# Institut Transdisciplinaire d'Information Quantique (INTRIQ)

### Fall 2013 INTRIQ meeting, November 5th & 6th 2013

**
At the Hotel of the Château Bromont
Organizer: Lilian Childress, McGill University
**

90, rue Stanstead, Bromont QC J2L 1K6 Téléphone : 1 800 304 3433 ## Directions(Note : the venue is at the Hôtel, not the Auberge) |

**Meeting program**

**Tuesday, November 5th**

8h30 - 9h00 Registration

9h00 - 9h15 Opening remarks

9h15 - 10h15 *Matteo Mariantoni*, Professor at University of Waterloo

**Tutorial: Towards a Fault-Tolerant Quantum Computer with the Surface Code**

10h15 - 10h45 Coffee break

10h45 - 11h10 *Kevin Lalumière*, Student at Université de Sherbrooke

*Interactions between superconducting qubits mediated by travelling photons*

11h10 - 11h35 *Farzad Qassemi*, Postdoc at Université de Sherbrooke

* Spin readout of a single electron in a double quantum dot*11h35 - 12h00

*Iyer Pavithran*, Student at Université de Sherbrooke

**Hardness of decoding stabilizer codes on the independent X-Z channel***Thomas Szkopek*, Professor at McGill University

*Would Error Correction Provide a Benefit in Classical Computers?**Bertrand Reulet*, Professor at Université de Sherbrooke

*Electron shot noise is quantum light**Daniel Lidar*, Professor at University of Southern California

**Quantum annealing and error correction with lots of qubits***2 slides presentation of current projects*

**Wednesday, November 6th**8h30 - 9h00 Check-out

*Wolfgang Tittel*, Professor at University of Calgary

*How to build a quantum repeater**Sébastien Francoeur*, Professor at École Polytechnique de Montréal

**Isoelectronic centers as building blocks for quantum information processing***Hichem Eleuch*, Invited researcher at McGill

*Theoretical study of beam splitting and entanglement generation with two particular states:*

*excited coherent states and squeezed coherent states of Morse potential**Abdulrahman Al-lahham*, Student at Université de Montréal

**An introduction to quantum walk based search algorithms***Dave Touchette*, Student at Université de Montréal

**Noisy Interactive Quantum Communication***Michael Hilke*, Professor at McGill University

**History of INTRIQ****Note : Business meeting from 15h30 to 17h00**

*INVITED SPEAKERS**Sébastien Francoeur*

École Polytechnique de Montréal

*Isoelectronic centers are semiconductor nanostructures the size of a single atom or a small molecule. Shrinking semiconductor nanostructures to atomic sizes provide a number of key advantages: the uniformity and predictability of atomic defects, the size and composition tunability of conventional quantum dots, a perfectly defined symmetry, and a confinement of electrons and holes to volumes of atomic dimension.*

**Isoelectronic centers as building blocks for quantum information processing**

In this presentation, I will describe what isoelectronic centers are and I will discuss our recent result on the quantum control of exciton qubits. We found that this little-known nanostructure provides a relatively high dipole moment, which could prove to be an essential ingredient for the large scale integration of two-qubit gates and the realization of quantum networks. Furthermore, excitation induced dephasing mechanisms found in other semiconductor nanostructures are suppressed, allowing high-fidelity qubit-state preparation and control on shorter time scale.

*Daniel Lidar*

**Quantum annealing and error correction with lots of qubits**In October 2011 USC and Lockheed-Martin jointly founded a quantum computing center housing D-Wave’s 128-qubit Rainier processor, which implements programmable quantum annealing using superconducting flux qubits. In March this year the processor was upgraded to the 512-qubit Vesuvius model. These are special-purpose processors designed to find the ground state of a broad class of 2D classical Ising models with as many spins as qubits. This talk will describe some of the work we have done to benchmark the processors against highly optimized classical algorithms, to test for quantum effects, and to perform error correction.

References:

"Experimental signature of programmable quantum annealing", Nature Comm. 4, 2067 (2013)

"Quantum annealing with more than one hundred qubits",arXiv:1304.4595

"MAX 2-SAT with up to 108 qubits", arXiv:1307.3931

"Error corrected quantum annealing with hundreds of qubits", arXiv:1307.8190

*Matteo Mariantoni*

In this tutorial, I will introduce the main concepts about the surface code. In particular, I will explain how stabilizer measurements allow the detection of quantum errors. I will show how logical qubits are realized and present a unified error model for the surface code. I will then demonstrate how logical operations can be performed between logical qubits. Finally, I will outline a possible realization of the surface code based on superconducting quantum circuits.

