Special Topics in Quantum Information Science (EE5105, 113-2, Spring 2025)
Project Topic Ideas
The following consists of a list of potential project topics for the course. This list is not exhaustive, and you are welcome to choose a topic not in this list.
Unitary synthesis
- Inverse-free Solovay-Kitaev algorithm [BG]
- Lower bound for unitary synthesis augmented with an oracle [LMW]
Algebraic problems
- Computing the unit group of an arbitrary degree number fileld [EHKS]
- Reducing number of qubits in factoring [CFS]
- Dihedral HSP and lattice problems [R]
- HSP for the symmetric group [HMRRS], [MRS]
- State hidden subgroup problem [BGW]
Learning quantum states and circuits
- Shadow tomography [KGKB]
- Learning shallow quantum circuits [HLBKALM]
- Learning Gibbs state [BLMT] and Hamiltonians [BLMT]
- Construct pseudorandom unitaries [MH], [MPSY]
- Approximate unitary t-design [LL], [SHH] [HLT]
- Anti-concentration of random quantum circuits [FGZ]
Quantum walk
Quantum query complexity
- Lower bound for symmetric functions [AA], [BCGKPW]
- Lower bound for k-sum [BS]
- Triangle finding [LG]
- Total functions [ABKRT]
- Time-space tradeoff [BKW], [CGLQ]
- Adiabatic quantum computing with no sign problem [H], [GV]
Optimization
- Quantum linear system solver [LS]
- Decoded quantum interferometry [JSWZSKIB]