# Axes 1 - Software

### Fall 2020 INTRIQ meeting

When : Monday-Tuesday, November 9^{th}&10^{th}

Organizers :

Pr Denis Seletskiy, Polytechnique Montréal

Pr Louis Salvail, Université de Montréal

**Online event **

**Partners of the Fall 2020 INTRIQ events**

*Discussion tables*

* **To see the video of : Institut quantique, Prompt, COPL, Quantino** & Quantino virtual tour**, Ki3 Photonics,** *

*2-day program of Fall INTRIQ Meeting*

**November 9 ^{th}**

9:00 - 9:10 Opening remarks (on Zoom)

9:10 - 9:45 Professor Nicolas Godbout, Polytechnique Montréal, Canada

**Québec Quantum overview**

9:45 - 10:30 Professor Jack Sankey, McGill University, Canada

* Sensing Stray Fields from Spin-Hall-Controlled Magnetic Nanowires with Nitrogen-Vacancy Centers in Diamond*10:30 - 11:00 Dr Joël Griesmar, Université de Sherbrooke, Canada

**11:00 - 11:30 Coffee break (on Remo platform)**

*Towards a Microwave Single Photon Detector Using Inelastic Cooper Pair Tunneling*

Visit discussion tables

Visit discussion tables

11:30 - 12:00 FRQNT strategic networks presentations (on Remo platform)

*Professor*

*Mounir Boukadoum, ReSMiQ director*

*Professor Sophie Larochelle, COPL director, Presentation slides*

12:00 - 13:00 Lunch (on Remo platform)

*Visit discussion tables*

13:00 - 14:00 Professor Christine Silberhorn, Paderborn University, Gemany (on Zoom)

*Non-linear integrated quantum optics with pulsed light*14:15 - 15:00 Partner's talk (on Remo platform)

Optonique

Prompt & Prima

Jérome Cabana, Mitacs - Mitacs supporting collaborative research

15:00 - 15:30 Coffee break (on Remo platform)

Visit discussions tables

Visit discussions tables

**Session in honor of Professor David Poulin's scientific contributions**

**(on Zoom)**15:30 - 16:00 Professor Raymond Laflamme, IQC - Waterloo University, Canada

* Algorithmic cooling*

16:00 - 16:30 Professor Professor Kenneth R. Brown, Duke University, USA

** Advantages of Subsystem Codes**

16:30 - 17:00 Dr Nicolas Delfosse, Microsoft, USA

*Decoding Hardware Requirements for Fault-Tolerant Quantum Computation*

17:00 - 17:30 Dr Steven T. Flammia, AWS Center for Quantum Computing, USA

*The XZZX Surface Code*

**November 10 ^{th}**

9:00 - 10:00 Professor Achim Kempf, Perimeter Institute, Canada (On zoom)

* Quantum Information Theoretic Methods in Inflationary Cosmology*

10:00 - 11:00 Coffee break (on Remo platform)

*Visit posters or discussions tables *

11:00 - 12:00 Professor Anand Natarajan, Massachusetts Institute of Technology (MIT), USA (On zoom)

*MIP* = RE*

12:00 - 13:00 Lunch (on Remo platform)

*Visit posters or discussions tables *

13:00 - 14:00 Professor Omar Fawzi, École normale supérieure de Lyon, France (Cancelled)

*Constant overhead fault-tolerance using quantum expander codes*

*Please joint us at the poster competition on Remo*

14:00 - 14:45 Professor Kartiek Agarwal, McGill University, Canada (On zoom)

**'Draiding' majoranas for quantum computing and Hamiltonian engineering**14:45 - 15:30 Coffee break (on Remo platform)

*Visit posters or discussions tables*

15:30 - 16:30 Professor Oussama Moutanabbir, Polytechnique Montréal, Canada (On zoom)

*An All-Group IV Platform for Photonics and Quantum Engineering*16:30 - 17:00 Dr Supartha Podder, Ottawa University, Canada (On zoom)

**17:00 - Poster awards announcement and closing remarks (On zoom)**

*Symmetries, graph properties, and quantum speedups*

*Invited speakers*

*Session in honor of Professor David Poulin's scientific contributions*

*Professor Kenneth R. BrownDuke University, USA*

**Advantages of Subsystem Codes**Quantum error correction allows us to make high-fidelity encoded qubits from noisy qubits. David Poulin pioneered subsystem quantum error correction where not all degrees of freedom are corrected. This gauge freedom can lead to improved decoding efficiency and remarkably better performance for errors outside the random Pauli error model. I will describe our theoretical work on leakage errors in the context of subsystem codes (arXiv:1903.03937) and our experimental implementation of the Bacon-Shor subsystem code with the University of Maryland (arXiv:2009.11482).

