baronefr / quantum-computing-unipd

Weekly homeworks of QIC course, UniPD, AY 2022/23

Quantum Information and Computing

The weekly homeworks of QIC class (Prof. Simone Montangero).

Topic 1: introduction to FORTRAN and LAPACK

HW 1 (due 1 nov)

Evaluation: ⭐⭐⭐⭐/4

1. Warm-up Fortran program | I choose to implement the 4th order central difference.
2. Integer and real numbers | Overflow issues of variable types.
3. Matrix product CPU time benchmarking | Benchmark the CPU time of matrix product functions: nested loops vs matmul.

HW 2 (due 8 nov)

Evaluation: ⭐⭐⭐⭐/4

1. Checkpoint subroutine | Write a checkpoint subroutine for debugging.
2. Documentation | Rewrite HW1/EXR3 with documentation.
3. 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

1. Matrix product CPU time benchmarking | Write a python script to automatize the benchmarking process (I already did this with a bash script in HW1).
2. Diagonalize a complex matrix | Use LAPACK routines to generate random hermitian matrices and diagonalize.
3. Random matrix theory | Study the eigenvalue spacing of random hermitian matrices (Wiger-Dyson statistics).

Topic 2: solutions to Schrödinger equation

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.

Topic 3: many-body systems

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.

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Quantum Information and Computing
AY 2022/2023 - University of Padua