realization of high quality factor superconducting resonator, tunable in frequency by means of an embedded SQUID and which can perform under magnetic fields.

* **Pr Max Hofheinz *

*Université de Sherbrooke*

In superconducting quantum circuits the Josephson junction is the key element because it is the only strongly nonlinear and dissipationless circuit element we know. Usually it is used in the superconducting state where it acts as a nonlinear inductor. But a small Josephson junction can be nonlinear and dissipationless also when a non-zero DC voltage below the gap is applied. In this case a Cooper pair current can flow through the junction when the energy 2eV of a tunneling Cooper pair can be dissipated in the linear circuit surrounding it, in the form of photons emitted into one or several of its modes. In this inelastic Cooper-pair tunneling regime, the junction acts as a nonlinear drive on the linear circuit. We have tailored this physics into quantum microwave sources, such as single photon sources and measurement devices, such as quantum limited amplifiers. I will show that while these devices tend to be much less coherent than their counter parts using the Josephson junction in the zero-voltage state of the junction, they still allow for quantum-limited performance and more readily accept very open configurations allowing for high bandwidth.

**Quantum microwave devices based on inelastic Cooper-pair tunneling**

*Dr Miles Stoudenmire*

*Flatiron Institute - Center for Computational Quantum Physics (CCQ)*

**Over the last decade, there have been enormous gains in machine learning technology primarily driven by neural networks. A major reason neural networks have outperformed older techniques is that the cost of optimizing them scales well with the size of the training dataset. But neural networks have the drawback that they are not very well understood theoretically.**

Classical and Quantum Machine Learning with Tensor Networks (pdf)

Classical and Quantum Machine Learning with Tensor Networks (pdf)

Recent work by several groups has explored an alternative approach to creating machine learning model functions based on tensor networks, which are a technique developed in physics to parameterize complicated many-body quantum wavefunctions. The cost of training tensor network models scales similarly to the cost of training neural networks. In addition, their relatively simple, linear structure has provided good theoretical understanding of their properties, and underpins many powerful techniques to optimize and manipulate them.

After introducing tensor network machine learning models, I will discuss some of the techniques to optimize them and results for supervised and generative machine learning tasks. Then I will discuss a recent tensor network based proposal to formulate hybrid quantum-classical algorithms for machine learning with quantum computers.

*Dr Dave Touchette*

*Institute for Quantum Computing and Perimeter Institute*

Shannon’s information theory has revolutionized our approach towards two prominent problems in unidirectional communication: source compression and noisy coding.

**Interactive Quantum Information Theory**

Over the last two decades, there has been significant progress made towards developing quantum analogues for these.

Meanwhile, an interactive information theory has also been developed over the last two decades for two-way classical communication problems, both for analogues of source compression and for noisy channel coding.

Two-way quantum communication has also been studied in depth over that span, providing unconditional quantitative quantum advantages. (Even exponential ones!)

In this talk, I will discuss the development in recent years of an interactive quantum information theory to study two-way quantum communication.

In particular, I will discuss how we can maintain quantum advantage for two-way communication over noisy quantum communication channels.

**INTRIQ SPEAKERS**

*Charles BédardDoctorate, Université de Montréal*Fundamentally data-driven, algorithmic information theory deals equally with the description of physical systems and their underlying theories. This provides the tools to quantify when, for a complex system, new structures emerge. To familiarize the audience to the insights that algorithmic information theory brings to physics, I shall first present examples from statistical physics.

**An Algorithmic Approach to Quantify Emergence (pdf)**

*Michael Hilke**Professor, McGill University**Decoherence in qutrits (3-qubit systems)*

I will start with an introduction on qutrit and qudit systems (instead of 2 level systems they are 3 or more level systems) and overview their potential advantages and physical realizations, before discussing our work with Mackenzie, Eleuch and Boudreault on the peculiar decoherence properties of qutrit systems.

*Olivier Landon-Cardinal**Postdoc, McGill Université** Quantitative Tomography for Continuous Variable Quantum Systems*We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error.

