Pith. sign in

REVIEW 14 cited by

Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2409.08180 v2 pith:OEE2MZNY submitted 2024-09-12 quant-ph cs.CCmath-phmath.MP

classification quant-phcs.CCmath-phmath.MP
keywords fermionicconvolutionnon-gaussianaccessibleadvantagecharacterizingcomponentscomputation
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components, which are essential to the computational advantage of fermionic systems. Using fermionic convolution, we propose an efficient protocol that tests the fermionic Gaussianity of pure states using three copies of the input state. We also introduce "Non-Gaussian Entropy," an experimentally accessible resource measure that quantifies fermionic non-Gaussianity. These results provide new insights into the study of fermionic quantum computation.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Williamson majorization theory of fermionic non-Gaussianity

    quant-ph 2026-08 accept novelty 8.0 of 10

    A pure state's Williamson spectrum is weakly majorized by its ensemble average under any fermionic Gaussian protocol, unifying monotones and conversion bounds for non-Gaussianity.

  2. Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions

    quant-ph 2026-07 accept novelty 8.0 of 10

    A unified Magic Rényi Entropy measure for spins, bosons, and fermions is shown to have a universal critical contribution determined by the Affleck-Ludwig boundary entropy.

  3. Learning the closest Slater determinant

    quant-ph 2026-07 conditional novelty 7.0 of 10

    First provable algorithms with complexity bounds for learning the closest Slater determinant to an arbitrary fermionic state, plus a sharp 2/3 fidelity threshold in the optimization landscape.

  4. Computable fermionic non-Gaussianity from the covariance matrix

    quant-ph 2026-07 unverdicted novelty 7.0 of 10

    Two covariance-matrix-derived entropy families are proven to be fermionic non-Gaussianity monotones, yielding SWAP-gate lower bounds and classical-simulation upper bounds.

  5. Practical Tests and Witnesses of Fermionic non-Gaussianity

    quant-ph 2026-05 unverdicted novelty 7.0 of 10

    Introduces practical witnesses of fermionic non-Gaussianity via antiflatness from covariance matrices, with two efficient measurement protocols, a purity-corrected version for mixed states, and experimental results on...

  6. Efficiently learning fermionic unitaries with few non-Gaussian gates

    quant-ph 2025-04 accept novelty 7.0 of 10

    An efficient learning algorithm reconstructs fermionic circuits built from Gaussian unitaries plus a constant number of parity-preserving non-Gaussian gates, up to small diamond-norm error.

  7. Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Fermionic entropy is proven to be a strong, efficiently measurable monotone for fermionic non-Gaussianity, yielding a Theta(n) doping lower bound for matchgate-based approximate state designs.

  8. Graphical Calculus for Fermionic Tensors

    quant-ph 2025-08 conditional novelty 6.0 of 10

    A parity-aware graphical calculus extends the ZX diagram language to fermionic modes, covering Gaussian states, partial traces, purification, fermionization/bosonization, and fermionic error-correcting codes.

  9. Emergence of Generic Entanglement Structure in Doped Matchgate Circuits

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Non-Gaussian doping of matchgate circuits restores generic entanglement growth in unitary evolution and, at extensive per-time injection rates, stabilizes a volume-law phase under measurements.

  10. Natural super-orbitals representation of many-body operators

    cond-mat.str-el 2025-07 conditional novelty 6.0 of 10

    In the impurity model, the natural-super-orbital occupations of both the time-evolution operator and a local operator decay exponentially with mode index, while in the t-V chain no preferred super-orbital basis emerges.

  11. Efficient Measurement of Bosonic Non-Gaussianity

    quant-ph 2025-07 conditional novelty 6.0 of 10

    A new measure, non-Gaussian entropy, and a beam-splitter protocol estimate bosonic non-Gaussianity using only a constant number of state copies, avoiding full tomography.

  12. 2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond

    quant-ph 2025-05 conditional novelty 6.0 of 10

    Clifford and matchgate circuits are two special cases of one 2D diagrammatic calculus, which also yields new tractable tensor-network families and diagrammatic proofs of Ising dualities.

  13. Measuring non-Gaussianity with Correlation

    quant-ph 2025-08 conditional novelty 5.0 of 10

    Non-Gaussianity of a quantum state equals the correlation its two copies generate at a 50:50 beam splitter, enabling a state-agnostic, sample-efficient measurement via SWAP tests.

  14. Displaced Fermionic Gaussian States and their Classical Simulation

    quant-ph 2024-11 conditional novelty 5.0 of 10

    Displaced fermionic Gaussian states and circuits, which include linear Majorana terms, are shown to be equivalent to matchgate circuits with single-qubit gates on the first line and are efficiently classically simulable.

Pith tools