# Institut Transdisciplinaire d'Information Quantique (INTRIQ)

### Spring 2013 INTRIQ meeting

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**Spring 2013 INTRIQ meeting, April 17th & 18th)**

**Organizer: Bertrand Reulet, Université de Sherbrooke**

## At the Hotel of the Château Bromont90, rue Stanstead, Bromont QC J2L 1K6 Téléphone : 1 800 304 3433 ## Directions(Note : the venue is at the Hôtel, not the Auberge) |

**Meeting program**

**Wednesday, April 17th**

6h30 - 8h00 Breakfast

8h30 - 9h00 Registration

9h00 - 9h15 Opening remarks

9h15 - 10h30 Nicolas Godbout (Polytechnique) *Tutorial on quantum communications*

10h30 - 11h00 Coffee break

15h30 - 16h00 Jack Sankey (McGill)

*Controlling Micromechanical Sensors with Light*

16h00 - 16h30 Michael Hilke (McGill) Addre

*ssing nuclear spins in the quantum Hall regime*

*2 slides presentation of current projects*

**Thursday, April 18th**

6h30 - 8h00 Breakfast

8h00 - 9h00 Check out

9h00 - 9h45 Aash Clerk (McGill) *Dissipative entanglement in quantum optomechanics*

9h45 - 10h30 David Poulin (Sherbrooke) *2D quantum codes*

10h30 - 11h00 Coffee break and check-out

11h00 - 12h00 Poster session

*Measurement and manipulation of qubits based on individual charges/spins in semiconductor quantum dots*

*Spin-qubit dynamics and decoherence*

*Analytical solution to the Schrödinger equation and the ERS method*

**Note : wisemen meeting from 15h30 to 17h00**

*SPEAKERS*

*Aashish Clerk*Professor, McGill University

**Dissipative entanglement in quantum optomechanics**

*Bill Coish*

Professor, McGill University

**Spin-qubit dynamics and decoherence**

I will present recent theoretical work we have done on the dynamics of spins in quantum dots and at defect centers. These systems may be used for long-lived quantum memories or as interfaces between different physical qubits. To realize these goals, it is important to understand and control the quantum-coherent dynamics of these spins. To this end, we have developed new theoretical tools for understanding coupled spin dynamics based on a Magnus expansion, which we have applied to hole spins in quantum dots and electron spins in the presence of a magnetic field gradient. I will discuss possible experiments to improve our understanding of coherence in these systems and other physical implementations where these methods may be useful.

*Claude Crépeau*

Professor, McGill University

**Tutorial on quantum teleportation**

*Thierry Debuisschert*

Thales Research & Technology - France

Campus Polytechnique

**Applied Quantum Physics at Thales Research & Technology - France**THALES Research & Technology-France (TRT-Fr) located in Palaiseau near Paris, is one of the research units of the THALES group, one of the major world players in aerospace, space, defense, and security. Through its internal activities and scientific links with industries and universities, either in France or internationally, TRT-Fr is participating in the preparation of THALES industrial future in strategic R&D fields.

Within TRT-Fr, the Physics Research Group has a strong expertise in classical and quantum physics. After giving an overview of the research at TRT-Fr, the talk will focus on quantum key distribution and Nitrogen-Vacancy (NV) color centers in diamond.

TRT-Fr has collaborated with Institut d’Optique Graduate School in order to develop continuous variable quantum key distribution (CVQKD) implemented over installed fiber optics links [Fossier2009]. CVQKD has been coupled with symmetric encryptors developed by Thales Communication in order to increase the overall security of secure communication links [Jouguet2012].

TRT-Fr is collaborating with academic laboratories with the long term objective of developing quantum sensors and quantum circuits based on NV color centers in diamond. The implantation of regularly spaced NV centers in ultrapure diamond using parallel processing based on electron lithography has been demonstrated [Spinicelli2010]. The magnetic-field-dependent photodynamics of single NV defects in diamond has been studied as well as its application to qualitative all-optical magnetic imaging [Tetienne2012]. The current work is oriented towards magnetometry with ensembles of NV centers, either to build a wide-field imager, or to couple them with infrared optical cavities [Dumeige2013].

[Fossier2009] S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype “, *New J. Phys.* **11**, 045023 (2009).

