An efficient Pauli decomposition algorithm for structured matrices

Daniel J. Spencer, Kishor Bharti, Alexey V. Gorshkov

Decomposing classical matrices into linear combinations of Pauli strings is a major bottleneck for end to end implementations of near term quantum algorithms. In this work, we consider a promise version of this Pauli decomposition problem in which the matrix is guaranteed to have support on only $k = \mathsf{poly}(n)$ Pauli strings and is given through classical sparse query access. Existing Pauli decomposition al...