[1] A.G. Fowler, M. Mariantoni, J.M. Martinis, and A.N. Cleland, Phys. Rev. A 86, 032324 (2012)

**How to build a quantum repeater**

Quantum communication, in particular quantum key distribution, holds great promise for the future of ICT. In my talk I will introduce the concept of a quantum repeater (first proposed by Briegel et al. in 1998 [1]), which combines the distribution of entangled states of light, entanglement swapping, and quantum memory to overcome the current distance barrier of around 200 km. Furthermore, I will present our recent work on frequency-multiplexed quantum memories [2], and discuss why (and how) it may allow building a quantum repeater within the next few years.

[1] H. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998)

[2] N. Sinclair et al, arXiv:1309.3202

** **

*INTRIQ SPEAKERS**Abdulrahman Al-lahham*

**An introduction to quantum walk based search algorithms**introduced along with its quantization. By combining these two ingredients, we get the MNRS algorithm: A quantum walk based search method. A quick application of this algorithm to element distinctness problem will be given as a conclusion.

*Farzad Qassemi*

**Spin readout of a single electron in a double quantum dot**In this talk, I present my work on single spin readout in double quantum dot. In laterally confined double quantum dots, electrons are controlled through gate voltages applied locally to each dot. The interdot tunneling, which is due to electrons wave functions overlap at two quantum dots, is generally spin independent. Hence, for reading out spin state in quantum transport, a scheme for spin-to-charge conversion is required. In the usual singlet-triplet quantum dots where initial and final spin states are orthogonal, the current is blocked by spin selection rules, leading to a phenomenon called Pauli spin blockade. However, interactions between the electron spin and the environment (e.g. nuclear spins in III-V semiconductors) lift this spin selection rule. Here, I present a new idea to measure a single spin in the first dot using the second dot as a spin filter.

*Hichem Eleuch*

**Theoretical study of beam splitting and entanglement generation with two particular states: excited coherent states and squeezed coherent states of Morse potential**[1] K. Berrada, S. Abdel-Khalek, H. Eleuch and Y. Hassouni, Quantum Inf. Process. 12, 69 (2013).

[2] A. Hertz, V. Hussin, H. Eleuch, paper in preparation.

*Michael Hilke*

**Realizing that most students and more than half of the PIs were not there at the beginnings almost a decade ago, I will give an illustrated anecdotal account of INTRIQ's history and subjective future.**

*History of INTRIQ*

*Kevin Lalumière*

*Iyer Pavithran*

*Bertrand Reulet*

*Thomas Szkopek*

*Dave Touchette*

**We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and is of particular importance for real-world applications of interactive quantum protocols, which can be proved to have exponentially lower communication costs than their classical counterparts for some problems. Under random noise, our simulation strategy has a communication rate proportional to the capacity of the channel used. In contrast, a naive strategy that individually encodes each particular round of communication to achieve comparable success would have asymptotic rate going to 0.**

*Noisy Interactive Quantum Communication*

Under adversarial noise, our strategy can withstand error rates up to 1/2, which we prove to be optimal. In contrast, the naive strategy described above would not work for any constant fraction of errors. Our results hold in particular in the quantum communication complexity setting of Yao's and Cleve-Buhrman's models.

This is joint work with Gilles Brassard, Ashwin Nayak, Alain Tapp, and Falk Unger.

Full version at: http://arxiv.org/abs/1309.2643

*KIOSK**Dolores Martinez*

*Christian Sarra-Bournet*

Coordinator of the Quantum Materials and Devices Infrastructure (IMDQ)

Département de Physique, Université de Sherbrooke

**Quebec’s Nanotechnology Infrastructure – Quantum Materials and Devices Infrastructure (IMDQ)**

Under the banner of NanoQuébec, Quebec's Nanotechnology Infrastructure (QNI) brings together the human and technical nanotechnology expertise found in Quebec’s universities. Its mission is to structure and consolidate this expertise, giving academic and industrial researchers optimal access to a full range of state-of-the-art nanotechnology equipment and expertise. Being an open infrastructure with more than $300 M in equipment and 180 highly qualified personnel, the QNI can provide users with a full range of services including training and support, use of equipment, as well as contractual services and development of major R&D projects.

