GSOC: Pauli string algebra and fast decomposition routine

[김현성 (믹스)]

Title: Pauli class implementation for Hamiltonain decomposition.

Idea: 

In 2023, Reggio et al, used xz code for determining the commutation of the given two Pauli string, P1, P2. I found that we can construct more efficient implementation of Pauli group structure with two integer tuple, xz code including the next things.

- Fast commuting determination.

- Pauli matrix algebra of 2^n dimension as n length binary representation of integer.

- Matrix-xz code transformation.

The matrix-xz code transformation is achieved through application of "Tensorized Pauli decomposition algorithm" method. They researched to find decomposed coefficient location of the given Hermit matrix. I found a transformation that xz code to corresponding coefficient location on the matrix.

Status: 

I almost implemented core structure and oprations in Opttrot repository of mine

as a prototype.

It was written in C at first, but python version also exists.

Matrix-xz code transformation routine is remained.

Involved Software

Tensorized Pauli decomposition algorithm paper code

Difficulty

Intermediate

Prerequisite Knowledge

Linear algebra,

Binary operation,

Basic group theory,

Project Length

175 hours

[Sangyub Lee]

I think that it is fairly a good proposal.
However, the only problems are that we may not be familiar with the physics, or quantum computation,
or we may not have clear roadmap whether the algorithm is significantly necessary for the module,
However, if you already have self-motivated knowledge and practice about the topic,
some people may be able to guide to complete your work with with general python programming or general mathematical background.

[김현성]

That's might be true.

I recently found that sympy also started to support basic quantum computation routines.

However, the coverage is narrow comparing to the other frameworks. 

I thought It would be useful for the researchers to work with Hamiltonian, but it is true that my proposal is more likely to focus on computationability of group element.

2024년 3월 29일 (금) 오후 8:29, Sangyub Lee <syle...@gmail.com>님이 작성:

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