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Pauli Decomposition by Character Theory: A Memory-Bounded Algorithm for Qubits and Qudits
Pauli decomposition underpins Trotterization, phase estimation, sparse-Hamiltonian simulation, and variational observables, at exponential naive cost. From the character theory of $(\mathbb{Z}_2)^n$, characters $χ_z(v)=(-1)^{\langle v,z\rangle}$ are the diagonal Pauli strings, so any diagonal operat
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