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The non-stabilizerness of fermionic Gaussian states

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The non-stabilizerness of fermionic Gaussian states

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AbstractWe introduce an efficient method to quantify nonstabilizerness in fermionic Gaussian states, overcoming the long-standing challenge posed by their extensive entanglement. Using a perfect sampling scheme based on an underlying determinantal point process, we compute the Stabilizer Renyi Entropies (SREs) for systems with hundreds of qubits. Benchmarking on random Gaussian states with and without particle conservation, we reveal an extensive leading behavior equal to that of Haar random states, with logarithmic subleading corrections. We support these findings with analytical calculations for a set of related quantities, the participation entropies in the computational (or Fock) basis, for which we derive an exact formula. We also investigate the time evolution of non-stabilizerness in a random unitary circuit with Gaussian gates, observing that it converges in a time that scales logarithmically with the system size. Applying the sampling algorithm to a two-dimensional free-fermionic topological model, we uncover a sharp transition in non-stabilizerness at the phase boundaries, highlighting the power of our approach in exploring different phases of quantum many-body systems, even in higher dimensions.► BibTeX data@article{Collura2026nonstabilizernessof, doi = {10.22331/q-2026-03-23-2036}, url = {https://doi.org/10.22331/q-2026-03-23-2036}, title = {The non-stabilizerness of fermionic {G}aussian states}, author = {Collura, Mario and Nardis, Jacopo De and Alba, Vincenzo and Lami, Guglielmo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2036}, month = mar, year = {2026} }► References [1] Eduardo Fradkin. ``Field Theories of Condensed Matter Physics''.

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Oxford University Press. (2017). https://doi.org/10.1093/acprof:oso/9780198785781.001.0001 [120] Masatoshi Sato and Yoichi Ando. ``Topological superconductors: a review''. Reports on Progress in Physics 80, 076501 (2017). https://doi.org/10.1088/1361-6633/aa6ac7Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-23 07:28:51: Could not fetch cited-by data for 10.22331/q-2026-03-23-2036 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-23 07:28:52: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe introduce an efficient method to quantify nonstabilizerness in fermionic Gaussian states, overcoming the long-standing challenge posed by their extensive entanglement. Using a perfect sampling scheme based on an underlying determinantal point process, we compute the Stabilizer Renyi Entropies (SREs) for systems with hundreds of qubits. Benchmarking on random Gaussian states with and without particle conservation, we reveal an extensive leading behavior equal to that of Haar random states, with logarithmic subleading corrections. We support these findings with analytical calculations for a set of related quantities, the participation entropies in the computational (or Fock) basis, for which we derive an exact formula. We also investigate the time evolution of non-stabilizerness in a random unitary circuit with Gaussian gates, observing that it converges in a time that scales logarithmically with the system size. Applying the sampling algorithm to a two-dimensional free-fermionic topological model, we uncover a sharp transition in non-stabilizerness at the phase boundaries, highlighting the power of our approach in exploring different phases of quantum many-body systems, even in higher dimensions.► BibTeX data@article{Collura2026nonstabilizernessof, doi = {10.22331/q-2026-03-23-2036}, url = {https://doi.org/10.22331/q-2026-03-23-2036}, title = {The non-stabilizerness of fermionic {G}aussian states}, author = {Collura, Mario and Nardis, Jacopo De and Alba, Vincenzo and Lami, Guglielmo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2036}, month = mar, year = {2026} }► References [1] Eduardo Fradkin. ``Field Theories of Condensed Matter Physics''.

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The non-stabilizerness of fermionic Gaussian states

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