Abstracts- QUBIT symposium

You can scroll down to see the talk's abstracts by order of speakers
or you could click on a specific speaker from the list below to see his abstract directly:
Tuesday 18th of March
Plenary talk by Israel Prize Laureate Mordechai (Moti) Segev
Photonic Quantum Simulations
Structure-based super-resolution quantum state tomography
We show that prior information, for example – that a quantum state is sparse in a known mathematical basis, enables algorithmic reconstruction of an initial three-photon state from two-fold coincidence measurements in a single experimental setup, thereby achieving quantum super-resolution. We further extend this concept of sparsity-based quantum super-resolution to cases where the sparsity basis is not known apriori, and demonstrate the recovery of the general three photon state from two-fold coincidence measurements. This approach enables a general reduction both in the number of measurements needed for state recovery and in their complexity, allowing, for example, multi photon state recovery without photon number-resolving detectors.
Two photon spontaneous emission as a possible source for photonic qubits
Quantum optics with semiconductor quantum dots
The dark exciton: a superior solid state spin qubit
Quantum transport in nanowires: developing platforms for semiconductor-based QIP
Low-bandgap semiconductor nanowires such as InAs and InSb have recently gained attention as materials for realizing topological states and spin-orbit qubits. Critical to understanding these experiments and designing nanowire-based quantum devices is a deep understanding of the radially confined modes and the shape of the radial potential that determines these states. Two recent experiments performed by my group help to illuminate the radial subband structure in InAs nanowires in two very different contexts. One is a study of the magnetic field and gate dependence of short-channel (quasiballistic) field-effect devices that shows how magnetoconductance provides a ‘fingerprint’ of the radial subband structure. The second is a study of proximity effect superconductivity in field-effect device with Nb contacts. A puzzling interference pattern in the critical current versus axial magnetic field is observed, which we explain by a model of quantum interference between the paths of electrons occupying subbands characterized by different angular momentum quantum numbers.
Fractal behavior of polaritons in a quasi-periodic potential : a quantum simulator of topological systems
I will present recent results obtained both theoretically and experimentally  on fractal spectral properties of a polariton gas in a Fibonacci quasi-periodic potential. The observed spectrum is accurately reproduced from a theoretical model that we shall present. We have observed for the first time log-periodic oscillations and the opening of mini-gaps following the gap labeling theorem. These results illustrate the potential of cavity polaritons as a quantum simulator in complex topological geometries.  
Light-matter interactions in photonic-crystal nanocavities: applications and potential for scalability
I will introduce our recent experiments with single, self-assembled InAs quantum dots embedded in GaAs photonic-crystal nanocavities. The small size of the photonic-crystal cavities and their compatibility with semiconductor fabrication processes make the coupled cavity-dot platform an excellent candidate for scaling up to more complex systems needed for practical devices. At the same time, the coupled cavity-dot system enables interactions between single photons, which we have used to demonstrate high-speed all-optical switching at ultra-low powers and generation of non-classical light.
I will also describe our latest work exploring the use of a single quantum emitter coupled to a cavity as a photon number filter, extending the concept of photon blockade from single photons to two-photon Fock state generation by coupling the probe laser to the second manifold of the Jaynes-Cummings ladder via a two-photon transition. This approach can be further generalized to create third- and higher-order photon states inside the cavity through multi-photon transitions to the corresponding manifold. We report the probing of these multi-photon transitions into the higher manifolds of the Jaynes-Cummings ladder of a strongly coupled quantum dot–photonic crystal nanocavity system by measuring the third-order autocorrelation function of a probe laser transmitted through such a system. We observe bunching in the third-order autocorrelation function for transmitted photons when the probe laser is resonant with the third manifold and anti-bunching when the probe laser is tuned away from resonance.
Lastly, I will discuss our first steps toward a network of interacting nonlinear cavities, focusing on our demonstration of strong coupling of a single quantum dot to a pair of proximity-coupled cavities.
Quantum complexity theory and the Bose-Hubbard model
This talk will be split in two parts.  The first will give a brief introduction to quantum complexity theory, which will allow a review of recent results classifying the complexity of several problems related to the Bose-Hubbard Hamiltonian.  The second part of the talk will focus on the graduate student experience at the University of Waterloo, with a focus on graduate studies at the IQC.
Wednesday 19th of March
The Nitrogen-Vacancy qubit in Diamond
Quantum computers and other potential quantum applications require the presence of Qubits. These must be realized in the laboratory in a controlled way.                                                                                    
The most promising qubit to date is the negatively charged Nitrogen-Vacancy (N-V) defect in diamond.
