Recently Updated Projects

We're working on ADAPT-VQE with Mafalda Ramôa and Dr. Economou's group at Virginia Tech. Quantum computing offers new computational methods for quantum mechanical analysis of molecular systems. We are testing TETRIS-ADAPT-VQE, an algorithm which optimizes a quantum circuit's parameters while adding new gates into the circuit from a pool of operators. The operators come from tiled unitary product states (tUPS), which preserve importation molecular symmetries like spin numbers.

Strongly correlated molecules present a significant challenge in quantum chemistry due to the complex electron interactions. These molecules, which often exhibit highly entangled electronic structures, require more sophisticated methods in calculating the ground state energies than traditional methods, which tend to produce large error, require greater circuit depth, and have less efficiency. To address this, our research focuses on testing the Adaptive Variational Quantum Eigensolver (ADAPT-VQE) algorithm, which is well-suited for handling strongly correlated systems. Our research compares the quantum observables, through the expectation value of the fermionic number, total spin, and Z spin projection operators, at each iteration in algorithm in both fixed (unitary coupled cluster singles and doubles (UCCSD)) and adaptive (fermionic-ADAPT-VQE) ansätze, which are combinations of complex operators from varying operator pools.

Our research proposes a novel method for photonic quantum computing using a single-photon, 2-qubit spatial mode system. By encoding qubits in the polarization states of individual spatial modes, we implement and analyze Bell State entanglement and Grover’s algorithm. Experimentally, we will use a 405 nm pump laser with a diode controller and BBO crystal, along with a combination of alignment mirrors, waveplates, and beamsplitters from the ThorLabs quantum optics kit. Computationally, we will use Perceval, a Python-based linear optical quantum computing library.

However, phase interferences introduced by the initial beam splitter operation, modeled as a "Black Box” operator, are shown to skew the measurement outcomes and influence the behavior of single-qubit gates. We mitigate these effects by balancing the circuit with Hadamard gates, effectively canceling extra phase contributions. Our approach enables us to construct a single photon controlled-NOT gate that achieves uniform Hong-Ou-Mandel (HOM) interference across all detectors. Our Bell State created with this gate successfully violates the Clauser-Horne-Shimony-Holt (CHSH) inequality. Expanding on this framework, we observe that Grover’s algorithm finds the marked state with 100% accuracy using Perceval’s noisy Strong Linear Optical Simulator (SLOS) and with 98.8% accuracy when random phase shifts are infused into the model. By training a simple linear regression model, we can predict the algorithm’s accuracy for specific nonrandom phase shifts with a mean squared error (MSE) of 3.70e-05 and an R^2 of 0.904.

This project explores how the Harrow-Hassidim-Lloyd (HHL) quantum algorithm can accelerate high-resolution turbulence simulations by solving linearized fluid equations, such as the pressure Poisson equation, on a quantum computer. Classical methods for solving these equations are computationally expensive, especially on high-resolution grids, which limits their scalability. The HHL algorithm, however, offers an exponential speedup for solving linear systems, making it a promising alternative to overcome these challenges.

My focus is on optimizing the HHL algorithm for fluid dynamics. By incorporating preconditioning techniques specifically designed for this problem, I aim to reduce the condition number of the pressure Poisson equation, improving computational efficiency. Additionally, by leveraging the sparsity and symmetry of these fluid equations, I work toward bridging the gap between quantum computing and turbulence modeling. My goal is to enable high-resolution simulations that were previously infeasible due to computational constraints.

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.

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.

My project focuses on utilizing Grover's Algorithm, an advanced quantum algorithm designed to enhance the probability of finding the correct solution in unstructured search problems. The primary application is in quantum cryptography, where Grover's Algorithm is used to analyze and potentially break classical encryption schemes by significantly reducing the time required for brute-force attacks. I am grateful to be under the guidance of Dr. Atul Mantri, a professor at Virginia Tech.

As part of this research, I am also applying Grover's Algorithm to Boolean satisfiability (SAT) problems, which involve determining whether there exists a set of inputs that satisfy a given logical formula. This serves as a foundational study for broader applications in optimization and problem-solving. In this case, I will utilize what I learned from these SAT problems to solve more complex encryption problems. Additionally, the project includes an analysis and comparison of Simon’s Algorithm, another quantum algorithm, and its potential uses in cryptography and data pattern recognition. These investigations aim to deepen our understanding of quantum computing’s implications for secure data systems and for future developments in quantum technology.