Projects

Here are selected project write-ups, including my thesis work and several projects completed in collaboration with wonderful peers. Some of these results were not developed into publications, but I hope they can still offer valuable insights by:

• Highlighting directions that did not work out, and identifying key challenges.
• Numerically verifying and confirming established results.
• Demonstrating how elegant theorems and algorithms can be applied to related problems and scenarios.

Limitations of Quantum Methods for Breaking Cryptography and Optimization
Doctoral Dissertation

Differentially Private SGD with Curriculum Learning

• We incorporated curriculum learning into stochastic gradient descent with differential privacy to better balance data privacy and model performance.
• We experimented different noise injection schedules (noise curriculum) and re-arranged sample ordering (sample curriculum) when training a deep learning model.
• Results show promising accuracy improvements with noise curriculum, but little evidence of performance gains from sample curriculum.

Differentiable Pulse-Based Variational Quantum Eigensolver (PPT)

• We proposed a polynomial parameterization method for pulse-based VQE, reducing parameters from $M \times Q$ to $n \times Q$ (where $M$ is the number of time segments and $Q$ is the number of qubits), along with an efficient analytic gradient formula that lowers computational cost to $O(1)$ compared to $O(M)$ in finite difference methods, though it applies to a limited set of pulse sequences.
• Implementations confirm the proposed pulse-based VQE is fast, but we cannot reach the theoretical minimum due to pulse sequence ansatz choices, which is limited by our gradient calculation method.

Quantum Dynamic Programming

• We applied the divide-and-conquer dynamic programming approach ABIKPV18 to NP-hard problems like graph coloring, minimum clique cover, and minimum dominating set, achieving time complexity improvements from $O(2.4423^n)$ classically to $O(1.9140^n)$ quantumly on certain instances.
• We highlighted that for problems like the dominating set and minimum vertex cover, dynamic programming underperforms compared to direct application of Grover’s algorithm on classical brute-force methods, suggesting the need for new approaches to utilize dynamic programming effectively.

Towards Physically-Consistent, Chaotic Spatiotemporal Dynamics with Echo State Networks

• This study investigates the use of echo state networks (ESNs) for time-series forecasting in chaotic physics.
• We compare a basic ESN with two physics-informed variants on the Lorenz attractor and then test the ESN on a large-scale atmospheric model and a real-world weather dataset.
• Results show that a well-tuned traditional ESN can outperform physics-informed methods. While the ESN accurately predicts the global evolution of atmospheric primitive equations over short periods (~67 hours), it struggles with real-world data.
• Accepted to AAAI Spring Symposium Series 2021

Investigation of Area Law for Local Hamiltonians
Undergraduate Thesis

• We implemented generic and RRG algorithms to find ground states of local Hamiltonians, including Heisenberg and AKLT models.
• We verified an area law for von Neumann entanglement entropy in the XXZ model for up to $14$ qubits.
• We confirmed exponential Schmidt coefficient distribution up to 13 qubits and predicted the slope for $14$ qubits, with discrepancies within $0.1$.