[Jouguet2012] Paul Jouguet, Sébastien Kunz-Jacques, Thierry Debuisschert, Simon Fossier, Eleni Diamanti, Romain Alléaume, Rosa Tualle-Brouri, Philippe Grangier, Anthony Leverrier, Philippe Pache, and Philippe Painchault. “ Field test of classical symmetric encryption with continuous variables quantum key distribution ”. Opt. Express, 20(13): 14030–14041, Jun 2012.

[Spinicelli2010] P. Spinicelli, A. Dréau, L. Rondin, F. Silva, J. Achard, S. Xavier, S. Bansropun, T. Debuisschert, S. Pezzagna, J. Meijer, V. Jacques, and J.-F. Roch, “ Engineered arrays of NV colour centres in diamond based on implantation of CN- molecules through nanoapertures “, New Journal of Physics, 13 (2011) 025014

[Tetienne2012] J-P Tetienne, L Rondin, P Spinicelli, M Chipaux, T Debuisschert, J-F Roch and V Jacques. “ Magnetic field-dependent photodynamics of single NV defects in diamond: an application to qualitative all-optical magnetic imaging “. New Journal of Physics, 14 (2012) 103033 .

[Dumeige2013] Y. Dumeige, M. Chipaux, V. Jacques, F. Treussart, J.-F. Roch, T. Debuisschert, V. M. Acosta, A. Jarmola, K. Jensen, P. Kehayias, and D. Budker. “ Magnetometry with nitrogen-vacancy ensembles in diamond based on infrared absorption in a doubly resonant optical cavity”, Phys. Rev. B, 87 :155202, Apr 2013.

*Hichem Eleuch*

Researcher, Université de Montréal

**Analytical solution to the Schrödinger equation and the ERS method**

In the first part of the talk, I will present exact analytical solutions for the Schrödinger equation with deformed potentials.

The second part of this talk will be devoted to our new developed ERS ( Eleuch- Rostovtsev-Scully) method. The ERS technique generates analytical solutions for general potentials beyond the adiabatic approximation for 1D and 3D Schrödinger equations. Then it will be shown that the ERS-solutions are more accurate than the WKB approximation.

*Nicolas Godbout*

Professor, École Polytechnique

**Tutorial on quantum communication**

*Michael Hilke*

Professor, McGill University

**Addressing nuclear spins in the quantum Hall regime**

*HongWen Jiang*

Department of Physics and Astronomy

University of California at Los Angeles

**M easurement and manipulation of qubits based on individual charges/spins in semiconductor quantum dots**The charge or spin degrees of freedom of an electron in semiconductor quantum dots are particularly attractive for the implementations of qubits. Experimental effort of measuring and manipulating individual charges/spins in quantum dots has generated considerable success and interest in the last several years. In this talk, I will describe our experiments at UCLA to measure spin-relaxation time and phase-coherence time of single spins in a Si spin qubit. I will also present results of an international collaboration that uses the Landau-Zener-Stucklberg interference to coherently manipulate a charge qubit on picosecond time scale.

*David Poulin*Professor, Université de Sherbrooke

**2D quantum codes**I will present a survey of two-dimensional quantum error correcting codes.

*Jack Sankey*

Professor, McGill University

**Controlling Micromechanical Sensors with Light**

In the field of optomechanics we have learned to use the forces exerted by laser light to gain a new level of control over a wide variety of mechanical systems. These systems range in size from kilogram-scale mirrors in gravitational wave detectors to nanomechanical elements in cryogenic environments.

In this talk I will discuss how a very modest source of laser light (about a thousand time weaker than a key chain LED) can profoundly affect the motion of a micromechanical "trampoline" resonator. I will also show how we are able to laser cool its mechanical motion to a very low temperature, and how we can generate a nonlinear optomechanical coupling that should enable a quantum nondemolition (QND) readout of the trampoline's phonon number state.

Our group is currently interested in using optomechanical forces as a replacement for the forces exerted by traditional elastic materials in micromechanical sensors. Since the behavior of laser light is fundamentally different from that of atoms in a flexible material, such devices should circumvent the limitations of the best existing technology and achieve an unprecedented level of force sensitivity. In the ultimate limit, we hope to use optically-supported mechanical elements as "quantum transducers" capable of connecting qubits to one another on chip or via photons in a standard telecom fiber.

