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.
Measuring Non-Gaussian Magic in Fermions: Convolution, Entropy, and the Violation of Wick's Theorem and the Matchgate Identity
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Classically hard to simulate quantum states, or "magic states", are prerequisites to quantum advantage, highlighting an apparent separation between classically and quantumly tractable problems. Classically simulable states such as Clifford circuits on stabilizer states, free bosonic states, free fermions, and matchgate circuits are all in some sense Gaussian. While free bosons and fermions arise from quadratic Hamiltonians, recent works have demonstrated that bosonic and qudit systems converge to Gaussians and stabilizers under convolution. In this work, we similarly identify convolution for fermions and find efficient measures of non-Gaussian magic in pure fermionic states. We demonstrate that three natural notions for the Gaussification of a state, (1) the Gaussian state with the same covariance matrix, (2) the fixed point of convolution, and (3) the closest Gaussian in relative entropy, coincide by proving a central limit theorem for fermionic systems. We then utilize the violation of Wick's theorem and the matchgate identity to quantify non-Gaussian magic in addition to a SWAP test.
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2026 8roles
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Defines bridge degree monotone for fermionic non-Gaussianity from Bell-sampling eigenvalues of Lambda, shows non-increase under Gaussian protocols for stronger no-go theorems, and gives polynomial-sample tests for Gaussianity and 2-designs.
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.
CovAngelo implements a QM/QM/MM embedding model using quantum-information metrics to compute reaction energy profiles and barriers for covalent drug binding at lower cost than conventional methods, demonstrated on zanubrutinib to BTK.
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
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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Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
Defines bridge degree monotone for fermionic non-Gaussianity from Bell-sampling eigenvalues of Lambda, shows non-increase under Gaussian protocols for stronger no-go theorems, and gives polynomial-sample tests for Gaussianity and 2-designs.
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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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CovAngelo: A hybrid quantum-classical computing platform for accurate and scalable drug discovery
CovAngelo implements a QM/QM/MM embedding model using quantum-information metrics to compute reaction energy profiles and barriers for covalent drug binding at lower cost than conventional methods, demonstrated on zanubrutinib to BTK.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
- Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions
- Computable fermionic non-Gaussianity from the covariance matrix