The Quantum Materials and Devices Infrastructure, located at the Physics Department at Université de Sherbrooke, is part of the QNI and is composed of clean rooms and state-of-the-art equipment for the **fabrication** and **characterization** of magnetic, supraconductor and semiconductor materials and devices. Researchers are thus able to develop their own quantum devices and characterize those in cryogenic temperature environment and in presence of intense magnetic fields. The expertise and know-how of our infrastructure is unique in Québec and is able to answer the current quantum information nano/microfabrication challenges.

**POSTER SESSION**

*Jonas Anderson*Postdoc, Université de Sherbrooke

*Director : David Poulin*

**Decoding Quantum LDPC Codes**

I will discuss the advantages of Quantum Low-Density Parity-Check (QLDPC) codes for use in future quantum computing architectures as well as the challenges involved in their decoding.*Félix Beaudoin*Student, McGill University

Director : Bill Coish

**Magnetic-field gradients are important for single-site addressability and electric-dipole spin resonance of spin qubits in semiconductor devices. We show that these advantages are offset by a potential reduction in coherence time due to the non-uniformity of the magnetic field experienced by a nuclear-spin bath interacting with the spin qubit. We theoretically study spins confined to quantum dots or at single donor impurities, considering both free-induction and spin-echo decay. For quantum dots in GaAs, we find that, in a realistic setting, a magnetic-field gradient can reduce the Hahn-echo coherence time by almost an order of magnitude. This problem can, however, be resolved by applying a moderate external magnetic field to enter a motional averaging regime. For quantum dots in silicon, we predict a cross-over from non-Markovian to Markovian behavior that is unique to these devices. Finally, for very small systems such as single phosphorus donors in silicon, we predict a breakdown of the common Gaussian approximation due to finite-size effects.**

*Enhanced hyperfine-induced spin dephasing in a magnetic-field gradient**Samuel Boutin*

**Numerical optimization of quantum gates and measurement in cQED**In this work, a version of the gradient ascent pulse engineering algorithm for open quantum systems (open GRAPE) is implemented and adapted to work with big Hilbert space in order to optimize the measurement of a superconducting qubit in the cQED architecture. Also, suggestions from the literature are added to the algorithm in order to accelerate the convergence and to take into account the constraints of the standard laboratory equipment used in that type of experiment. In this talk, the cQED architecture is briefly introduced. The numerical methods at the core of this work are then discussed. Finally, some preliminary results on the optimization of the measurement protocol are presented.

*Winton Brown*

Postdoc, Université de Sherbrooke

Director : David Poulin

**Thermalization and Quantum Information Theory**

*Julien Camirand-Lemyre*

Director : Michel Pioro-Ladrière

**Measuring the spin state of a single electron in a double quantum dot**In presence of a magnetic field gradient between the two dots the dipolar moment of the electron couples to it's spin degree of freedom allowing for spin to charge conversion. I will present the first results of the experiment using the magnetic field gradient produced by the nuclear spins and explain why micromagnet need to be added to the device.

*Christopher Chamberland*

**Geometric dephasing for adiabatic state transfer***Benjamin D'Anjou*

Student, McGill University

Director : Bill Coish

** Anomalous magnetotransport through reflection-symmetric molecules**We calculate magnetotransport oscillations in current through a triple-quantum-dot molecule, accounting for higher harmonics (having flux period h/ne, with n an integer). For a reflection-symmetric triple quantum dot, we find that harmonics with n odd can dominate over those with n even. This is opposite to the behavior theoretically predicted due to `dark-state' localization, but has been observed in recent experiments [L. Gaudreau et al., Phys. Rev. B, 80, 075415 (2009)], albeit in a triple-dot that may not exhibit reflection symmetry. This feature arises from a more general result: In the weak-coupling limit, we find that the current is flux-independent for an arbitrary reflection-symmetric Aharonov-Bohm network. We further show that these effects are observable in nanoscale systems even in the presence of typical dephasing sources.