*Dr Nicolas DelfosseMicrosoft, USA*

**Decoding Hardware Requirements for Fault-Tolerant Quantum Computation**A major challenge for quantum error correction is to design a decoder capable of identifying errors faster than they accumulate. In this talk, I will describe a decoder micro-architecture for surface code error correction which can be executed fast enough to correct errors in a large scale quantum computer. I will discuss different computer architecture techniques which provides simultaneously a hardware acceleration of the decoder and a significant reduction of the bandwidth and decoding hardware requirements.

*Based on joint work with Poulami Das, Chris Pattison, Bobbie Manne, Doug Carmean, Krysta Svore, Moin Qureshi*

*https://arxiv.org/abs/2001.06598*

*https://arxiv.org/abs/2001.11427*

*Dr Steven T. FlammiaAWS Center for Quantum Computing, Pasadena, USA*

**The XZZX Surface Code**We show that a variant of the surface code---the XZZX code---offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favorable sub-threshold resource scaling that can be obtained by specializing a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation. We finally suggest some small-scale experiments that could exploit noise bias to reduce qubit overhead in two-dimensional architectures. Joint work with J. P. Bonilla Ataides, D. K. Tuckett, S. D. Bartlett, and B. J. Brown, preprint: arXiv:2009.07851.

*Professor Raymond Laflamme**Institute for quantum computing (IQC) - Waterloo Unversity, Canada Algorithmic coolingAlgorithmic cooling has been shown to purify qubits by redistribution of entropy and multiple contact with a heat-bath. In this talk, I will give an overview of*

*the field and mention recent results where an implicit restriction assumed in all previous work about the interaction with the bath has been removed. I will show that more efficient algorithmic cooling can be achieved. I will then turn to another application of algorithmic cooling, distinguishing state preparation and measurment errors in quantum computers.*

*INTRIQ Meeting invited speakers*

*Professor Achim KempfPerimeter Institute - Waterloo Unversity, Canada*

**Quantum Information Theoretic Methods in Inflationary Cosmology**At the Planck scale, and in the very early universe, the very notions of space-time and of matter are expected to reach the limit of their range of applicability. The use of quantum information-theoretic tools could be useful in these circumstances because even if the phenomena at the Planck scale are far removed from our intuition, it should always make sense to quantify how much information processing is involved. I will first review related information-theoretic concepts such as covariant bandlimitation. I will then focus on the prospect that information-theoretic features of Planck scale physics have left an imprint in inflation and, therefore, possibly observably, in the cosmic microwave background.

*Professor Omar FawziÉcole normale supérieure de Lyon, France Constant overhead fault-tolerance using quantum expander codes We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the number of logical qubits involved in the ideal computation is asymptotically constant, and can even be taken arbitrarily close to 1 in the limit of small physical error rate. This improves on the polylogarithmic overhead promised by the standard threshold theorem. To achieve this, we exploit a framework introduced by Gottesman together with a family of constant rate quantum codes, quantum expander codes. Our main technical contribution is to analyze an efficient decoding algorithm for these codes and prove that it remains robust in the presence of noisy syndrome measurements, a property which is crucial for fault-tolerant circuits. We also establish two additional features of the decoding algorithm that make it attractive for quantum computation: it can be parallelized to run in logarithmic depth, and is single-shot, meaning that it only requires a single round of noisy syndrome measurement.Based on joint work with Antoine Grospellier and Anthony Leverrieravailable https://arxiv.org/abs/1808.03821.*

*Professor Oussama MoutanabbirPolytechnique Montréal, Canada An All-Group IV Platform for Photonics and Quantum EngineeringCompound semiconductors have been successfully used for precise and simultaneous control of lattice parameters and bandgap directness bringing to existence a variety of functional heterostructures and low-dimensional systems. Extending this paradigm to group IV semiconductors will be a true breakthrough that will pave the way to create an entirely new class of scalable, silicon-integrated optoelectronic, photonic, and quantum devices. In this presentation, I will share with the INTRQ community strategies and new material systems to independently engineer lattice dynamics and band structure in group IV device structures. The materials to be discussed are grown epitaxially using chemical vapor deposition system equipped with isotopically enriched precursors with purity higher than 99.9%: 28SiH4, 29SiH4, 30SiH4, 74GeH4, and 76GeH4 in addition to Sn precursors. I will address (Si)GeSn semiconductors and their use in Si-based mid-infrared photonics and optoelectronics. I will also describe our progress in materials and metrology to control stable isotopes as an additional degree of freedom the tailor the basic behavior of semiconductor quantum structures.*

