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We construct quantum circuits that exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced “qubitization” framework, one can use quantum phase estimation to sample states in the Hamiltonian eigenbasis with optimal query complexity O (λ/ε), where λ is an absolute sum of Hamiltonian coefficients and ε is the target precision. For both the Hubbard model and electronic structure Hamiltonian in a second quantized basis diagonalizing the Coulomb operator, our circuits have T-gate complexity O (N+ log (1/ε)), where N is the number of orbitals in the basis. This scenario enables sampling in the eigenbasis of electronic structure Hamiltonians with T complexity O (N 3/ε+ N 2 log (1/ε)/ε). Compared to prior approaches, our algorithms are asymptotically more efficient in gate complexity and require fewer T gates near the …