*Guillaume Dauphinais*

Student, Université de Sherbrooke

Director : David Poulin

**Quantum Error Correction with Non-Abelian Anyons**

Non-abelian anyons are interesting from the point of view of quantum information as one can use them in principle to encode quantum states, and perform gates which are topologically protected. Majorana fermions is an example of such a system that has recently attracted a lost of interest. In this project, a decoding algorithm for a phenomenological noise model applied to Majorana fermions on a torus is developped and its performances are studied.*Nicolas Delfosse*

Postdoc, Université de Sherbrooke

Director : David Poulin

*Decoding color codes by projection onto surface codes*

Surface codes and color codes are two families of quantum error correcting codes which are particularly well suited to fault-tolerant quantum computing. They are defined by local constraints on qubits placed on a surface and they allow for efficient decoding.

We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. These results are based on a chain complex interpretation of surface codes and color codes.

Nicolas Didier

Postdoc, McGill University

Directors : Aashish Clerk and Alexandre Blais**Perfect squeezing by damping modulation in circuit quantum electrodynamics**

Dissipation-driven quantum state engineering uses the environment to steer the state of quantum systems and preserve quantum coherence in the steady state. We show that modulating the damping rate of a microwave resonator generates a new squeezing mechanism that creates a vacuum squeezed state of arbitrary squeezing strength, thereby allowing perfect squeezing. Given the recent experimental realizations in circuit QED of a microwave resonator with a tunable damping rate, superconducting circuits are an ideal playground to implement this technique. By dispersively coupling a qubit to the microwave resonator, it is possible to obtain qubit-state dependent squeezing.*Guillaume Duclos-Cianci*

`Student, Université de Sherbrooke`

Director : David Poulin

**A family of magic states and their distillation circuits**

In this work we introduce a family of magic states to implement arbitrary one-qubit Pauli rotations of angle 2\pi / 2^k. We describe the states, give a circuit necessary to perform distillation on these and analyze how errors behave. Preliminary results show an improvement in resource consumption compared to existing techniques.*Gabriel Gasse*

Student, Université de Sherbrooke

Director : Bertrand Reulet

**Observation of Squeezing in the Electron Quantum Shot Noise of a Tunnel Junction**

We report the measurement of the fluctuations of the two quadratures of the electromagnetic field generated by a quantum conductor, a dc- and ac-biased tunnel junction placed at very low temperature.We observe that the variance of the fluctuations on one quadrature can go below that of vacuum, i.e., that the radiated field is squeezed. This demonstrates the quantum nature of the radiated electromagnetic field.*Erika Janitz*

Student, McGill University

Director : Lilian Childress

**Cavity Assisted Quantum Processes with NV Centers**

The peculiar properties of quantum mechanics provide tools to explore novel types of information processing that could achieve unprecedented computational speed and security. Realizing such technologies requires precise control over a quantum system, and a method of joining individual elements into a scalable network. Spins in solids have been proposed as quantum bits, and recently it has been shown that individual spins in diamond can be addressed via an optically-active defect called the nitrogen-vacancy center. The central goal of this project is to develop an efficient quantum interface between these defects and light, enabling optically mediated interactions between distant spins. Our approach will involve placing these defects in a highly tunable microscopic cavity formed by optical fibers, thereby enhancing coherent coupling between light and a single nitrogen-vacancy center. This flexible platform will directly impact quantum information applications, and will also open new avenues for exploring fundamental quantum optics with condensed matter systems.*Saeed Khan*

Student, McGill University

Director : Aashish Clerk

**Large gain quantum-limited qubit state measurement using a two mode nonlinear cavity**

A single nonlinear cavity dispersively coupled to a qubit functions as a large gain detector near a bifurcation, but also has an unavoidable large backaction that prevents QND measurement at weak couplings [1]. We show theoretically that a modified setup involving two cavities (one linear, one nonlinear) and a dispersively coupled qubit allows for a far more optimal measurement. In particular, operating near a point of bifurcation, one is able to both achieve a large gain as well as a near quantum-limited backaction. We present analytic results for the gain and noise of this detector and a heuristic understanding of the physics, thus presenting a complete description of this new way of performing weak qubit state measurements. The setup we describe can easily be realised in experiments with superconducting circuits involving Josephson junctions [2, 3].