*Professor Anand NatarajanMassachusetts Institute of Technology (MIT), USA*

**MIP* = RE**Interactive proof systems are a classic idea in theoretical computer science, and have led to fundamental advances in complexity theory and cryptography. Remarkably, in quantum information, interactive proof systems with multiple provers have become an important tool for studying quantum entanglement and nonlocality, extending the pioneering work of Bell in the 1960s and Tsirelson in the 80s. In this talk I will discuss our recent work characterizing the power of the complexity class MIP* of such proof systems where the provers share entanglement. On the complexity side, we show that MIP* is equal to the class of recursively enumerable languages, a class including the halting problem. As consequence we show a separation between two models of quantum nonlocality: the tensor product and the commuting operator model. This answers Tsirelson’s problem, and also implies a negative answer to the Connes embedding problem in operator algebras. At the heart of this work are new protocols that use classical PCP techniques together with the rules of quantum mechanics to let a classical client precisely control an untrusted quantum server.

*Based on https://arxiv.org/abs/2001.04383, joint with Zhengfeng Ji, Thomas Vidick, John Wright, and Henry Yuen*

*Professor Christine SilberhornIntegrated Quantum Optics, Department Physics, Universität Paderborn, Germany*

**Non-linear integrated quantum optics with pulsed light***Quantum technologies promise a change of paradigm for many fields of application, for example in communication systems, in high-performance computing and simulation of quantum systems, as well as in sensor technology. They can shift the boundaries of today’s systems and devices beyond classical limits and seemingly fundamental limitations. Photonic systems, which comprise multiple optical modes as well as many nonclassical light quantum*

*states of light, have been investigated intensively in various theoretical proposals over the last decades. However, their implementation requires advanced setups of high complexity, which poses a considerable challenge on the experimental side. The successful realization of controlled quantum network structures is key for many applications in quantum optics and quantum information science.*

*INTRIQ speakers*

*Professor Kartiek AgarwalMcGill University*

**'Draiding' majoranas for quantum computing and Hamiltonian engineering**We propose and analyze a family of periodic braiding protocols in systems with multiple localized Majorana modes (majoranas) for the purposes of Hamiltonian engineering. The protocols rely on double braids – draids – which flip the signs of both majoranas, as one is taken all the way around the other. Rapid draiding can be used to dynamically suppresses some or all inter-majorana couplings. Suppressing all couplings can drastically reduce residual majorana dynamics, producing a more robust computational subspace. Non-trivial topological models can be obtained by selectively applying draids to some of the overlapping (imperfect) majoranas. Remarkably, draids can be implemented without having to physically braid majoranas or performing projective measurements. For instance, we show that draids can be performed by periodically modulating the coupling between a quantum dot and a topological superconducting wire to dynamically suppress the hybridization of majoranas in the quantum wire. In current experimental setups, this could lead to suppression of this coupling by a few orders of magnitude. The robustness of this protocol can be shown to parallel the topological robustness of physically braided majoranas. We propose an architecture that implements draids between distant majorana modes within quantum register using a setup with multiple quantum dots and also discuss measurement-based ways of implementing the same.

*Dr Joël GriesmarPostdoctoral fellow at Université de SherbrookeSupervisor : Max Hofheinz*

**Towards a Microwave Single Photon Detector Using Inelastic Cooper Pair Tunneling**The detection of single photons is a fundamental quantum measurement, complementary to linear amplification. However, in the microwave domain this is a difficult task due to the low energy of the photons. We present here a photo-multiplier using the energy of a Cooper pair tunneling across a voltage-biased Josephson junction to convert one microwave photon into several photons at a different frequency. This process relies on the strong non-linearity provided by the interaction between a Josephson junction and its high-impedance electromagnetic environment. We have fabricated and measured a device composed of a low critical current SQUID galvanically coupled to two high-impedance resonators. It showed conversion from one to two photons with an efficiency of 80% and also exhibited conversion from one to three photons. By cascading two of these multiplication stages and adding a quantum limited amplifier, it should be possible to discriminate itinerant single photon states from vacuum without dead time.

