Two covariance-matrix-derived entropy families are proven to be fermionic non-Gaussianity monotones, yielding SWAP-gate lower bounds and classical-simulation upper bounds.
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In the large-N limit of the SYK model, quantum magic of pure KM states dual to black holes is linear in N with a temperature-tunable slope between 0 and 1/2.
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.
Fermionic non-Gaussianity can be tested with O(n²/ϵ²) two-copy Bell shots or O(n³/ϵ⁴) single-copy shots and certified in noisy mixed states by a purity-corrected covariance witness.
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.
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
Polfed.jl provides an efficient implementation of polynomially filtered Lanczos diagonalization for mid-spectrum eigenpairs in quantum many-body systems, supporting larger sizes via on-the-fly polynomial transformations and GPU acceleration.
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Computable fermionic non-Gaussianity from the covariance matrix
Two covariance-matrix-derived entropy families are proven to be fermionic non-Gaussianity monotones, yielding SWAP-gate lower bounds and classical-simulation upper bounds.
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Tuning quantum magic of pure quantum chaotic states with a gravity dual
In the large-N limit of the SYK model, quantum magic of pure KM states dual to black holes is linear in N with a temperature-tunable slope between 0 and 1/2.
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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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Practical Tests and Witnesses of Fermionic non-Gaussianity
Fermionic non-Gaussianity can be tested with O(n²/ϵ²) two-copy Bell shots or O(n³/ϵ⁴) single-copy shots and certified in noisy mixed states by a purity-corrected covariance witness.
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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.
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Coherence dynamics in quantum many-body systems with conservation laws
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
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Computing eigenpairs of quantum many-body systems with Polfed.jl
Polfed.jl provides an efficient implementation of polynomially filtered Lanczos diagonalization for mid-spectrum eigenpairs in quantum many-body systems, supporting larger sizes via on-the-fly polynomial transformations and GPU acceleration.
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