The fast matrix composition of Pauli polynomial.

This research is about the algorithm of fast matrix composition of Pauli polynomial through a proper coefficient matix of the polynomial. Using XZ simplex mapping and matrix index, we can reveal the coefficient matrix index of the corresponding Pauli term which is generated  by the decompostiion algorithm suggested by Hantzo et al.

The complexity of the composition algorithm is O(8^n) and which is twice more faster than the common term-by-term methods where O(16^n + 4^n(f(n)-1)), f(n) is a  single term composition complexity. Comparing to the Qiskit, pennylane and Pauli composer routines, the implemented algorithm is practically useful for manipulate the Pauli polynomial.

This repository contains the preprint about the research and the python implementation of the algorithm.