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    Lower Bounds on Average-Case and Non-Local Quantum Computation
    (University of Waterloo, 2026-02-06) Asadi, Vahid Reza
    This thesis studies computational and information-theoretic limitations in both classical and quantum models of computation. It is organized into two parts, each addressing a different aspect of computational hardness. Despite their differences, both parts share a common goal: understanding how structural and physical constraints shape what classical and quantum algorithms can achieve. In Part I, we present lower bounds on the average-case complexity of certain tasks in classical and quantum settings. We develop a general framework for constructing efficient worst-case to average-case reductions. Applying this framework, we obtain such reductions for fundamental problems in a variety of computational models; namely, algorithms for matrix multiplication, streaming algorithms for the online matrix-vector multiplication problem, and static data structures for all linear problems, as well as the multivariate polynomial evaluation problem. We further extend this framework to the setting of quantum algorithms, along the way obtaining a tight bound on the average-case quantum query complexity of the matrix-vector multiplication problem. Our techniques rely crucially on tools from additive combinatorics. In particular, we show local correction lemmas that rely on new probabilistic and noise-robust versions of the quasi-polynomial Bogolyubov-Ruzsa lemma. In Part II, we give quantum gate and entanglement lower bounds on certain non-local tasks. A non-local quantum computation (NLQC) replaces direct interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, f-routing and f-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, under the assumption of perfect correctness. Within this setting, we give a lower bound on the Schmidt rank of any entangled state that completes these tasks for a given function f(x,y) in terms of the rank of a matrix G whose entries are zero when f(x,y)=0 and strictly positive otherwise. This also leads to a lower bound in terms of the non-deterministic quantum communication complexity of f. Due to a relationship between f-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we obtain a new technique for lower bounding the randomness complexity of CDS. Finally, we show that the number of quantum gates plus single-qubit measurements required to implement a function f is at least linear in the entanglement-assisted simultaneous-message-passing communication complexity of f. As a consequence, we derive a linear lower bound for the inner-product function.
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    Directional dependence of phase transition splitting by uniaxial strain: A new test to determine strontium ruthenate superconducting states
    (University of Waterloo, 2014-06) Chen, Anffany
    Since the discovery of superconductivity in strontium ruthenate, there has been a widespread effort to understand its properties on a phenomenological level. To this date, there is not enough coherent experimental evidence to conclude if the superconducting phase has broken time-reversal symmetry. In this article we propose a new test based on the fact that for a multi-component order parameter, the application of uniaxial stress could cause phase transition splitting. Our analysis shows that such splitting depends on the direction of applied stress, and such directional dependence is different for every predicted superconducting phase. In particular, splitting occurs at all directions if and only if the superconducting phase is the one with broken time-reversal symmetry.
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    Ancestry Deconvolution via Differential Privacy
    (University of Waterloo, 2026-02-05) Chowdhury, Raiyan
    This thesis presents the first study of ancestry determination under differential privacy (DP). Direct-to-consumer genomics companies, such as 23andMe, offer ancestry testing to millions of individuals, yet remain vulnerable to severe data breaches. Such incidents are especially concerning because genomic data is uniquely identifying, highly correlated, and permanent once exposed. At the time of writing, 23andMe disclosed a catastrophic breach in October 2023 that compromised the genetic profiles of an estimated 6.9 million users, underscoring the urgent need for stronger privacy guarantees in genomic analysis. In this work, we investigate the application of DP to ancestry deconvolution. Using the 1000 Genomes dataset and Gnomix, a state-of-the-art ancestry inference model, we evaluate how privatizing single nucleotide polymorphism (SNP) data affects ancestry classification accuracy. We implement both naïve and correlation-aware local differential privacy (LDP) mechanisms across varying privacy budgets, enabling a systematic study of the privacy-utility trade-off in ancestry inference. Our results demonstrate that while naïve DP perturbations significantly degrade accuracy, correlation-aware LDP mechanisms preserve substantially more predictive power by accounting for linkage disequilibrium (LD). This thesis establishes a foundation for private ancestry deconvolution, providing an empirical benchmark of state-of-the-art DP methods in genomics and highlighting both the challenges and potential of integrating DP into ancestry testing.
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    Cultural ecosystem services and sense of place: post-rehabilitation assessment of Wadi Hanifah’s performance from a socio-cultural lens
    (Taylor & Francis Ltd., 2025-12-24) Kashmiri, Shahad; Khirfan, Luna
    This paper evaluates the socio-cultural performance of urban ecological rehabilitation through the lens of cultural ecosystem services (CES) and sense of place. Accordingly, it introduces a dynamic, context-sensitive evaluative framework that integrates place image, identity, and attachment as key performance indicators. The framework is applied to the rehabilitation of Wadi Hanifah in Riyadh, Saudi Arabia, using a mixed-methods approach that combines document reviews, online surveys, and semi-structured interviews to assess shifts in the Wadi’s meaning and use post-rehabilitation. Findings reveal a transformation in the Wadi’s place image – from associations with degradation and utilitarian function to one centered on recreation and heritage. The results underscore how ecological rehabilitation can foster socio-cultural value and strengthen collective identity. The proposed framework not only supports future evaluations of Wadi Hanifah but also offers a transferable model for assessing similar projects elsewhere, advancing more holistic understandings of the interplay between ecosystems and human experience.
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    NAVIGATING SETTLEMENT AND WELL-BEING: EXPERIENCES OF NEWCOMER WEST AFRICAN IMMIGRANTS IN ONTARIO
    (University of Waterloo, 2026-02-04) Oko-Oboh, Ehinomen
    Background: Canada has become a popular destination for immigrants, with a significant proportion arriving through economic immigration pathways. Despite the growing population, African economic immigrants remain understudied and are often grouped with other immigrant subgroups whose experiences may differ significantly from theirs. Although many arrive with strong educational and professional qualifications, African newcomers frequently encounter structural barriers and cultural transitions that shape their well-being, settlement experiences, and help-seeking behaviours. Understanding these experiences is important in improving culturally centered support. Objective: This study examined how settlement stressors, cultural perspectives, and changes in sociocultural realities shape West African economic immigrants’ settlement experiences, understanding of well-being, and their engagement with support services in Ontario. Methodology: This study employed a qualitative research design using semi-structured, in-depth interviews with nine West African economic immigrants who had lived in Ontario for between nine months and four years. Data were analyzed sequentially using Braun and Clarke’s six-step thematic analysis. Interpretation was conducted inductively and informed by Ager and Strang’s Integration Framework and Berry’s Acculturative Stress Theory. Results: Inductive coding identified six themes that captured the participants’ settlement journeys, identity negotiations, and well-being experiences. These themes were organized into three overarching domains: (1) Starting Over, which described participants’ lives before immigrating, emotional transitions, and early settlement stressors; (2) Identity and Systems Navigation, which highlighted cultural adjustments, racialization, experiences of ‘sudden’ Blackness, employment barriers, and housing challenges; and (3) Resilience and Well-being, which reflected key coping strategies, including faith, community support, and cultural maintenance. Conclusion: The findings highlighted that well-being among West African economic immigrants is multidimensional and shaped by the interaction of cultural identity, settlement challenges, racialization, and structural inequities. Overall, greater attention is needed to center the experiences of economic immigrants to develop meaningful and culturally responsive approaches to settlement support and integration.