Block-product paired non-Gaussian fermionic states allow efficient classical additive-error approximation of transition amplitudes, overlaps, and high-weight correlators under free-fermionic dynamics using multivariate Pfaffian polynomials.
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Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.
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Classical simulation of free-fermionic dynamics and quantum chemistry with magic input
Block-product paired non-Gaussian fermionic states allow efficient classical additive-error approximation of transition amplitudes, overlaps, and high-weight correlators under free-fermionic dynamics using multivariate Pfaffian polynomials.
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Non-Gaussianity of random quantum states
Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.