**POSTER SESSION***Félix Beaudoin*Student, McGill University

Director : Bill Coish

**Hyperfine-induced spin dephasing in a magnetic field gradient**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 the nuclear-spin bath. We investigate spins confined to lateral quantum dots or at single donor impurities, considering both free-induction and spin-echo decay. For lateral 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 lateral 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.

*Chloé Bureau-Oxton*Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Single Electron Spin Qubit in a Double Quantum Dot**

This poster shows how a nanomagnet deposited onto a double quantum dot can lead to fast spin- and phase-flip operations. Characterization of the quantum dot and the nanomagnet are also presented.

*Julien Camirand Lemyre*Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Measuring the spin state of a single electron in a double quantum dot**

Measuring the spin state of a single electron in quantum dots requires spin to charge conversion. In actual approaches an additional electron is needed to perform such a task via Pauli spin blockade. In our experiment a single electron is trapped 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 basic ideas about this new readout scheme as well as the preliminary results of the ongoing experiment.

*Chen-Fu Chiang*Postdoc, Université de Sherbrooke

Director : David Poulin

**Cost function for selecting efficient inverse Quantum Fourier Transform (QFT)**

Inverse QFT is a commonly used technique in quantum algorithms. The most known one is the quantum phase estimation which comprises two stages: phase kick back and inverse QFT. The former is always the dominating part. We are interested in comparing Kitaev's approach, ours and some other implementations of QPE in term of their cost (circuit size). And suppose the cost of the phase kick back is the same for all implementation, We are interested in comparing the approaches from a lower level by obtaining the cost functions of building the required rotation gates.

*Christopher Chamberland*Student, McGill University

Directors : Bill Coish and Aashish Clerk

**Adiabatic quantum state transfer**

*Benjamin D'Anjou*Student, McGill University

Director : Bill Coish

**Anomalous magnetotransport in reflection-symmetric artificial molecules**We calculate magnetotransport oscillations in current through a triple-quantum-dot molecule, accounting for higher harmonics (having ux 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 Duclos-Cianci*Student, Université de Sherbrooke

Director : David Poulin

**Generalizations of a Renormnalization Group Decoder for Kitaev's Topological Code**We study a previously introduced renormalization group decoder for Kitaev's topological code (KTC) generalized to (a) the fault-tolerant setting with faulty syndrome measurements and (b) the quantum error-correction of qudit versions of KTC.

*Andy Ferris*Postdoc, Université de Sherbrooke

Directors : David Poulin and Alexandre Blais

**Numerical simulations of many-body systems: combining series expansion with DMRG**

The numerically-linked cluster expansion (NLCE) is a successful series expansion technique for studying large, many-body systems at equilibrium. This technique is based on the solution of small clusters for arbitrary temperatures. We report our progress in utilizing DMRG as a solver in order to deal with larger clusters, substantially increasing the order of the series expansion (and thus the accuracy) in the zero-temperature limit.

*Gabriel Gasse*Student, Université de Sherbrooke

Director : Bertrand Reulet

**Squeezing in the Photo-assisted Electron Shot Noise of a Tunnel Junction**The current/voltage fluctuations generated by a conductor are another point of view of a randomly fluctuating electromagnetic field, i.e. "white" light. We demonstrate experimentally that this light is naturally squeezed, i.e. that the noise on one quadrature can go below the vacuum fluctuations, for a tunnel junction at very low temperature irradiated by a microwave. A classical current in a conductor generates a coherent state of light. We show that a quantum current can emit non-classical light.

*Patrick Harvey-Collard *Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Fabrication of Silicon Single Electron Transistors: a Nanodamascene Approach**Trapping electrons in quantum dots allows very interesting device behaviors for both classical and quantum information, such as single electron transistors and quantum memories. Nevertheless, fabricating semiconducting islands of sub-20 nm feature size is quite challenging. In this poster, I will introduce a novel way of patterning such small nanocrystals self-aligned between two electrodes. I will explain the fabrication process and demonstrate each step. Then, I will show results of electrical characterization of the device showing Coulomb blockade, single electron and hole regimes and large 100 meV addition energies. A giant 1200 meV addition energy is observed for the central Diamond because of the silicon gap, which could enable room temperature operation and applications as low power transistors. I will explain the challenges and highlights of this method and give some perspectives.