Olivier Landon-Cardinal, Luke C.G. Govia, and Aashish A. Clerk

Phys. Rev. Lett. 120, 090501 (2018)

*Sergei Studenikin**Senior researcher, National Research Council Canada**Hole spin qubits in laterla GaAs/AlGaAs double quantum dots*

The motivation for developing the hole spin platform in GaAs is based on a list of potentially attractive features such as a predicted reduced hyperfine interaction between hole and nuclear spins, optically active direct band-gap material and an in situ tuneable effective g-factor with field orientation down to zero (useful properties for hybrid spin-photonic devices), and large spin-orbit coupling for fast gate operations and spin readout. In my talk I will present our resent results on the single hole hybrid spin-charge qubits, and two-hole singlet-triplet qubit.

The single hole regime has been explored via the Landau-Zener-Stuckelberg (LZS) interferometry which involves both spin conserving and spin-flip tunneling processes. The LZS patterns evolve with microwave frequency from discreet, often referred as photon assisted tunneling or PAT, at high frequencies to continuous LZS fringes at low frequencies. Taking LZS measurements at different magnetic fields we observe two separate sets of LZS fringes offset by the Zeeman energy [1]. In order to measure spin relaxation time T1 of a single hole spin vs magnetic field we suggest a novel single-shot technique employing charge latching mechanism [2] in combination with large spin-orbit coupling for fast spin-selective tunnelling and readout. Additionally, we extend our LZS measurements to the two-hole regime near the (02)-(11) transition. The results of the LZS interferometry of the singlet-triplet spin qubit will be presented vs. detuning, magnetic field, and pulse duration.

[1] A. Bogan et al., arXiv:1711.03492 (2017); PRL (in press)

[2] S. A. Studenikin, et al., Appl. Phys. Lett. 101, 233101 (2012).

*POSTER SESSION*

*Thomas E. Baker**Postdoc, Université de Sherbrooke**Director: Glen Evenbly** Selecting initial states from Genetic Tempering for efficient Monte Carlo sampling*An alternative to Monte Carlo techniques requiring large sampling times is presented here. Ideas from a genetic algorithm are used to select the best initial states from many independent, parallel Metropolis-Hastings iterations that are run on a single graphics processing unit. This algorithm represents the idealized limit of the parallel tempering method and, if the threads are selected perfectly, this algorithm converges without any Monte Carlo iterations--although some are required in practice. Models tested here (Ising, anti-ferromagnetic Kagome, and random-bond Ising) are sampled quickly with a small uncertainty that is free from auto-correlation.

[1] T.E. Baker, arXiv:1801.09379

*Simon Bertrand,**Doctorate, McGill University**Director: Jack Sankey***Progress toward optical control of mechanical geometry**

We report progress toward creating a tunable, localized mechanical mode in a phononic crystal using radiation pressure from light [1]. Specifically, we describe fabrication techniques producing consistently 100 nm to 300 nm thick stoichiometric SiN freestanding crystals with an area as large as 20 mm², up to 2750 crystal unit cells, and tethers as narrow as ~ 1 μm. 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 mid-gap frequency as high as 0.8), consistent with COMSOL simulations. We expect a localization length of ~ 1 unit cell for our optimal devices. We first attempt to localize the band-edge mode by modifying its mechanical frequency via a position-dependent bolometric force. Here, we use a low-finesse Fabry-Pérot cavity formed by the tip of an optical fiber and a Pt-coated phononic crystal. The position of the phononic crystal modulates the bolometric force, thereby creating a bolometric spring when slightly detuned from the cavity resonance. We measure a 9% decrease in the band-edge mode frequency by augmenting the input power by a factor of 5, before blowing up the device due to heat absorption or antidamping. To avoid this, we are now shifting the experiment toward using radiation pressure from light instead, by placing a phononic crystal inside a fiber cavity. We discuss design considerations for such a cavity.

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

*Julien Camirand*

*Doctorate, Université de Sherbrooke*

*Director: Michel Pioro-Ladrière*

*Silicon Platform for quantum Dot Spin Qubits*

*Agustin Di Paolo*

*Doctorate, Université de Sherbrooke*

*Director: Alexandre Blais*

*Nanowire Superinductance Fluxonium Qubit*Disordered superconducting materials provide a new capability to implement novel circuit designs due to their high kinetic inductance. Here, we realize a fluxonium qubit in which a long NbTiN nanowire shunts a single Josephson junction. We explain the measured fluxonium energy spectrum with a nonperturbative theory accounting for the multimode structure of the device in a large frequency range. Making use of multiphoton Raman spectroscopy, we address forbidden fluxonium transitions and observe multilevel Autler-Townes splitting. Finally, we measure lifetimes of several excited states ranging from T1 = 620 ns to T1 = 20 μs, by applying consecutive π-pulses between multiple fluxonium levels. Our measurements demonstrate that NbTiN is a suitable material for novel superconducting qubit designs.

