A complete list of my publications and preprints. See also my Google Scholar profile for citation metrics.
PHYS 437B — Undergraduate Thesis, University of Waterloo, April 2025
In this project, we will illustrate the theoretical concept of circuit benchmarking, an efficient and scalable protocol to “lower bound” the process fidelity of a circuit. Finding a lower bound to the process fidelity is crucial because it tells us what is the worst-case error rate in our quantum circuit. We will exhaustively run simulations on quantum circuits with different error models and error strengths to measure the closeness of the theoretical bound imposed by the circuit benchmarking theory with respect to the actual process fidelity. We will find that in several cases there is a minimal or zero gap, and thus not only we have found a lower bound, but rather a good approximation to the process fidelity.
Theory of Quantum Information — Course Project, University of Waterloo, 2025
Cycle benchmarking is a scalable protocol used to measure the error rate of a specific cycle of quantum gates implemented in parallel. We will introduce the cycle benchmarking protocol, explain how it works, and numerically illustrate its effectiveness. We demonstrate that relaxing the assumptions required to accurately estimate the process fidelity can lead to inaccurate results; in particular, allowing gate-dependent noise on the twirling gates can cause a misestimation of the process fidelity. However, we also show that highly gate-dependent errors can still yield accurate results in certain regimes. Finally, when the gate-independent condition is relaxed, we show that it is possible to reconcile the estimated and theoretical fidelities by measuring in a different basis via a unitary transformation which depends on both the chosen error model on the twirling gates and the targeted gateset.
Quantum Machine Learning — Course Project, University of Waterloo, 2025
This project explores the application of Quantum Machine Learning (QML) to predict the outcomes of Major League Baseball (MLB) games, specifically the Postseason matches that took place throughout the month of October. Using features such as team batting averages, pitching performance, and game context (e.g. home vs. away), we implemented two QML algorithms: the Quantum Support Vector Machine (QSVM) and the Variational Quantum Classifier (VQC), using the Qiskit framework. We then compared these quantum classifiers to their classical counterparts, namely the Support Vector Machine (SVM) and a classical neural network, the Multi- Layer Perceptron (MLP) Classifier. We found that the QML algorithms achieved prediction accuracies comparable to those of the classical algorithms; however, training the QML models was significantly more time-consuming. We therefore conclude that, in this setting, there is no quantum advantage, and that classical prediction models remain the preferable choice.
AMATH 900 — Advanced Quantum Theory, University of Waterloo, Spring 2024
We introduce the concept of superoperators, which are math ematical constructs used to describe the evolution of quantum states. We will we focus on completely positive and trace-preserving maps, which are essential in quantum information theory as they represent the most general form of physical quantum operations. Next, we delve into different representations of superoperators. We define each of these representations in detail and prove several theorems that demonstrate their importance. Then, we prove that all the different representations of a superoperator are equivalent. This equivalence is important because it allows us to convert between representations with ease, depending on which one is more convenient for the problem at hand. Consequently, we analyze the properties of these representations when we add the restrictions that the superoperators are trace-preserving and/or completely positive. Finally, we visualize specific quantum channels using these representations. This analysis provides a new perspective on how the representations depict the channels and allows us to examine their properties in greater detail.