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Phases of matter in quantum information and error correction
(University of Waterloo, 2026-06-17) Negari, Amirreza
This thesis investigates phases of matter and phase transitions through the lens of quantum information, with an emphasis on phenomena not fully captured by conventional local observables or equilibrium order parameters. While the traditional framework of phase transitions relies on correlation functions and order parameters, entanglement and other information-theoretic quantities provide a broader language for characterizing both equilibrium and non-equilibrium many-body systems. A central perspective developed here is that such quantities furnish sharp diagnostics of phases and criticality, particularly in topological phases subjected to noise and measurement. First, we study how measurements on topological quantum states reshape entanglement structure and induce phase transitions. Focusing on the toric code, we show that measuring part of the system generates distinct entanglement phases in the remaining degrees of freedom, and that tuning the measurement protocol drives transitions between them. To analyze these phenomena, we develop analytical tools that track the entanglement structure of the post-measurement state and reveal a rich phase diagram. Next, we turn to topological codes in the presence of noise, where information-theoretic probes reveal forms of non-equilibrium criticality invisible to conventional observables. In this setting, we identify extended critical behavior in mixed states and show that conditional mutual information diagnoses transitions between distinct regimes of information retention and loss. Interpreted through quantum error correction, these transitions distinguish phases in which logical information is robustly preserved, only partially accessible, or completely lost. Building on this connection, we extend the mixed-state perspective from static codes to fault-tolerant dynamics by relating faulty syndrome-extraction circuits to the mixed-state structure of an associated higher-dimensional resource state. This leads to a decoder-independent diagnostic of fault tolerance based on the conditional mutual information of syndrome data across spacetime. The resulting spacetime Markov length diverges at the fault-tolerance threshold, providing an intrinsic information-theoretic characterization of the preservation and breakdown of logical information in noisy quantum circuits. Finally, we develop structural results for thermal and symmetry-constrained mixed states. We show that symmetry can obstruct the sudden death of entanglement in thermal states: for canonical ensembles and for Gibbs states subject to superselection rules, entanglement persists, and in broad settings remains nonzero at arbitrarily high temperatures. In fermionic systems, this identifies parity superselection as a generic mechanism protecting mixed-state entanglement and fermionic negativity. Complementing this perspective, we study extendibility as a tractable probe of entanglement structure in fermionic Gaussian states, showing that it admits an efficient characterization and provides practical criteria for mixed-state entanglement, including an extendibility transition in the disordered Kitaev chain. Taken together, these results support a unified picture in which information-theoretic quantities serve as fundamental diagnostics of phase transitions and criticality in both equilibrium and non-equilibrium quantum systems.
Chemical Looping Combustion with an Industrial Waste: Kinetic Modeling and Pilot-Scale Design using Red Mud
(University of Waterloo, 2026-06-17) Ronson, Dana
Chemical looping combustion (CLC) is an emerging carbon capture process that can produce a high-purity stream of CO2 without the energy-intensive separation that is associated with traditional carbon capture strategies. In the process, a solid metal oxygen carrier (OC) facilitates the splitting of the conventional combustion reaction into distinct oxidation and reduction subreactions such that the fuel and air atmospheres remain separate. CLC has yet to be implemented at industrial scale; hence, there is interest in further developing this emerging technology. One such area of development is the OC material, as the overall performance of a CLC system is crucially dependent on the performance of the OC. While synthetic OCs have been the dominant materials used for CLC development, they demand valuable materials. Thus, there has been a recent interest in utilizing lower-cost materials such as industrial wastes in CLC. The use of industrial waste OCs in CLC has gained recent attention as these materials demonstrate the potential to be a cost-effective alternative to synthetic OCs. A key limitation in the development of CLC with industrial waste OCs is the lack of modeling efforts on CLC systems with these materials. This work presents a dynamic multiscale packed bed reactor CLC model to investigate the performance of red mud, an industrial waste from the alumina refining industry, as an OC. Kinetics describing the oxidation reaction of red mud with oxygen as well as reduction reactions of red mud with CH4, CO, and H2 fuels were identified and validated using lab-scale experimental data. Sensitivity analyses were performed on kinetic parameters and reactor operating conditions, where the model exhibited reasonable predictions. The model developed in this work serves to advance the development of CLC by enabling simulation and model-based design methods for the packed bed reactor with a red mud OC. A proposed nominal pilot scale design exhibits moderate utilization of the red mud OC and high fuel conversion. By producing approximately 848.1 MJ of energy in a single cycle, this design demonstrates the potential for red mud to be an effective OC in large scale CLC. The red mud pilot-scale design was compared to a similar system from the literature that used a synthetic OC, and it was found that the red mud system produced less heat as a result of its low density leading to a smaller solids inventory. Nevertheless, red mud boasts lower material costs than traditional synthetic OCs. An economic optimization of the pilot scale design for separate reduction and oxidation stages revealed that it is crucial to consider the integration of both stages to determine an optimal design for a complete cycle of the CLC system (i.e., jointly considering how the performance of reduction impacts the economics of oxidation).