*Vincent Dumont**Doctorate, McGill University**Ultra-short Optomechanical Fabry-Perot Cavities*

We report progress toward creating a wavelength-scale, flexural Fabry-Perot cavity comprising a flat mirror and a ~90 nm thick SiN membrane. Using this structure as a "compound input mirror" of a 10-cm-long high-finesse optical cavity, we show that we can tune the optomechanical coupling from purely dispersive to purely dissipative. With the incorporation of a fiber mirror in the membrane's etch pit, this system could also enable "membrane-in-the-middle" optomechanical systems having cavity lengths comparable to telecom laser wavelengths -- a feature more commonly associated with on-chip systems – wherein the optomechanical coupling rate would be significantly larger than that of existing free space or fiber cavity systems.

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

*Pierre Février**Postdoc, Université de Sherbrooke**Director: Bertrand Reulet**Non-Gaussian micro-wave field generation by a tunnel junction*

Quantum nature of voltage fluctuations across a tunnel junction have been demonstrated in previous works [1][2]. The generated states of the E.M. field (One and two modes squeezed vacuum) are only characterized by second order voltage correlators (covariances). In this project we go a step farther with the generation of non-gaussian states, characterized by third order voltage correlators (coskewnesses), by photoassisting the tunnel junction at three time the detection frequency. In this poster, I show preliminary results in the classical regime (hf<kT), where the junction is adiabatically driven. I'll show that the probability density in the phase-space defined by the two quadradures of the measured voltage have a third order rotational symmetry. I'll also identify several contributions to the third order voltage correlator, such as feedback by the environment. This measurement validates our experimental setup, for future measurements in the quantum limit (hf>kT).

[1] G. Gasse, C. Lupien, and B. Reulet, Phys. Rev. Lett. 111, 2013

[2] J.C. Forgues, C. Lupien, and B. Reulet, Phys. Rev. Lett. 113, 2014

*Louis Haeberle**Master, Université de Sherbrooke**Director: Michel Pioro-Ladrière**Frequency-tunable 3D Microwave Resonator for Coherent Control of Large NV Ensembles*

Nitrogen-vacancy color centers in diamond show promise as high-sensitivity vector magnetometers, due to their excellent room temperature coherence time, and the ability to address them using optical and microwave pulses (Optically Detected Magnetic Resonance). One way to increase the sensitivity of measurements is to use large ensembles of NV⁻ centers to gain a statistical advantage; however, this requires the ability to apply an uniform microwave field to the whole ensemble. Combining optical excitation and readout with uniform microwave excitation in the same device has been shown to be challenging in past experimental realizations. Here, we report the development of a three-dimensional, re-entrant microwave resonator geometry which allows uniform (0.3% RMS error in field amplitude) and frequency-tunable (300 MHz tuning range) microwave excitation on macroscopic (~3mm³) volumes, as well as laser excitation and photoluminescence measurement. We also show results of ODMR measurements of a large (>10¹² spins) NV⁻ ensemble. This work will be used in an enhanced-sensitivity room-temperature magnetometer, but could also be applied to any experiments measuring spin resonance on large samples.

*Samuel Houle*

*Doctorate, Université de Sherbrooke*

*Director: Bertrand Reulet*

*Photo-Assisted Dynamical Coulomb Blockade*The P(E) theory has proven itself a powerful tool for explaining transport through a tunnel junction exhibiting Dynamical Coulomb Blockade (DCB), describing DCB as an inelastic exchange of photons between the tunneling electrons and their electromagnetic environment. Although very efficient, that theory does not detail in a clear way how the dynamical response of the environment influences DCB i.e. how the feedback of the interaction between the electromagnetic environment and a tunneling electron impacts the following ones. This experiment, using ac excitation, aims at unveiling this dynamical aspect of DCB.