[1] C. LaFlamme, A.A. Clerk, Phys. Rev. A 83, 033803 (2011)

[2] F.R. Ong et al., Phys. Rev. Lett. 106, 167002 (2011)

[3] M. Hatridge et al., Phys. Rev. B 83, 134501 (2011)*Dany Lachance-Quirion*

Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Coupling a single-electron spin qubit and a superconducting microwave resonator for hybrid quantum circuits**

Superconducting qubits in the circuit quantum electrodynamics (cQED) architecture have proven to have all the requirements of a solid-state quantum processor. However their coherence times are currently limited to fractions of a millisecond, thus requiring a quantum memory to build a universal quantum computer. Spin qubits are one of the most promising candidates for this task because of their potentially very long coherence time. In this poster I will show how a spin qubit defined as a single-electron in a double quantum dot (DQD) with a large magnetic field anisotropy can be strongly coupled to a superconducting resonator. I will also show how this coupling can be manipulated electrically in a timescale shorter than the spin qubit coherence time, thus enabling the resonator to act as a quantum bus.*Pawel Mazurek*

Student, McGill University

Director : Bill Coish

**Sensitivity of the decay of entanglement of quantum dot spin qubits to the magnetic ﬁeld**

We study the decay of entanglement of quantum dot electron-spin qubits under hyperﬁne interaction mediated decoherence. We show that two qubit entanglement of a single entangled initial state may exhibit decay characteristic of the two disentanglement regimes in a single sample, when the external magnetic ﬁeld is changed. The transition is manifested by the supression of time-dependent entanglement oscillations which are superimposed on the slowly varying entanglement decay related to phase decoherence (which result in oscillatory behaviour of entanglement sudden death time as a function of the magnetic ﬁeld). This unique behaviour allows us to propose the double quantum dot two-electron spin Bell state as a promising candidate for precise measurements of the magnetic ﬁeld.*Clemens Mueller*Postdoc, Université de Sherbrooke

Director : Alexandre Blais

**T1-Fluctuations in Superconducting Circuits - The Revenge of the Two-Level Fluctuators**Spurious two-level systems (TLS) as sources of noise are ubiquitous in solid state systems, be it as the simplest possible theoretical model or as real physical entities observed in experiment. Here, I will show how ensembles of interacting TLS can be responsible for fluctuations of qubit decoherence rates, a phenomenon which has recently been observed in high-coherence superconducting 3D transmon samples.

*Pericles Philippopoulos*

Student, McGill University

Director : Bill Coish

**Hyperfine Interaction in Materials with Strong Spin-Orbit Coupling:Group Theoretic Analysis**Due to the anisotropic nature of the hyperfine coupling for hole spins in semiconductor quantum dots, these systems may show significantly longer coherence times than electron spins given the correct quantum-dot geometry and magnetic field orientation. This advantage of hole spins relies on the hyperfine tensor taking-on an Ising-like form. This Ising-like form of the hyperfine coupling has been recently called into question with experiments that extrapolate their results suggesting a strong hybridization of p-like and d-like components for the valence band. However, this extrapolation relies on two assumptions: (1) That spin-orbit coupling is weak in these systems compared to the anisotropic crystal field, and (2) that higher-angular-momentum (f-like, g-like, ...) contributions are negligible. Assumption (1) is questionable in light of the fact that the spin-orbit energy is even larger than the principle gap in InAs, and assumption (2) is generally questionable in any crystal that breaks pure rotational symmetry. Using a generalization of the group-theoretic analysis in [1], we show here that relaxing either of these assumptions can restore the Ising-like nature of the hyperfine tensor, albeit for a particular choice of coupling constants. Future work will address the issue of a generic limit in which the Ising-like hyperfine coupling will be robust for hole spins.

*David Racicot-Desloges*

Student, Université de Sherbrooke

Director : David Poulin

**Degenerate Decoding for Quantum Turbo Codes**

Emily Pelchat and David Poulin presented, in "Degenerate Viterbi Deconding", an algorithm for quantum convolutional codes that finds the class of degenerate errors with the largest probability, conditioned on a given syndrome. Monte Carlo simulations strongly suggested that the algorithm gives better results than its non-degenerate counterpart, particularly at low error rates. Thus, a natural next step would be to use the degenerate decoder in turbo codes, where its benefits could be further amplified. I shall present this extension in my poster.*Sophie Rochette*

Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

*Integration of micro-magnets to silicon quantum dots: Towards long coherence time spin control for quantum information*

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