Course Projects

Quantum Algorithm for Solving PDEs and Its Applications

Surveyed three families of quantum PDE approaches and compared space/time complexity with classical solvers; identified boundary handling, state preparation, and Trotter error as key bottlenecks; pointed to qubitization and better observable extraction as next steps.

• Wave-equation Hamiltonian simulation (log qubit scaling).
• Advection via block-encoded nonunitary steps with postselection reuse.
• High-order finite-difference mappings to banded Hamiltonians.

Regression and Bayesian Inference: Mean Squared Error

Showed how Gaussian-noise linear regression links MSE minimization to maximum likelihood; with a Gaussian prior, MAP recovers ridge regression with penalty strength λ = σ²/τ².

Exact Decoding of Quantum Error-Correcting Codes

Explored exact decoding algorithms for QEC with an eye to performance/scalability and regimes where exact methods are viable.

• Motivated by Prof. Chun-Ming Chen’s Coding Theory (NTU).
• Reference: PRL 134, 190603.

The Features of Optical Computing

Introduced photonic computing and why it is attractive (parallelism, low-loss links, low cross-talk, one-way propagation, very high carrier bandwidth ~500 THz); outlined hurdles in architecture co-design, materials, and reducing system bulk.

Comparing Gate-Based vs. Unitary-Based Pulse Generation with Qiskit Pulse (in progress)

Contrasts predefined gate pulses vs. custom unitary-based pulses on IBM Quantum hardware—fidelity, flexibility, and implementation complexity.