*Pavithran Iyer**Doctorate, Université de Sherbrooke**Director: David Poulin**chflow -- A software tool for quantum error correction and noise characterization*

Arbitrary-precision control of quantum systems is a lofty goal due to the sensitivity of quantum states to environmental influences that manifest themselves as errors in a quantum algorithm. Quantum error correction and, in general, fault-tolerant schemes have been invented to guarantee reliable quantum computation in the presence of noise. However, in most cases they have been developed assuming a simplified error model corresponding to probabilistic application of Pauli operators. While Pauli noise models are convenient for demonstrating proof of concepts, many quantum processes are poorly approximated by the Pauli errors. Nevertheless, it is crucial to have precise estimates of the quality and quantity of hardware resources required for a quantum algorithm before attempting to build a physical realization. Inspired by this requirement, we have developed a software tool, called "chflow", (available online on GitHub), that provides numerical estimates of the performance of an error correction scheme under different noise processes. Concretely, the software tool can be applied to study the response of any stabilizer error correction scheme under any completely positive trace preserving (CPTP) noise process. Simulations of quantum error correction with generic noise processes are quite resource intensive. However, these could be avoided if the noise on the logical information can be accurately estimated using some parameter(s) of the physical noise model. In the work of [arXiv:1711.04736], it has been observed that standard error metrics can only provide very coarse estimates of the noise on the logical information. The tools in "chflow" use machine learning techniques to derive new operational definitions of noise strength in physical processes that help provide better estimates of the noise on the logical information than previously known metrics.

*Pericles Philippopoulos*

*Doctorate, McGill University*

*Director: Bill Coish*

*First-Principles Hyperfine Tensors in Si and GaAs*Electron (hole) spins confined to semiconductor nanostructures interact with the nuclear spins making up the nanostructure via the hyperfine interaction. It is important to understand the hyperfine interaction so that first, the decoherence it causes can be limited, and second, to use the induced dynamics to our advantage. We have used density-functional theory (DFT) to calculate the wavefunctions of the states at the conduction-band minima and valence-band maximum in GaAs and Si so that we may evaluate the hyperfine constants for electrons and holes in these materials. This method allows us to include non-collinear terms and compute effects of the nuclear-orbital interaction. For the electrons in silicon and GaAs, our results are consistent with past experiments only when the fully-relativistic hyperfine operator is considered. For holes, we find that the form of the hyperfine Hamiltonian in the heavy-hole subspace is Ising-like which can yield interesting benefits such as driving the system to motional-averaging regime with an applied in-plane magnetic field, which limits the hyperfine interaction's ability to induce decoherence on the hole spin.

*Édouard Pinsolle*

*Professional, Université de Sherbrooke*

*Director: Bertrand Reulet*

*We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the cross-over from elastic to inelastic transport.*

**Non-Gaussian Current Fluctuations in a Short Diffusive Conductor**

*Claude ROhrbacher**Master, Université de Sherbrooke**Director: Michel Pioro-Ladrière**Fan-Out Process on 28nm FD-SOI CMOS structure for Cryogenic Characterisation*

The compatibility of silicon qubits with CMOS technology shows great promise for co-integration of quantum systems with classical control and read-out systems for large scale integration [1-2]. To achieve co-integration, the behaviour of classical MOS structure at cryogenic temperature needs to be investigate as solid state quantum systems need to operate at such temperature. Since these devices are fabricated within STMicroelectronics multi projects wafers, the devices size and location makes them hard to connect for cryogenic characterization. To overcome this issue we present here a Back-End Of Line (BEOL) Fan-Out process on a CMOS advanced structure for co-integration to facilitate cryogenic characterisation. This process is compatible with flip chip using an interposer as an alternative to wire bonding.

*Marc-Antoine Roux**Master, Université de Sherbrooke**Director: Michel Pioro-Ladrière**Use of a guard ring as an ESD protection component for tunnel junctions*

Modern electronic fabrication processes allow to make nanoscale devices. However, the small size of those devices increases their sensibility to electrostatic discharge (ESD). In many cases, it becomes challenging to manipulate and characterize samples without damaging them especially when many preparation steps are required before the final experiment. Therefore, the use of a guard ring that shorts every connection on the samples can protect them when used with simple ESD precautions. The guard ring can then be removed after the preparation process with a diamond tip when the samples are adequately grounded. On Al/Co tunnel junctions that can tolerate only a maximum tension of a few volts, it has been possible to achieve a yield of 93% throughout the preparation process which includes dicing and wire bonding. The effect of sharp edges in the junction design has also been investigated but the geometry of the junctions doesn’t influence ESD occurrences when the work functions of the metals are similar.

