Thesis defence

Subscribe to Thesis defence

Melissa Henderson PhD Thesis Defence

Neutron Scattering Investigations of Three-Dimensional Topological States

Physics, 200 University Ave West, Room PHY 352
Waterloo, ON, CA N2L 3G1

Magnetic skyrmions represent a unique class of topological magnet characterized by nanometric swirling spin-textures which possess a non-trivial Berry curvature. The combination of their topological stability, unique transport properties, and emergent dynamics has made skyrmions the forerunner for novel spintronic high-density memory and ultra-low power logic device applications. In this thesis, we explore the development and application of various neutron scattering tomography and structured neutron beam techniques for three-dimensional investigations of bulk magnetic topological materials and their defect-mediated dynamical phenomena. Characterization of the disordered multi-phase bulk skyrmion material, Co8Zn8Mn4, was performed through detailed SANS measurements over the entire temperature-magnetic field phase diagram of the material as a function of a dynamic skyrmion ordering sequence. 2D SANS images in combination with micromagnetic simulations reveal a novel disordered-to-ordered skyrmion square lattice transition pathway which represents a new type of non-charge conserving topological transition. In the metastable skyrmion triangular lattice phase, dynamical field-dependent skyrmion responses showed an exotic memory phase in spite of hysteresis protocols involving field-induced saturation into the ferromagnetic phase. Three-dimensional examinations of skyrmion stabilization mechanisms and their dynamical defect pathways were explored using a novel SANS tomography technique which processes multi-projection neutron scattering images as its input. Application of the technique to the ordered thermal equilibrium skyrmion triangular lattice phase yielded the first three-dimensional visualizations of a bulk skyrmion lattice. The reconstructions unveiled a host of exotic skyrmion features, such as branching, segmented, twisting, and filament structures, mediated by three-dimensional topological transitions through two different emergent monopole (MP)-antimonopole (AMP) defect pathways. Finally, the direct identification and determination of topological features and defects in bulk micromagnetic materials, without a priori knowledge of the sample, was explored using holographic approaches for the generation of neutron helical waves. Linear neutron waves in a conventional SANS setup were input on microfabricated gratings which consist of arrays of various q-fold fork-dislocation phase-gratings with nanometric spatial dimensions. Far-field scattering images exhibited doughnut intensity profiles centered on the first diffraction orders, thereby demonstrating the tunable generation of topological neutron states for phase- and topology-matched studies of quantum materials. The amalgamation of these works demonstrates the development and application of novel tools for direct investigations of bulk topological magnetic materials, while uncovering a diverse collection of skyrmion energetics, disorder-dependent dynamics, and three-dimensional topological transition defect pathways. These methods and results open the door to a new generation of neutron scattering techniques for the probing of exotic topological interactions and the complete standalone characterization of quantum materials and their topological phenomena.

Jamal Busnaina PhD Thesis Defence

Analog Quantum Simulation via Parametric Interactions in Superconducting Circuits

While universal quantum computers are still years away from being used for simulating complicated quantum systems, analog quantum simulators have become an increasingly attractive approach to studying classically intractable quantum systems in condensed matter physics, chemistry, and high-energy physics. In this dissertation, we utilize superconducting cavities and qubits to establish analog quantum simulation (AQS) platforms to study systems of interest. 

An approach of AQS that has gained interest lately is the use of photonic lattices to simulate popular lattice models. These systems consist of an array of cavities or resonators arranged on a lattice with some couplings graph between modes. We propose an in situ programmable platform based on a superconducting multimode cavity. The unique design of the cavity allows us to program arbitrarily connected lattices where the coupling strength and phase of each individual coupling are highly programmable via parametrically activated interactions. Virtually any quadratic bosonic Hamiltonian can be realized in our platform with a straightforward pumping scheme.

The effectiveness of the cavity-based AQS platform was demonstrated by the experimental simulation of two interesting models. First, we simulated the effect of a fictitious magnetic field on a 4-site plaquette of a bosonic Creutz ladder, a paradigmatic topological model from high-energy physics.  Under the right magnetic field conditions, we observed topological features such as emergent edge states and localized soliton states. The platform's ability is further explored by introducing pairing (downconversion) terms to simulate the Bosonic Kitaev chain (BKC), the bosonic version of the famous Fermionic Kitaev chain that hosts Majorana fermions. We observe interesting properties of BKC, such as chiral transport and sensitivity to boundary conditions.  

