QISCA advanced study
Study plan
This study treats partial differential equation solvers on a quantum computer. The algorithms assume fault-tolerant quantum computing, and they sit next to linear solvers such as HHL, quantum singular value transformation, and the linear combination of Hamiltonian simulation.
Understand the main types of PDEs and the quantum algorithms used to solve them.
- Format
- Online, in Korean
- Length
- 15–16 weeks
- Time
- Sundays, 20:00–22:00
- Level
- Junior or senior undergraduates, and graduate students
Preparation: Linear algebra and advanced mathematics beforehand.
References
Schedule
Sessions follow the report. Discretization comes immediately after the overview, before block encodings and linear-system solvers. Cauchy's formula for the linear solver is covered with the 10/25 and 11/01 sessions, together with Chapters 7 and 9, rather than as its own week.
| Session | Sunday | Topic | Report |
|---|---|---|---|
| 1 | 9/13 | Overview: PDEs, algorithms, and the pipeline | Ch. 1–2 |
| 2 | 9/20 | Discretization | Ch. 3 |
| 3 | 9/27 | Block encoding and qubitization | Ch. 4 |
| 4 | 10/04 | Amplitude algorithms and quantum signal processing | Ch. 5 |
| 5 | 10/11 | Quantum singular value transformation | Ch. 5 |
| 6 | 10/18 | Hamiltonian simulation | Ch. 6 |
| 7 | 10/25 | Solving linear systems | Ch. 7 |
| 8 | 11/01 | Linear differential equations and LCHS | Ch. 8 |
| 9 | 11/08 | Elliptic PDEs | Ch. 10 |
| 10 | 11/15 | Hyperbolic PDEs | Ch. 11 |
| 11 | 11/22 | Parabolic PDEs | Ch. 12 |
| 12 | 11/29 | Nonlinear PDEs | Ch. 13 |
| 13–15 | 12/06–12/20 | VQLS and NISQ, latest research, summary | Ch. 14–15 |