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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: (pdf)
Code repository:
Date submitted: 2021-11-03 21:52
Submitted by: Stevenson, Paul
Submitted to: SciPost Physics Codebases
Academic field: Physics
  • Nuclear Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


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:
Editor-in-charge assigned

Submission & Refereeing History

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Submission 2111.00627v1 on 3 November 2021

Reports on this Submission

Anonymous Report 1 on 2021-12-1 (Invited Report)


I am unable to find any strong points on the code and/or manuscript.


1- Attempts to solve a well understood problem by a brute-force 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.


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 real-symmetric matrix.
The Pauli decomposition is done by brute-force search of the 4^N Pauli operators of an N-qubit 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

Addressing point-by-point 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 non-existent, 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 brut-force search and linear-equation 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.

  • validity: poor
  • significance: poor
  • originality: low
  • clarity: ok
  • formatting: below threshold
  • grammar: below threshold

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