Recently Updated Projects

The rapid growth of global trade, outpacing real-adjusted GDP, has amplified the environmental footprint of international value chains, a prominent trend in recent decades that has been ineffectively addressed due to the complexity of global supply chains and discrepancies in sustainable policy. To inform sustainable policy-making, we integrate quantum computing and econometrics in a novel framework, leveraging usage of a Multi-Regional Input-Ouput (MRIO) model to quantify embodied CO2-emissions across global supply chains and model intersectoral relations across regions. Our approach builds upon the quantum-inspired notion of complex network optimisation, drawing from the Harrow-Hassidim-Lloyd algorithm to solve the linear system and optimise environmental policy interventions within a MRIO model. Through encoding the optimisation problem for quantum computation, we seek to achieve a faster and more efficient method of emission reduction strategies across large supply chains. Within this simulated pseudo-economy, we also provide a higher dimension of scenario analysis to evaluate the environmental impacts of global trade interventions. This paper ultimately seeks to provide empirical support for global policies to push for the sustainable management of supply chains, as well as contributing to the emerging paradigm of quantum economics.

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.