TENSORIZED PAULI COMPOSER

In the paper, a new method was designed to construct a hamiltonian matrix which is given by a form
of weighted summation of Pauli operators. A symplectic representation of Pauli terms allows us to
express finite dimension Hilbert space as a matrix form. Therefore, Pauli basis representation of
hamiltonian could be treated as one kind of symplectic representation. A transformation between
two specific symplectic representations was designed. One is a common XZ code and the other is an
index of Pauli basis matrix of TPD algorithm[1]. With inversed TPD algorithm, the transformation
of the code yields a common matrix representation from weighted Pauli summation. The transfor-
mation between two codes consist of simple bitwise XOR operation. Consequently, the benefit of
original benefit of TPD is preserved in iTPD. In addition to the algorithm, a term-chasing version
was developed for sparse matrix in Pauli basis. It is roughly O(16n) time complexity but, in sparse
case and < 5 qubit system, it showed 10 time faster than the prior algorithm. The algorithm has
O(n4n) time complexity in the worst case, and comparing to the term-by-term construction method
with O(n16n) complexity, it is computationally efficient for general case.