Efficient Sampling for Many-Body Fermionic Non-Gaussianity
Abstract
Fermionic non-Gaussianity is a key resource for universal quantum computation, and its behavior in quantum many-body systems has attracted growing interest. Recently, a convolution-based measure, which we call the magic Rényi entropy (MRE), has been proposed as a resource measure of non-Gaussianity, but its evaluation is limited to small systems due to the computational cost growing exponentially with system size. In this work, we develop a perfect-sampling method to calculate the second-order MRE from matrix product states (MPSs). Our method uses a bounded estimator to control sampling fluctuations and a recursive sweep to draw the samples directly from the input MPS, which allows us to generate each sample with 𝒪(nD3) time, where n and D denote the number of modes and MPS bond dimension, respectively. We benchmark our method on the XXZ chain with up to $128$ sites, demonstrating that the MRE captures intricate higher-order correlations at large scales, which are inaccessible to covariance-based measures. These results provide a computational tool that quantitatively evaluates many-body fermionic non-Gaussianity by accounting for higher-order correlations.
Related
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- Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
- Phase-noise induced many-body interference suppression in Gaussian Boson Sampling
- Computable fermionic non-Gaussianity from the covariance matrix
- Efficient MPO Construction for Long-Range Hamiltonians with Periodic Boundary Conditions: Application to Many-Body Dynamics
BibTeX
@misc{matsuda2026efficient,
title = {{Efficient Sampling for Many-Body Fermionic Non-Gaussianity}},
author = {Ryota Matsuda and Masahiro Hoshino and Yuto Ashida},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03492},
eprint = {2610.03492},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03492},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient Sampling for Many-Body Fermionic Non-Gaussianity
AU - Ryota Matsuda
AU - Masahiro Hoshino
AU - Yuto Ashida
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03492
UR - https://arxiv.org/abs/2610.03492
AB - Fermionic non-Gaussianity is a key resource for universal quantum computation, and its behavior in quantum many-body systems has attracted growing interest. Recently, a convolution-based measure, which we call the magic Rényi entropy (MRE), has been proposed as a resource measure of non-Gaussianity, but its evaluation is limited to small systems due to the computational cost growing exponentially with system size. In this work, we develop a perfect-sampling method to calculate the second-order MRE from matrix product states (MPSs). Our method uses a bounded estimator to control sampling fluctuations and a recursive sweep to draw the samples directly from the input MPS, which allows us to generate each sample with 𝒪(nD^3) time, where n and D denote the number of modes and MPS bond dimension, respectively. We benchmark our method on the XXZ chain with up to $128$ sites, demonstrating that the MRE captures intricate higher-order correlations at large scales, which are inaccessible to covariance-based measures. These results provide a computational tool that quantitatively evaluates many-body fermionic non-Gaussianity by accounting for higher-order correlations.
ER -