quantum-computing-gqsp

Low-Degree GQSP in Qiskit

This repository contains my mini-project notebook on Generalised Quantum Signal Processing (GQSP), based on Motlagh and Wiebe's paper (https://arxiv.org/abs/2308.01501)

Project summary

The class notebook had already introduced the same paper and some low-degree verification examples. This project does NOT claim to implement the baseline setup from scratch. It uses the class material as a starting point and then extends it in a few small directions.

My notebook does 5 things:

1. Re-implement the recursive GQSP angle-recovery procedure for one degree-2 example used in class.
2. Verify that the resulting block matrices match the expected transforms of polynomials $P(U)$ and $Q(U)$.
3. Explore a small low-degree experiment for recovering a complementary polynomial from a chosen bounded polynomial.
4. Extend to a toy fractional-power check inspired by the paper's Theorem 10.
5. Extend to a numerical stability experiement where the recovered angles are perturbed.

Files

• low degree gqsp.ipynb - main notebook

Requirements

The notebook uses Python with:

• numpy
• matplotlib
• scipy
• qiskit

Notes

This is a low-degree toy implementation rather than a full large-scale implementation of hte paper's later routines and applications, such as full Hamiltonian simulations. The goal of this project was to understand and implement the core constructive part of GQSP in a small, reasonable setting.