The following is a list of some potential project topics, with one or two key references for each. This list is by no means exhaustive, and you are welcome to choose a topic not on this list. (In particular, you might find other topics of interest in the Quantum Algorithm Zoo.)

- Algebraic problems
- Quantum algorithms for solvable groups [Watrous]
- Quantum algorithm for counting points on algebraic curves [Kedlaya]
- Connection between the dihedral HSP and lattice problems [Regev]
- Quantum algorithms for hidden shift problems [DHI] [Roetteler]
- Quantum reductions for the HSP: Hidden translation and orbit coset [FIMSS]
- Entangled measurements are required for the symmetric group [MRS] [HMRRS]
- Quantum algorithms for arbitrary-degree number fields [EHKS] [BS16]

- Quantum walk
- General framework for quantum walk search algorithms [MNRS]
- Finding marked items with quantum walks [AGJK]
- Verifying matrix products [BS06]
- Testing group commutativity [MN]
- Quantum walk speedup of backtracking algorithms [Montanaro]

- Quantum query complexity
- Lower bounds for quantum state generation [AMRR]
- Limitations on quantum algorithms for symmetric functions [AA] [Chailloux] [BCGKPW]
- Adversary lower bounds for element distinctness, collision, and
*k*-sum [Belovs] [BS12] [BR] - Time-space tradeoffs [KSW]
- Triangle finding [Le Gall]
- Superquadratic separations for total functions [ABBLSS] [ABK]
- Limitations on quantum speedup for total functions [ABKRT]
- Graph connectivity with cut queries [LSZ]

- Quantum simulation
- Simulating lattice Hamiltonians [HHKL]
- Simulation with nearly optimal dependence on spectral norm [Low]
- Product formula error bounds [CSTWZ]
- Quantum algorithms for quantum chemistry [LBGHMWB] [LBHSRRT]
- Simulating low-energy states [SS]
- Universality results for analog simulation [CMP]

- Other topics