*David Roy-GuayPostdoc, Université de SherbrookeDirector: Michel Pioro-Ladrière*

**Qmag and QMSat : Prototyping Diamond Based Magnetometry for On Ground and Space Geophysics**

*Baptiste Royer**Doctorate, Université de Sherbrooke**Director: Alexandre Blais**Qubit Parity Measurement by Parametric Driving in Circuit QED*

Multi-qubit parity measurements are essential to quantum error correction. Current realizations of these measurements often rely on ancilla qubits, a method that is sensitive to faulty two-qubit gates and which requires significant experimental overhead. We introduce a hardware-efficient multi-qubit parity measurement exploiting the bifurcation dynamics of a parametrically driven nonlinear oscillator. This approach takes advantage of the resonator's parametric oscillation threshold which is a function of the joint parity of dispersively coupled qubits, leading to high-amplitude oscillations for one parity subspace and no oscillation for the other. We present analytical and numerical results for two- and four-qubit parity measurements with high-fidelity readout preserving the parity eigenspaces. Moreover, we discuss a possible realization which can be readily implemented with the current circuit QED experimental toolbox. These results could lead to significant simplifications in the experimental implementation of quantum error correction, and notably of the surface code.

*Lucas St-JeanMaster, Université de Sherbrooke*

*Director: Alexandre Blais*

*Hardware Efficient Schemes for Quantum Computation with Photonic Cat States*Fault tolerant quantum computing protocols require thousands of physical qubits per logical qubit in order to carry out quantum computations in the presence of unknown noise processes. The resulting overhead of physical qubits presents a daunting challenge for experimental realization of a large scale, fault-tolerant, quantum computer. However, a better understanding of the noise inflicting the hardware elements can help significantly reduce the overhead for fault tolerance. Precisely, systems with biased noise can be used to improve standard error correction schemes, with a small overhead. A particularly attractive candidate for such a system with highly biased noise is using stabilized microwave-photon cat states. We will present cat state stabilization schemes and discuss how photonic noise processes affect the underlying quantum information in this framework. Moreover, we examine the performance of a simple 5-qubit repetition code with these stabilized cat states and compare it with the well-known 5-qubit code using standard Fock states and their unbiased noise. The tradeoff between fidelity of encoded information and the associated overhead is better in the first case which highlights the potential advantage of optimizing error correction for biased noise in cat states. Further investigations on fault tolerant quantum computation schemes optimized for cat states’ error model could exhibit a reduced resource overhead compared to schemes for unbiased noise.

*Sara Turcotte**Master, Université de Sherbrooke**Director: Michel Pioro-Ladrière**Micro-magnet induced spin-orbit coupling for Majorana modes*

Majorana fermions are topologically protected quasi-particles that appear at the end of unidimensional semiconducting wires with large spin-orbit coupling and induced superconductivity. While recent implementations mostly rely on nanowires with large intrinsic spin-orbit coupling, these approaches offer poor control on properties such as the length of the wire and the confinement potential. Here, versatile designs consisting of a micro-magnet arrays are explored to engineer the spin-orbit coupling in a two- dimensional electron gas. On one hand we find, suitable conditions for the experimental observation of Majorana fermions in gallium arsenide and silicon through numerical simulations. On the other hand, we present first experimental steps toward direct measurement of the spin-orbit coupling induced by a single magnet in a magnetic focusing setup.

*Maxime Tremblay**Master, Université de Sherbrooke**Director: David Poulin** A tensor network approach to coding theory*This work is based on two recent developments in information theory and many-body physics. The first one being the introduction of capacity achieving error correcting codes named polar codes by Erdal Arikan in 2009 and the second one being the introduction of branching MERA by Glen Evenbly and Guifre Vidal in 2014. Later in the same year, it has been shown by Andy Ferris and David Poulin that the task of decoding can be map to contracting a tensor network. Therefore, it is possible to design an efficient decoder by finding an efficiently contractable tensor network. Based on that idea, it was possible to generalize polar codes to a broad family of codes called branching MERA codes that we can decode in an efficient manner using the so called successive cancellation decoder. Here we present the methods and software that we developed in order to analyse codes in that family and the underlying theory that allows us to link error correcting codes and tensor networks.