*Pavithran Iyer*Student, Université de Sherbrooke

Director : David Poulin

**Hardness of correcting degenerate errors on a general stabilizer code**

Error correcting codes are used to protect information, either classical or quantum, against various sources of noise. After preparing the system in an encoded state, certain check operators can be measured on the system to verify if errors have affected its state. The decoding problem consists in finding the optimal recovery given the outcome of these check measurements. Thus, it is a statistical inference problem. We would like to analyze the computational complexity of decoding a general quantum stabilizer code.

However, the stabilizer formalism introduces a new class of "equivalent" errors, called degenerate errors. A decoder for a stabilizer code must therefore account for the degeneracy in the errors it must correct. Following this a decoding problem for a stabilizer code will be defined, as an enumeration problem and its computation hardness will be addressed.

We shall show that the problem of interest belongs to the class of #P-Hard problems. In course of the outline of the proof, some concepts from linear codes such as Weight Enumerators, shall also be described.

*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. 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

*Dany Lachance-Quirion*Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Hybrid quantum circuits coupling spin qubits and spin ensemble to a superconducting microwave resonator**

Hybrid quantum circuits offer the possibility to combine the strengths of different systems. For instance, superconducting qubits and spins could respectively be used as a quantum processor and a quantum memory in a hybrid quantum computer as they respectively offer fast manipulation and long coherence time. As in circuit quantum electrodynamics, a superconducting microwave resonator can be used as a quantum bus to couple superconducting qubits to a spin system. As the coupling strength between a single isolated spin and the cavity-induced magnetic field is rather weak (g_s~10-100 Hz), two strategies are investigated to get strong spin-photon coupling. First, a single electron spin confined in a double quantum dot can be strongly coupled to the cavity by creating an inhomogeneous magnetic field across the double quantum dot using a micro-magnet. Also, a spin ensemble can be used to increase the coupling strength g_(ens) proportionally to g_s\sqrt(n_s), where n_s is the spin density. The experimental progresses to get strong spin-photon coupling will be discussed for those two strategies, respectively in a GaAs double quantum dot and a Mn^(2+) spin ensemble in Mn-doped colloidal quantum dots.

*Marc-Antoine Lemonde*Student, McGill University

Director : Aashish Clerk

**Single-photon strong coupling effects in a strongly driven optomechanical cavity**In this poster I show how we can enhance the single-photon effects, coming from the non-linear part of the interaction between phonons and photons inside an optomechanical cavity, using a strong drive. More precisely, I show how, by properly tuning the drive, we can make some processes generated by this non-linear interaction to become resonant. These resonant processes will dramaticaly modify the Optomechanically induced transparency (OMIT) spectrum so that it can be observed with achievable experimental setups.

*Kevin Milner*Student, McGill University

Director : Patrick Hayden

**The Complexity of Separability**

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum circuit produce a state that is separable or entangled? Here, we give evidence that it is computationally hard to decide the answer to this question, even if one has access to the power of quantum computation. We begin by exhibiting a two-message quantum interactive proof system that can decide the answer to a promise version of the question. We then prove that the promise problem is hard for the class of promise problems with "quantum statistical zero knowledge" (QSZK) proof systems by demonstrating a polynomial-time Karp reduction from the QSZK-complete promise problem "quantum state distinguishability" to our quantum separability problem. By exploiting Knill's efficient encoding of a matrix description of a state into a description of a circuit to generate the state, we can show that our promise problem is NP-hard with respect to Cook reductions. Thus, the quantum separability problem (as phrased above) constitutes the first nontrivial promise problem decidable by a two-message quantum interactive proof system while being hard for both NP and QSZK. We also consider a variant of the problem, in which a given polynomial-time mixed-state quantum circuit accepts a quantum state as input, and the question is to decide if there is an input to this circuit which makes its output separable across some bipartite cut. We prove that this problem is a complete promise problem for the class QIP of problems decidable by quantum interactive proof systems. Finally, we show that a two-message quantum interactive proof system can also decide a multipartite generalization of the quantum separability problem.

