Recently Updated Projects

Ergodicity, the ability of a system to explore all accessible phase states, is a fundamental assumption in statistical mechanics, particularly in the thermodynamic representations of many-body systems. However, not all many-body systems are ergodic. Quantum scars represent a weaker form of ergodicity breaking, where certain eigenstates exhibit atypically low entanglement and resist full thermalization, leading to long-lived coherent dynamics. Partnering with VTech professor Dr. Tianci Zhou, this project looks to numerically investigate the entanglement of eigenstates of Hamiltonians, which will be used to reproduce the low-entanglement signatures found in the quantum scars phenomenon. By analyzing how these anomalous entanglement patterns evolve in time or scale with system size, we aim to ultimately gain insight into the behavior of quantum scars and their underlying mechanisms in many-body localization, constrained dynamics, and related non-equilibrium phenomena.

ADAPT-VQE is a Variational Quantum Eigensolver (VQE) for solving quantum chemistry simulations and optimization problems. However, in the real world, we can only use a finite number of measurement shots to estimate expectation values, limiting the performance of the algorithm. This is known as sampling noise, which impacts the accuracy of energy evaluations and the gradients for variational parameter optimization. In this work, we analyze the performance of ADAPT-VQE under realistic noise conditions to compare multiple classical optimizers such as gradient descent, quasi-Newton methods, and simplex-based approaches. We hope that our findings contribute to the development of more accurate and efficient variational algorithms with fewer measurements.

This research project aims to investigate the application of Grover’s algorithm, a quantum search algorithm, to optimize options pricing in discrete-time financial models, specifically by utilizing a binomial time distribution. Binomial models approximate the behavior of an asset’s price by modeling it as a series of up or down movements over discrete time steps. These models are typically used for pricing American-style options, where holders can exercise the option at any time before expiration. This project focuses on encoding the binomial model into a quantum search Boolean Satisfiability problem. Each node in the binomial price tree will represent a possible asset price and decision point. Grover’s will be used to search through every node and identify the optimal exercise strategy using the predicted payoff at each node. Ultimately, the goal of this project will be to create as accurate as possible of a model for exercising options in American markets, and will compare results to those of European Market estimations.

As cybersecurity threats grow, quantum computing offers both solutions and challenges to encryption methods. My research explores Grover’s Algorithm, a quantum search algorithm that significantly accelerates brute-force attacks on cryptographic systems. Specifically, I am investigating how Grover’s Algorithm can be applied to password key encryption by reducing the search complexity from classical computing to using quantum superposition and amplitude amplification. Through theoretical analysis and quantum simulation, I am studying how this speedup affects the security of common encryption schemes, such as AES, and how cryptographic resilience must adapt in a post-quantum landscape. Additionally, I am experimenting with Qiskit to simulate quantum circuits, implementing Grover’s Algorithm on small-scale datasets to analyze its practical implications. By bridging quantum computing principles with real-world cryptographic challenges, this project aims to understand both the vulnerabilities and potential countermeasures needed for future encryption standards.

Recent deep learning research has widely popularized the transformer model. Transformers have now ubiquitously been implemented in state-of-the-art models like GPT, Whisper, DALLE, GoogleViT, Facebook DETR, among many others. However, the true success of these models has to do with their adaptability to different downstream tasks. Traditional fine-tuning approaches involve re-training all of the weights of the model, which can increase inference latency and decrease efficiency due to the millions or even billions of parameters potentially involved, making full fine-tuning prohibitive. To avoid full fine-tuning, researchers developed Low Rank Adaptation (LoRA), which greatly reduces the number of parameters necessary to train. We propose a novel method of LoRA that takes advantage of a quantum circuit module that applies U3 transformations to inputs treated as normalized quantum superposition state vectors. In doing so, we aim to achieve superior accuracy or faster convergence to a reasonable accuracy in comparison to other state-of-the-art fine-tuning methods. Our new LoRA method can be applied to any pre-existing deep learning architectures that utilize weight matrices, as a method of parameter efficient fine tuning. This includes large language models, diffusers, and more. The research can empower others to create deep learning models specific to their own tasks efficiently while avoiding expensive training. In the future, we propose exploring the use of other gates and operators, as well as photonic operations that are not necessarily spin based.

Hamiltonian cycles are a cycle in a graph where each vertex is visited only once. Similar to the travelling salesman problem, the aim of finding hamiltonian cycles is to reduce the number of edges traversed while still visiting every vertex. As the graph size gets bigger, it becomes exponentially more difficult to find a cycle. Using Quantum Approximation Optimization Algorithms (QAOA), it becomes possible to turn a single hamiltonian cycle to two smaller problems, with the potential to beat the speed of classical algorithms.

The Earth is continuously exposed to a stream of high-energy particles originating from extraterrestrial space. Such particles come in various forms, including galactic cosmic rays (GCRs) traveling from distant galaxies or solar energetic particles (SEPs) exuding from the Sun. Although Earth's magnetosphere acts as a shield for much of this radiation, interactions between cosmic particles and our atmosphere result in secondary particles, causing adverse health effects particularly prominent to those at an aviation altitude. Specifically, intense solar particle events known as ground level enhancements (GLEs) can produce photons with energies exceeding 200 MeV. In order to effectively assess the health risk to those at altitudes susceptible to secondary radiation, computational analysis can be conducted using the Geant4 toolkit, which utilizes Monte Carlo radiation transport codes to simulate the passage of particles through matter. In this study, we use this toolkit to develop a software to measure the radiation dosimetry due to GLEs at aviation altitudes.