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Several linear algebra routines for quantum computing use a basis of tensorproducts of identity and Pauli operators to describe linear operators, andobtaining the coordinates for any given linear operator from its matrixrepresentation requires a basis transformation, which for an $\mathrmN\times\mathrm N$ matrix generally involves $\mathcal O(\mathrm N^4)$arithmetic operations. Herein, we present an efficient algorithm that for ourparticular basis transformation only involves $\mathcal O(\mathrmN^2\log_2\mathrm N)$ operations. Because this algorithm requires fewer than$\mathcal O(\mathrm N^3)$ operations, for large $\mathrm N$, it could be usedas a preprocessing step for quantum computing algorithms for certainapplications. As a demonstration, we apply our algorithm to a Hamiltoniandescribing a system of relativistic interacting spin-zero bosons and calculatethe ground-state energy using the variational quantum eigensolver algorithm ona quantum computer.

Efficient algorithm for generating Pauli coordinates for an arbitrary linear operator