*Professor Jack SankeyMcGill University*

**Sensing Stray Fields from Spin-Hall-Controlled Magnetic Nanowires with Nitrogen-Vacancy Centers in Diamond**The individual spins associated with nitrogen-vacancy (NV) centers in diamond can serve as exquisite nanoscale magnetic field sensors, enabling (among other things) the measurement of stray fields near YIG [1] and Py [2] films influenced by spin transfer torques. This presentation provides an overview of our latest efforts to (i) reliably fabricate high-quality Py/Pt nanowires on a single-crystal diamond substrate while maintaining the performance of NVs implanted 10's of nanometers below the surface, (ii) develop a Bayesian protocol for optimal estimation of NV spin relaxation, and (iii) estimate thermal time scales in these (and other) nanocircuits while calibrating the applied microwave current. Time permitting, I will also discuss preliminary measurements (microwave transport and NV magnetometry) of driven and thermally populated spin wave modes controlled by spin Hall torques.

*Dr Supartha PodderPostdoctoral fellow at Ottawa UniversitySupervisor : Anne Broadbent*

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

arxiv:2006.12760

**Symmetries, graph properties, and quantum speedups**Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

arxiv:2006.12760

*Posters*

*Sophie Berthelette (reference : poster #1) See the Poster and see the Video**PhD student at Université de Montréal**Supervisor : Gilles Brassard**From Pseudo-Telepathy Games to Kochen-Specker Sets**It is known that, for a pseudo-telepathy (PT) game with 2 players, the minimal input cardinality is 3 x 3, the minimal output cardinality is 2 x 3 and the minimal dimension of the shared entangled state is 3 x 3. Some PT games are known such that 2 out of these 3 minimal conditions are met (e.g. the impossible coloring game), but no game is known such that all 3 conditions are met simultaneously. Is there such a "minimal" PT game? In fact, it falls down to asking the following question: what is the size of the smallest Kochen-Specker (KS) set in 3 dimensions? These intriguing sets of vectors show the incompatibility between realism and non-contextuality in quantum mechanics. Wolf and Renner showed that there is an interesting link between PT games and KS sets. I will explore this relation and explain how it could be used to prove the existence (or not) of a "minimal" PT game.*

*Patrick Cusson (reference : poster #2) See the Poster and see the VidéoPhD student at Polytechnique MontréalSupervisor : Denis Seletskiy*

**Conditioned thermal states for subcycle sampling of quantum fields**Time-domain quantum electrodynamics is coming of age with recent demonstrations of direct probing of femtosecond quantum fields. In current experimental implementations, the achievable signal-to-noise ratio of these weak measurements is ultimately limited by the onset of quantum back-action. Here, we propose to get around this issue by harnessing nonclassical states of light from the post-selection of bright entangled sources, dramatically improving detection capabilities for field-resolved metrology.

*Felix Fehse (reference : poster #3) See the Poster and see the Video**PhD student at McGill University**Supervisor : Bill Coish**Adiabatic conversion for qubit readout: Optimal pulse shapes and dephasing*

*The balance between 'adiabaticity' and dephasing of adiabatic conversion schemes can be optimized to improve performance. We give an explicit construction that allows for optimal state conversion in qubit readouts. Applying this scheme to the specific case of spin qubits in quantum dots, we show that a high-fidelity (better than 99.9%) single-shot all-electrical readout is possible.*

*Tristan Martin (reference : poster #4) See the Poster and see the Video**Undergraduate intern at McGill University**Supervisor : Kartiek Agarwal**Exploring the effect of noise on (polyfractal) driving to create multiple symmetries in many-body quantum systems**Symmetries (and their spontaneous rupturing) can be used to protect and engender novel quantum phases and lead to interesting collective phenomena. In [1], the authors described a general dynamical decoupling (“polyfractal”) protocol that can be used to dynamically engineer multiple discrete symmetries in many-body systems. The present work expands on [1] by studying the effect of noise on such a dynamical scheme. To make the analysis tractable, and numerical simulations efficient, we insert errors in the pattern of a Fibonacci replacement sequence. We find generically that the scheme yields symmetries that are protected up to exponentially long times in the inverse error rate. We also discuss how such symmetries can be engineered to protect quantum information and the affect of noise using this scheme. **1. K. Agarwal, I. Martin, Dynamical enhancement of symmetries in many-body systems, Phys Rev. Lett. 125, 080602 (2020)*

