The weekly homeworks of QIC class (Prof. Simone Montangero).
HW 1 (due 1 nov)
Evaluation: ⭐⭐⭐⭐/4
- Warm-up Fortran program | I choose to implement the 4th order central difference.
- Integer and real numbers | Overflow issues of variable types.
- Matrix product CPU time benchmarking | Benchmark the CPU time of matrix product functions: nested loops vs
matmul
.
HW 2 (due 8 nov)
Evaluation: ⭐⭐⭐⭐/4
- Checkpoint subroutine | Write a checkpoint subroutine for debugging.
- Documentation | Rewrite HW1/EXR3 with documentation.
- Complex matrix type | Define a Complex Matrix type, with appropriate routines for initialization, deallocation and some math interfaces.
HW 3 (due 22 nov)
Evaluation: ⭐⭐⭐⭐/4
- Matrix product CPU time benchmarking | Write a python script to automatize the benchmarking process (I already did this with a bash script in HW1).
- Diagonalize a complex matrix | Use LAPACK routines to generate random hermitian matrices and diagonalize.
- Random matrix theory | Study the eigenvalue spacing of random hermitian matrices (Wiger-Dyson statistics).
HW 4 (due 29 nov)
Evaluation: ⭐⭐⭐⭐/4
- Solution of the time independent Schrödinger equation. Finite difference methods have been used to compute the second order derivative.
HW 5 (due 6 dec)
Evaluation: ⭐⭐⭐⭐/4
- Solution of the time dependent Schrödinger equation with Trotter-Suzuki expansion.
HW 6 (due 13 dec)
Evaluation: ⭐⭐⭐⭐/4
- Description of systems with density matrices: representation in FORTRAN and implementation of partial trace subroutine.
HW 7 (due 20 dec)
Evaluation: ⭐⭐⭐⭐/4
-
Transverse field Ising model: exact diagonalization of
$N$ spin-1/2 particles on a one-dimensional lattice.
HW 8 (due 6 jan)
Evaluation: ⭐⭐⭐⭐/4
My evaluation:⭐⭐⭐☆/4
I could have done something better, to improve the convergence speed. Maybe I will play with this HW again later on...
- Transverse field Ising model with Real Space Renormalization Group and Infinite Density Matrix Renormalization Group.