Here we will overview the quantum properties of this defect showing why it is most suitable for the realization of qubits.
We’ll describe how it is realized in the laboratory by the use of ion implantation, stressing still existing difficulties.
The photons emitted by the qubit must be controlled and manipulated.  This is best done in Photonic Crystal structures realized in the NV center containing diamond.                                                                      
Ways of realizing such structures in diamond and their properties will be reviewed. 
Superconducting flux quantum bits: control and quantum sensing
Superconducting artificial atoms provide a new testbed for the study of quantum control, decoherence, and light-matter interaction and have applications in quantum information processing and quantum sensing.
I will discuss our recent work on superconducting artificial atoms of the flux type, also called flux quantum bits (qubits) in the context of quantum information processing. We study flux qubits coupled to superconducting coplanar waveguide resonators. I will present our results on measurements of coherence and on implementation of single- and two- qubit control.
In the second part of the talk, I will present experiments in which we employ the high sensitivity of flux qubits to magnetic fields to design a magnetometer with unprecedented sensitivity over the frequency range from tens of kHz to tens of MHz
The use of braid operators for implementing entangled large n-qubits states (n>2)
Braid theories are applied to quantum computation processes, where to each crossing in the Braid diagram a unitary Yang-Baxter operator R is associated, representing either a Braiding matrix or a universal quantum gate. By operating with Braid operators on the computational basis of n-QUBITS states, orthonormal entangled states are obtained, referred here as general Bell states. The 3-QUBITS Bell states are explicitly developed and the present methods are generalized to any n-QUBITS system. The quantum properties of the general Bell states are analyzed and these properties are related to concurrence.
Dissipative encoding and state preparation for topological order
We study the suitability of dissipative (non-unitary) processes for (a) encoding logical information into a topologically ordered ground space and (b) preparing an (arbitrary) topologically ordered state. We give a construction achieving (a) in time O(L) for the L×L-toric code by evolution under a geometrically local, time-independent Liouvillean. We show that this scaling is optimal: even the easier problem (b) takes at least Ω(L) time when allowing arbitrary (possibly time-dependent) dissipative evolution. For more general topological codes, we obtain similar lower bounds on the required time for (a) and (b). These bounds involve the code distance and the dimensionality of the lattice. The proof involves Lieb-Robinson bounds, recent cleaning-lemma-type arguments for topological codes, as well as uncertainty relations between complementary observables. By allowing general locality-preserving evolutions (including, e.g., circuits of CPTPMs), our work extends earlier work characterizing unitary state preparation.
This is joint work with John Dengis and Fernando Pastawski.
Engineering new platforms for topological quantum computing

Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers.

Topological quantum computation aims to achieve this task by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a non-local manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Despite progress in the field, experimentally controlling and manipulating non-Abelian quantum Hall states still proves to be a highly challenging task. We consider the possibility to engineer new non-Abelian systems by interfacing simpler, Abelian components. We show that this route leads to zero modes exhibiting a new type of non-Abelian statistics. Furthermore, judicially coupling these zero modes leads to new topological phases of matter, which can harbor excitations with computationally universal braid statistics

Flux braiding and anyons in Pauli hamiltonian
Aharonov and Casher  showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of N fluxons with non integer fluxes.
The holonomies associated with closed paths need not be topological in general. We find however that if all the fluxons are  subcritical, (i.e.<1), and the number of zero modes is D=N-1, then fluxon braiding is
topological. In the special case that the fluxons carry identical fluxes they can be interpreted as non abelian anyons that satisfy the Burau representations of the braid group.
Plenary talk by IQC director Raymond Laflamme 
Experimental quantum error correction
To realize the potential of quantum information processors requires the ability to overcome the imprecision and imperfection inherent in physical systems. Quantum error correction (QEC) has provided a solution, showing that errors can be corrected with a reasonable amount of resources as long as their rate is sufficiently small. Implementing QEC protocols remains one of the most important challenges in QIP. In the experimental arena, the quest to build quantum processors that could outperform their classical counterparts has led to many blueprint proposals for potential devices based on NMR, electron spin resonance, ion traps, atom traps, optics, superconducting devices and nitrogen-vacancy centres, among others. Many have demonstrated not only the possibility of controlling quantum bits, but also the ability to do so in practice, showing the progression of quantum information science from the blackboard to the laboratory. My presentation will give an overview of some of the recent results in quantum information science on the way to implement quantum error correction.   I will show how noise can be characterize efficiently when our goal is to find suitable quantum error correcting codes. I will show demonstrations of control to implement some quantum error correcting codes and finally how can noise be extracted through algorithmic cooling. I will comments on some challenges that need to be solved and a path towards implementing many round of quantum error correction.
