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Recent Submissions

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    Tensor probabilistic model checking of finite-horizon Markov chains (extended version)
    (University of Waterloo, 2026) Li, Jianlin; Guo, Nick; Ye, Peter; Zhang, Yizhou
    We reexamine the problem of verifying Markov chains with respect to step-bounded reachability probabilities. Prevailing approaches rely on encoding the state-transition matrix using either explicit or symbolic representations. While these approaches are effective for sparse transition dynamics, they scale less favorably in the dense regime. Our insight is to cast probabilistic model checking of Markov chains as computations over dense tensors. This methodology enables the use of off-the-shelf compiler toolchains for optimized execution of these tensor computations on hardware accelerators. We prove the soundness of the methodology of mapping probabilistic model checking to tensor computations. We implement our approach in a tool called Tessa. Empirical evaluation shows that Tessa unlocks massive speedups over state-of-the-art methods on selected benchmarks from the literature.
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    Virtualizing continuations (extended version)
    (University of Waterloo, 2026) Ma, Cong; Jung, Jonghyun; Zhang, Yizhou
    Effect handlers and multishot continuations are powerful abstractions for managing control flow; together, they offer concise and modular ways to express and handle nondeterminism, randomness, and more. However, implementing multishot continuations in the presence of stack-allocated lexical resources - lexical effect handlers in particular - is challenging, since stack copying invalidates references to these resources. We present a novel implementation strategy for lexical effect handlers that fully supports multishot continuations. The key idea is to virtualize the stack space used by continuations. Each stack-allocated handler instances is assigned a virtual address, and all effect invocations through these virtual addresses are mediated by an address translation mechanism. A software-based memory management unit in the runtime system performs these translations efficiently, exploiting the lexical scoping discipline of effect handlers. We capture the essence of our approach via a new operational semantics for lexical effect handlers and prove it correct with respect to the standard semantics. We also implement it in a compiler and runtime system. Compared to prior languages with lexical effect handlers, our implementation increases expressivity by fully supporting multishot continuations - and, as a happy consequence, unlocks significant performance gains by enabling parallel execution of multishot continuations.
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    Curvature continuous piecewise Pythagorean hodograph curves
    (University of Waterloo, 2026) Mann, Stephen
    This report develops constructions for cubic, quartic, and quintic Pythagorean hodograph curves (PHC). The cubic construction is a rederivation of an earlier cubic PHC construction, but in the real plane rather than the imaginary plane. The quartic construction is also a rederivation of an earlier construction, again in the real plane rather than the imaginary plane. In addition, the free parameter in this quartic construction is used to interpolate curvature at one end of the curve. The quintic construction builds a quintic PHC cure that interpolates the position, tangent, and curvature at two points.
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    Qudit Quantum Computation on Trapped Barium-137 Ions
    (University of Waterloo, 2026-07-29) Zutt, Nicholas Covey Fleming
    Quantum processors promise to revolutionise humanity’s computational prowess. Today’s leading quantum processors are built on trapped atomic ions, using one particular isotope of barium. In this thesis, we explore a less pursued avenue toward using this promising ion, 137Ba+, as the quantum system for fully scaled and fault-tolerant quantum computing. We explore the advantages and trade-offs inherent in using this atomic playground to encode not just the typical two level systems that make the canonical qubits of today’s quantum computers, but instead pushing this boundary out to encoding dozens of levels (qudits) in individual ions. Starting from precision spectroscopy of the stable and meta-stable manifolds within the ion that make this high-dimensional control possible, we first design protocols for high-fidelity state preparation and measurement (SPAM) over 25 distinct levels which we implement with an average fidelity of 99.51%. Using an extension of the classic Ramsey interferometric techniques for probing the noise and coherence of quantum systems, we study the coherence properties of multi-level superpositions in this ion. We develop a no-free-parameters model of the behaviour of this system in which noise sources such as laser frequency fluctuations, magnetic field drifts, calibration errors, and coherent errors are independently characterised in order to fully capture system performance. We use this demonstrated coherent control to execute small quantum algorithms by encoding multiple virtual qubits within a single trapped 137Ba+ ion. We implement the well-known Bernstein-Vazirani key-finding algorithms on 2- and 3-virtual qubit encodings and demonstrate secret key guessing success probabilities of 98% and 84% respectively. We also implement Grover’s database search algorithm on 2-virtual qubits, showing a 96% success rate. We then demonstrate a simple and scalable “all-software” approach to compensating for one of the largest sources of noise in our system: AC power-line synchronous magnetic field fluctuations. By characterising this source precisely, and compensating the attendant frequency and phase shifts associated with this coherent noise source, we are able to push the implementation of the Bernstein-Vazirani algorithm up to a 16-level qudit, with a 70% algorithm success rate. This is a record high dimension on which to implement a full algorithm for any qudit, across any quantum computing platform. Finally, we demonstrate fully Haar-random unitary gate set benchmarking on qudits of varying dimension in this platform and comment on the future feasibility of high-dimensional encoding in trapped ion processors. Taken together, these results present a strong case for quantum processors with primitives that encode more than the typical two states in any given single ion.
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    Emergency System Strain, Code Black Events, and Climate Change in Thunder Bay, Ontario: A Data-Driven Evaluation of Contributing Factors and Predictive Insights
    (University of Waterloo, 2026-07-29) Coady, Isabella
    Background: Code Black ambulance events, a blackout period in emergency medical services, occur when paramedics are unable to be dispatched on new calls. Typically, due to delays in transferring previous patients from paramedic care to hospital staff in the ED, Code Blacks pose a serious risk to public health and safety. At the Thunder Bay Regional Health Sciences Centre (TBRHSC) and Superior North EMS, Code Black events have become a common occurrence. This Master's thesis aims to investigate the underlying causes of Code Black events and EMS strain by analyzing ED and EMS data. It will also examine the influence of climate change and extreme weather conditions on Code Blacks. Research Question: The objective of this thesis is to understand the factors contributing to Code Black events and EMS strain in Thunder Bay, and how an exploratory analysis of ED, EMS, and climate data, along with machine learning methods, can be used to understand system overload. Methods: This retrospective observational study integrates perspectives from public health, emergency medicine, and climate change to address the research question. ED, EMS, and climate data will be used to identify patterns and predictive indicators of Code Black events at TBRHSC. A variety of methods will be employed to address the research question, including descriptive statistical analyses, data visualization techniques, and machine learning approaches. Expected Outcomes: The goal of this thesis is to identify the factors contributing to Code Black events and system strain to develop predictive insights that support equitable and resilient resource planning.