*Clemens Mueller*

Postdoc, Université de Sherbrooke

Director : Alexandre Blais

**Measurement of Majorana Fermions in circuit QED**

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*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**Spins are a promising avenue for the implementation of a quantum computer. Information is encoded in the electron spin, which is confined electrostatically by a quantum dot (QD) in a semi-conductor substrate, and manipulated by micro-magnets. Unfortunately, progress is limited by the fast decoherence arising from the host material’s nuclear spins, usually gallium arsenite. By using a material with a smaller nuclear field, such as silicon, we could reduce the decoherence in our QDs. In this poster, we describe the design of enhancement mode Si MOS DQD developped by the group of Malcolm S. Carroll, from Sandia National Laboratories, and present preliminary results of micro-magnet integration on those devices and simulations.

*David Roy-Guay**Marc-Olivier Lessard*Students, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Nitrogen-Vacancy centers for magnetic ﬁeld sensing at the nanoscale**Nitrogen vacancy (NV) centers in diamond are nanoscale color centers with long coherence times, used as qubits and quantum memories for quantum information. Alternatively, their very sharp magnetic resonances can be used as accurate electromagnetic nanosensors, reaching single spin detection. As a novel approach, we propose using electric ﬁeld modulation of the NV resonance in order to enhance their magnetic ﬁeld sensing accuracy. Using a NV center array, the magnetic field CCD created will be relevant to map local magnetic ﬁelds produced by micromagnets, as used in spin qubits architectures.

*Olivier Saint-Jean*Student, Université de Sherbrooke

Director : Michel Pioro-Ladrière

**Construction of a tunable radio-frequency detector for double quantum dot charge readout**

We developed a system for the detection of the charge state of a GaAs double quantum dot using reflectometry on a RLC circuit. This circuit is built using a tunable capacitor diode, and a QPC electrostatically coupled to the quantum dots; parameters can then be tuned for maximal sensitivity of the dots' charge.

*Benno Salwey*Student, Université de Montréal

Directors : Gilles Brassard and Alain Tapp

**Distillation of non-locality**We will introduce the concept of distillation of non-locality and provide some known examples. We will also remind the connection between non-signaling distillation and privacy amplification in the context of general non-signaling adversaries. Then we will show a partial no-go result in the case of special non-signaling correlations, called "isotropic" PRboxes, which amount to a noisy version of the standart PRbox.

*Benjamin Schmidt*Student, McGill University

Director : Guillaume Gervais

**Probing fractional quantum hall states with adiabatic cooling**

The 5/2 fractional quantum hall state is one of the leading candidate solid state systems believed to support non-Abelian anyons as low-energy excitations. If the non-Abelian description of the state is correct, it must have a large ground state entropy proportional to the number of quasiparticles. We are trying to detect the effect of that entropy by measuring the temperature change when quasiparticles are adiabatically added to the system by changing the magnetic field. This poster will present the theory and current experimental status of the project, including applications of the technique to states other than 5/2.

*Kevin Spahr*Student, Université de Sherbrooke

Director : Bertrand Reulet

**Dynamics of SNS Junctions**We probe the dynamics of a Superconductor /Normal Metal/ Superconductor junction (SNS: Nb / Al above its critical temperature / Nb) by measuring its voltage / current characteristics while applying an ac current of frequency in the range 1-200 MHz. We observe a dynamical phase transition as a function of the frequency and amplitude of the ac current. At low frequency there is a continuous change in the dynamical behavior of the junction, replaced an abrupt change and hysteresis at high frequency. The crossover frequency between the two regimes has a strong temperature dependence similar to that of the electron-phonon interaction rate.

*Xiaoya Wang*Student, McGill University

Director : Bill Coish

**Spin-Echo Dynamics of a Heavy Hole in a Quantum Dot**We develop a theory for the spin-echo dynamics of a heavy hole in a quantum dot, accounting for both hyperfine- and electric-field-induced fluctuations. We show that a moderate applied magnetic field can drive this system to a motional-averaging regime, making the hyperfine interaction ineffective as a decoherence source. Furthermore, we show that decay of the spin-echo envelope is highly sensitive to the geometry. In particular, we find a specific choice of initialization and -pulse axes which can be used to study intrinsic hyperfine-induced hole-spin dynamics, even in systems with substantial electric-field-induced dephasing. These results point the way to designed hole-spin qubits as a robust and long-lived alternative to electron spins.