Order in the Open: Symmetries and Entanglement of Many-Body Mixed States
(University of Waterloo, 2026-06-17) Almeida Lessa, Leonardo
Real-world quantum systems are open and interact with their environments, requiring a statistical description via mixed states. This thesis investigates the interplay between global symmetries and quantum entanglement in open many-body systems, asking whether symmetries can robustly enforce long-range entanglement and correlation patterns, even under severe decoherence or high temperatures. In the first half, we extend quantum anomalies to mixed states and establish the anomaly-nonseparability correspondence: mixed states that are strongly symmetric --- where every state in the statistical ensemble possesses the same symmetry charge --- exhibit long-range multipartite entanglement. We show that the unique multipartite structure of this anomalous entanglement gives rise to entirely new phases of matter that are intrinsically mixed, i.e., lacking any pure state representative. Conversely, we demonstrate that strong-weak mixed anomalies, such as Lieb-Schultz-Mattis anomalies, imply long-range correlations without strictly requiring quantum entanglement. Broadening this correspondence to higher-form symmetries, we introduce a definition of mixed-state phases of matter that is insensitive to long-range classical correlations, thereby only capturing distinct patterns of long-range entanglement. We argue that strong symmetries and their anomalies are the defining features of such phases. In the second half, we shift focus to non-anomalous symmetries and show when they alone suffice to enforce entanglement. We investigate maximally mixed states invariant under on-site symmetries, which naturally emerge as steady states of generic quantum evolutions that preserve these symmetries strongly. We exactly calculate the values of several entanglement measures that are notoriously difficult to tackle analytically or numerically, such as the entanglement of formation and distillation. For continuous non-Abelian symmetries, we find high amounts of long-range entanglement, despite the states being maximally mixed within the symmetric subspace. Finally, we prove that the same strong symmetry conditions and superselection rules prevent the sudden death of entanglement at finite temperatures, even for Abelian symmetries. This explains previously observed behavior in canonical ensembles with Ising symmetry and in fermionic systems.
Influenza forecasting with Google Flu Trends
(Public Library of Science, 2013-02-14) Dugas, Andrea Freyer; Jalalpour, Mehdi; Gel, Yulia; Levin, Scott; Torcaso, Fred; Igusa, Takeru; Rothman, Richard E.
Background We developed a practical influenza forecast model based on real-time, geographically focused, and easy to access data, designed to provide individual medical centers with advanced warning of the expected number of influenza cases, thus allowing for sufficient time to implement interventions. Secondly, we evaluated the effects of incorporating a real-time influenza surveillance system, Google Flu Trends, and meteorological and temporal information on forecast accuracy. Methods Forecast models designed to predict one week in advance were developed from weekly counts of confirmed influenza cases over seven seasons (2004-2011) divided into seven training and out-of-sample verification sets. Forecasting procedures using classical Box-Jenkins, generalized linear models (GLM), and generalized linear autoregressive moving average (GARMA) methods were employed to develop the final model and assess the relative contribution of external variables such as, Google Flu Trends, meteorological data, and temporal information. Results A GARMA(3,0) forecast model with Negative Binomial distribution integrating Google Flu Trends information provided the most accurate influenza case predictions. The model, on the average, predicts weekly influenza cases during 7 out-of-sample outbreaks within 7 cases for 83% of estimates. Google Flu Trend data was the only source of external information to provide statistically significant forecast improvements over the base model in four of the seven out-of-sample verification sets. Overall, the p-value of adding this external information to the model is 0.0005. The other exogenous variables did not yield a statistically significant improvement in any of the verification sets. Conclusions Integer-valued autoregression of influenza cases provides a strong base forecast model, which is enhanced by the addition of Google Flu Trends confirming the predictive capabilities of search query based syndromic surveillance. This accessible and flexible forecast model can be used by individual medical centers to provide advanced warning of future influenza cases.
Multi-parametric clustering for sensor mode coordination in cognitive wireless sensor networks
(Public Library of Science, 2013-02-13) Wang, Xiao Yu; Wong, Alexander
The deployment of wireless sensor networks for healthcare applications have been motivated and driven by the increasing demand for real-time monitoring of patients in hospital and large disaster response environments. A major challenge in developing such sensor networks is the need for coordinating a large number of randomly deployed sensor nodes. In this study, we propose a multi-parametric clustering scheme designed to aid in the coordination of sensor nodes within cognitive wireless sensor networks. In the proposed scheme, sensor nodes are clustered together based on similar network behaviour across multiple network parameters, such as channel availability, interference characteristics, and topological characteristics, followed by mechanisms for forming, joining and switching clusters. Extensive performance evaluation is conducted to study the impact on important factors such as clustering overhead, cluster joining estimation error, interference probability, as well as probability of reclustering. Results show that the proposed clustering scheme can be an excellent candidate for use in large scale cognitive wireless sensor network deployments with high dynamics.