Modern electron spin resonance for quantum computing
There are many suggestions for quantum computer architectures that make use of electron spins as a physical system for quantum bits (qubit).  Electron Spin Resonance (ESR) is a well-established technique in physics and chemistry, which provides information about unpaired electron spins in a variety of paramagnetic materials.  Thus, it may seem natural to make use of ESR a tool in the field of quantum computing (QC).  However, conventional ESR has very bad spin sensitivity, making it unsuitable for tacking most of the challenges associated with QC, which often require single qubit (spin) manipulating and reading capability.  In this talk we will show how modern techniques and methodologies that were recently developed in the field of ESR, such us ultra-high sensitive resonators and ultra-high imaging resolution can be used in a possible novel architecture for a spin-based quantum computer.
Measuring weak values with operational constraints
Weak values are an interesting and useful characteristic  of quantum systems with past (pre selected) and future (post selected) boundary conditions. In  theory they can be observed directly by in a relatively simple setup of `weak measurements'.  In reality weak values may be hard or even impossible to measure due to operational constraints. For example the absence of projective measurements in ensemble quantum processors poses an obstacle in the post-selection stage. I will present a method for sidestepping this obstacle  and present experimental results of the first weak measurement in NMR.  The experiment involves 3 qubits but can be extended to larger systems of up to 12 qubits using conventional methods.  Moreover the method for implementing the post selection stage can be useful for more general purposes.
Joint work with Dawei Lu, Jun Li, Hang Li and  Raymond Laflamme,
Maximally entangled states
Every maximally entangled state (MES) is shown to be a product state expressed in (suitably chosen) collective coordinates. Such product state may be viewed as defining an origin for a "phase space" like d  ^2 array representing d^2 orthonormal  MES. (Straight) Lines in this "phase space" is shown to effect reversal of the Schmidt diagonalization: it gives particles product state in terms of d terms of MES.
Limitations of algorithmic cooling
Heat-bath algorithmic cooling (AC) of spins is a powerful spin-cooling approach that (ideally) cools exponentially better than cooling by reversible entropy manipulations. I will discuss two limitations of AC.
For non-ideal AC, we studied the impact of realistic relaxation times of spins on the achievable cooling. We derived, by simulations, the attainable cooling levels for given ratios of relaxation times. We expect this analysis of the limitations to be valuable for the planning of future experiments. For ideal and optimal AC, I will discuss some bounds on the number of required steps (based on entropy considerations). These bounds present important consequences of using AC for improving signal-to-noise ratio in magnetic resonance spectroscopy.
Experimental heat bath cooling and algorithmic cooling in liquid state NMR
Heat-bath algorithmic cooling (AC) utilizes thermalization to purify a subset of qubits, such that the total Shannon entropy of the qubit system is reduced. AC was originally developed for scalable quantum computers, and was initially demonstrated in solid-state nuclear magnetic resonance (NMR), where rapid removal of entropy was achieved via spin diffusion. Alternatively, AC may be applied for quantum simulation, as recently demonstrated by cooling quantum gases near absolute zero, and by distilling states in quantum optics.
We utilized gradient ascent pulse engineering (GRAPE), an optimal control algorithm, to apply AC in liquid state NMR, where entropy removal is hindered by the relatively small differences in relaxation times among the spins. Various cooling algorithms were applied onto the three qubits of 13C-labeled trichloroethylene, cooling the system beyond Shannon's entropy bound. For example, in one experiment, one of the two carbon qubits was cooled by a factor of 4.61 ± 0.02 after seven cycles of AC, beyond the initial information content of the spin system.
A state separator
Alice Bob and Eve in quantum land
Quantum key distribution (QKD), in contrast to `classical' key distribution, is in principle information-theoretic secure.
I will briefly present several recent results. On the one hand I'll present a QKD protocol in which one of the parties (Alice, or Bob) is classical, and I will argue that it is still secure.
On the other hand, I'll present a novel attack against practical QKD, called the reversed-space attack, and a special case of that attack – the `fixed apparatus' attack. I'll show that QKD implementations in which the receiver's apparatus is fixed (namely, does not depend on a choice of basis at each qubit transmission) are totally insecure against a strong eavesdropper that has a one-time
(single) access to the receiver's equipment.