Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
Non-Local Magic Resources for Fermionic Gaussian States
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity generally requires a prohibitive minimization over the full Hilbert space, making it computationally inaccessible beyond a few qubits. Here, we overcome this bottleneck by suggesting a closed-form expression for the non-local stabilizer entropies of fermionic Gaussian states over local Gaussian unitaries, which can be evaluated in polynomial time directly from the eigenvalues of the reduced Majorana covariance matrix. We apply this framework to characterize fermionic non-local magic across diverse physical regimes: we derive an exact Page-like curve for typical random states, reveal logarithmic scaling at the quantum critical point of the XY model, and establish a quasiparticle picture for magic generation during out-of-equilibrium quantum quenches. Crucially, because our result relies solely on two-point correlation functions, it provides a scalable route for the experimental estimation of fermionic non-local magic in large-scale quantum processors via fermionic shadow tomography.
fields
quant-ph 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
Defines antiflatness of entanglement spectra, introduces antiflat majorization and FPOs for state convertibility, unifies measures via escort distributions and Bregman divergences, expresses Capacity of Entanglement as KL divergence derivative linked to QFI, and identifies maximal antiflatness on a
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
Non-stabilizerness in the Hubbard dimer is quantified via robustness of magic and stabilizer Renyi entropy, revealing the latter's failure on mixed states and distinguishing it from non-Gaussianity and superselected entanglement.
citing papers explorer
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Unitary Designs from Doped Matchgate Circuits
Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
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A journey through Flatland: What does the antiflatness of a spectrum teach us?
Defines antiflatness of entanglement spectra, introduces antiflat majorization and FPOs for state convertibility, unifies measures via escort distributions and Bregman divergences, expresses Capacity of Entanglement as KL divergence derivative linked to QFI, and identifies maximal antiflatness on a
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Long-range nonstabilizerness of topologically encoded states from mutual information
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
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Quantum magic of strongly correlated fermions $-$ the Hubbard dimer
Non-stabilizerness in the Hubbard dimer is quantified via robustness of magic and stabilizer Renyi entropy, revealing the latter's failure on mixed states and distinguishing it from non-Gaussianity and superselected entanglement.