SciPost Submission Page
H2ZIXY: Pauli spin matrix decomposition of real symmetric matrices
by Rocco Monteiro Nunes Pesce, Paul D. Stevenson
Submission summary
As Contributors:  Paul Stevenson 
Arxiv Link:  https://arxiv.org/abs/2111.00627v1 (pdf) 
Code repository:  http://personal.ph.surrey.ac.uk/~phs3ps/h2zixy.py 
Date submitted:  20211103 21:52 
Submitted by:  Stevenson, Paul 
Submitted to:  SciPost Physics Codebases 
Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We present a code in Python3 which takes a square real symmetric matrix, of arbitrary size, and decomposes it as a tensor product of Pauli spin matrices. The application to the decomposition of a Hamiltonian of relevance to nuclear physics for implementation on quantum computer is given.
Current status:
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2021121 (Invited Report)
Strengths
I am unable to find any strong points on the code and/or manuscript.
Weaknesses
1 Attempts to solve a well understood problem by a bruteforce method.
2 The method proposed is not scalable; impossible to use even for small number of qubits.
3 The code does not provide any new insight or remarkable feature to speed up the problem.
4 The code does not come with proper documentation and testing, and therefore can not be considered a package.
Report
The code and complementary manuscript "H2ZIXY: Pauli spin matrix decomposition of real symmetric matrices" describe a function to find the Pauli matrix decomposition of a realsymmetric matrix.
The Pauli decomposition is done by bruteforce search of the 4^N Pauli operators of an Nqubit Hamiltonian.
I am unable to accept the code and attached manuscript for publication in SciPost codebases because it does not match any of the acceptance criteria described in https://scipost.org/SciPostPhysCodeb/about#criteria.
Addressing pointbypoint the acceptance criteria:
1 There exist plenty of algorithms and packages that perform the Pauli decomposition of Hermitian matrices, thus the code does not address a need of the community.
2 The user guide is nonexistent, only the comments on the code. The comments in the code do not serve as a guide, nor explain its and usability.
The code is based on brutforce search and linearequation solver, therefore there is no new insight on how to solve this problem.
3 The authors provide an example of the code usage. However, a quick test on 6 qubits takes a large amount of time and resources on a laptop.
Scalability and usability are of essence for a code that aims at be widely used.
4 The code lacks of testing, benchmarking and comparison to other packages/methods for the same problem.
Requested changes
1 The code must first provide a new algorithm/method to find the Pauli decomposition of any real or imaginary Hermitian matrix without exponential cost.
2 The authors must search existing packages as a benchmarking and comparison of their method.
3 Test of the code are necessary for the code quality.