In the final part of the dissertation, we propose and implement a parametrically activated 3-qubit interaction in a circuit QED architecture as the simplest building block to simulate lattice gauge theories (LGT). LGT is a framework for studying gauge theories in discretized space-time, often used when perturbative methods fail.   The gauge symmetries lead to conservation laws, such as Gauss's law in electrodynamics, which impose constraints tying the configuration of the gauge field to the configuration of ''matter'' sites.  Therefore, any quantum simulation approach for LGTs must maintain these conservation laws, with one strategy in AQS being to build them in at the hardware level.  Here, the gauge constraints are explicitly included using a higher-order parametric process between three qubits. The simplest 2-site U(1) LGT building block is realized with two qubits as matter sites and a third qubit as the gauge field mediating the matter-matter interaction, which is crucial to maintain the symmetry of U(1) LGTs.  

Stefanie Beale PhD Thesis Defence

Modeling and managing noise in quantum error correction 

Simulating a quantum system to full accuracy is very costly and often impossible as we do not know the exact dynamics of a given system. In particular, the dynamics of measurement noise are not well understood. For this reason, and especially in the context of quantum error correction, where we are studying a larger system with branching outcomes due to syndrome measurement, studies often assume a probabilistic Pauli (or Weyl) noise model on the system with probabilistically misreported outcomes for the measurements. In this thesis, we explore methods to decrease the computational complexity of simulating encoded memory channels by deriving conditions under which effective channels are equivalent up to logical operations. Leveraging this method allows for a significant reduction in computational complexity when simulating quantum error correcting codes. We then propose methods to enforce a model consistent with the typical assumptions of stochastic Pauli (or Weyl) noise with probabilistically misreported measurement outcomes. First, via a new protocol we call measurement randomized compiling, which enforces an average noise on measurements wherein measure- ment outcomes are probabilistically misreported. Then, by another new protocol we call logical randomized compiling, which enforces the same model on syndrome measurements and a probabilistic Pauli (or Weyl) noise model on all other operations (including idling). Together, these results enable more efficient simulation of quantum error correction systems by enforcing effective noise of a form which is easier to model and by reducing the simulation overhead further via symmetries. The enforced effective noise model is additionally consistent with standard error correction procedures and enables techniques founded upon the standard assumptions to be applied in any setting where our protocols are simultaneously applied. 

TC Fraser PhD Thesis Defence

An estimation theoretic approach to quantum realizability problems

This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form under which conditions does there exists a quantum state exhibiting a given collection of properties? The approach adopted by this thesis is to utilize mathematical techniques previously developed for the related problem of property estimation which is concerned with learning or estimating the properties of an unknown quantum state. Our primary result is to recognize a correspondence between (i) property values which are realized by some quantum state, and (ii) property values which are occasionally produced as estimates of a generic quantum state. In Chapter 3, we review the concepts of stability and norm minimization from geometric invariant theory and non-commutative optimization theory for the purposes of characterizing the flow of a quantum state under the action of a reductive group.

In particular, we discover that most properties of quantum states are related to the gradient of this flow, also known as the moment map. Afterwards, Chapter 4 demonstrates how to estimate the value of the moment map of a quantum state by performing a covariant quantum measurement on a large number of identical copies of the quantum state. These measurement schemes for estimating the moment map of a quantum state arise naturally from the decomposition of a large tensor-power representation into its irreducible sub-representations.

Then, in Chapter 5, we prove an exact correspondence between the realizability of a moment map value on one hand and the asymptotic likelihood it is produced as an estimate on the other hand. In particular, by composing these estimation schemes, we derive necessary and sufficient conditions for the existence of a quantum state jointly realizing any finite collection of moment maps. Finally, in Chapter 6 we apply these techniques to the quantum marginals problem which aims to characterize precisely the relationships between the marginal density operators describing the various subsystems of composite quantum state. We make progress toward an analytic solution to the quantum marginals problem by deriving a complete hierarchy of necessary inequality constraints.