analiza aiqbench
This paper advances the theoretical foundations of Gaussian Boson Sampling by establishing rigorous bounds on local anticoncentration through conditional Wishart geometry and Fourier interpolation techniques. The work provides explicit polynomial coefficients for hafnian estimates in complex Gaussian ensembles, which is critical for validating the sampling complexity required to demonstrate quantum advantage. By proving these properties for finite Haar interferometers, the study strengthens the mathematical framework necessary for scaling photonic quantum computing architectures.
Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry
arXiv:2610.00112v1 Announce Type: cross Abstract: Local anticoncentration controls the conversion of additive output probability estimates to relative estimates in Gaussian boson sampling. We prove a center-uniform quadratic small-ball bound for hafnians of complex Gaussian transpose Gram matrices for $2n$ selected modes, with an explicit finite coefficient that is polynomial when the number of Gaussian rows is at least of order $n^2/\log n$. Letting the Gaussian row count tend to infinity yields anticoncentration for the independent complex symmetric Gaussian ensemble. For the transpose Gram hafnian bound, the proof compresses dependent hafnian cofactors by Fourier interpolation and controls their self-coupled variance through a conditional Wishart identity that preserves the transpose Gram coordinate. Independent perturbations satisfy related bounds, and a positive mixture density shows that the local quadratic power is exact. Together with the uniform hiding theorem in the companion paper, the result gives local anticoncentration for finite Haar interferometers.
Abstract:Local anticoncentration controls the conversion of additive output probability estimates to relative estimates in Gaussian boson sampling. We prove a center-uniform quadratic small-ball bound for hafnians of complex Gaussian transpose Gram matrices for $2n$ selected modes, with an explicit finite coefficient that is polynomial when the number of Gaussian rows is at least of order $n^2/\log n$. Letting the Gaussian row count tend to infinity yields anticoncentration for the independent complex symmetric Gaussian ensemble. For the transpose Gram hafnian bound, the proof compresses dependent hafnian cofactors by Fourier interpolation and controls their self-coupled variance through a conditional Wishart identity that preserves the transpose Gram coordinate. Independent perturbations satisfy related bounds, and a positive mixture density shows that the local quadratic power is exact. Together with the uniform hiding theorem in the companion paper, the result gives local anticoncentration for finite Haar interferometers.
39 pages, 4 figures, 1 table. Includes all appendices
Probability (math.PR); Quantum Physics (quant-ph)
arXiv:2610.00112 [math.PR]
(or arXiv:2610.00112v1 [math.PR] for this version)
https://doi.org/10.48550/arXiv.2610.00112 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 245 cuvinte
Subiecte conexe
Measurement incompatibility in Bayesian multiparameter quantum estimation
Quantum Journal · 13 aug. 2026
The Golden Junction of Gaussian Covariance Geometries: Sector Anisotropy, Relative-Entropy Response, and Local Penalties
arXiv · 17 sept. 2026
Early Signatures of Memorization in Diffusion Models via Basin Geometry and Cyclic Denoising
arXiv · 9 oct. 2026
The magic cost of fermionic randomness
arXiv · 6 oct. 2026