*Zoé McIntyre (reference : poster #5) See the Poster and see the Video**PhD student at McGill University**Supervisor : Bill Coish**Non-Markovian qubit spectroscopy in cavity QED*

*Markovian models of qubit dynamics break down for charge qubits coupled to 1/f noise and for spin qubits coupled to slow nuclear-spin baths. For spin/charge qubits also coupled to a cavity, it can be difficult to directly extract time-domain coherence dynamics because the AC control fields used to prepare and measure these qubits have the potential to excite the cavity mode. We present a way of extracting the coherence dynamics of a qubit coupled to a cavity purely from frequency-dependent measurements of the cavity response in cavity quantum electrodynamics (QED). In contrast to a more standard equation-of-motion approach, we make neither a Markov approximation nor a weak-coupling approximation for the qubit-bath dynamics. Using this approach, we calculate the spectroscopic response of a spin qubit coupled to nuclear spins. This response shows pronounced non-Lorentzian features, indicative of non-Markovian dynamics, arising from a many-spin collective mode. We also consider the case of a qubit coupled to a single bosonic mode corresponding to, e.g., a mechanical degree of freedom, phonon, or cavity mode. In this instance, strong coupling gives rise to higher harmonics in the qubit coherence spectrum.*

*Brett Min (reference : poster #6) See the Poster and see the Video**Master student at McGill University**Supervisor : Kartiek Agarwal**Reducing Majorana Hybridization via Periodic Driving**It is an ongoing challenge to engineer setups where Majorana zero modes at the ends of one-dimensional topological superconductors are well isolated which is the essence of topological protection. Recent developments have indicated that periodic driving of a system can dynamically induce symmetries that its static counterpart does not possess [1]. We further develop the original protocol [2] where this idea [1] is applied to a system of a quantum dot (QD) coupled to a Kitaev chain hosting imperfect (overlapping) Majoranas. We numerically simulate a dynamical protocol in which an electron hops back and forth from the QD and the chain by Landau-Zener transition driven via time periodic local potential on the QD. We demonstrate that the current protocol reduces a non-zero hybridization energy that manifests from imperfect Majoranas by orders of magnitude.[1] K. Agarwal and I. Martin, Phys. Rev. Lett. 125, 080602 (2020) [2] I. Martin and K. Agarwal, arXiv preprint arXiv:2004.11385 (2020).*

*Alev Orfi (reference : poster #7) See the Poster and see the VideoUndergraduate intern at McGill UniversitySupervisor : Bill Coish*

**The Use of Restricted Boltzmann Machines for Modeling a Many-body Quantum System**Many-body quantum systems are computationally challenging to simulate, since the number of amplitudes required to describe a general quantum state grows exponentially with the number of particles. For some specific many-body problems, machine-learning algorithms have been effective in reducing this complexity. We are investigating the use of a restricted Boltzmann machine, to more efficiently simulate the central-spin model. This model describes the interaction between a central spin and multiple environmental spins. It is used in describing the hyperfine interaction between an electron spin in a quantum dot and surrounding nuclear spins. In addition, the central-spin model can be mapped to the BCS model of superconductivity. If more efficient modeling methods are found for the central-spin model, then they could be additionally applied to problems in non-equilibrium superconductivity.

*Adrian Solyom (reference : poster #8) See the Poster and see the Video**PhD student at McGill University**Supervisor : Lilian Childress**Sensing Stray Fields From Magnetic Nanocircuits With Nitrogen-Vacancy Defects**We discuss our latest efforts toward using a single, optically active nitrogen-vacancy (NV) spin sensor (implanted in a single-crystal diamond substrate) to measure magnetic thermal noise modified by spin Hall torques [1] in a Py/Pt nanowire [2]. In this poster, we first present our subtractive method for fabricating magnetic nanocircuits on diamond, and initial characterization of working Py(5 nm)/Pt(5 nm) nanowires. We reliably achieve contacts with few-ohms of resistance and 200 nm of overlap at each end of the 2-µm-long, 400-nm-wide wire, and we observe an anisotropic magnetoresistance of 0.4%. Importantly, we observe that the subtractive patterning process (masked ion milling) used to define the devices reduces the NV spin resonance contrast by a factor of ~5, but that subsequent exposure to an oxygen plasma returned the contrast to its nominal level without affecting the nanowire behavior. Finally, we present progress toward u
*