Every matrix element of a fermionic Gaussian operator between arbitrary Pauli product states is expressed as a single Pfaffian of a 2L by 2L kernel with explicitly tabulated sign matrices.
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Matrix Elements of Fermionic Gaussian Operators in Arbitrary Pauli Bases: A Pfaffian Formula
Every matrix element of a fermionic Gaussian operator between arbitrary Pauli product states is expressed as a single Pfaffian of a 2L by 2L kernel with explicitly tabulated sign matrices.