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This is theoretical work on quantum many-body physics: when a free-fermion ground state can be prepared using only local dissipation. It gives a spectral criterion and a no-go result, with the caveat that extra obstructions appear in higher dimensions. For quantum computing readers, it clarifies which target states can be reached by dissipative state-preparation schemes at all, which bears on engineered-reservoir approaches to quantum simulation and state initialization.
Locality in Dissipative Ground-State Preparation
arXiv:2610.40628v1 Announce Type: new Abstract: Can the ground state of a local Hamiltonian be prepared by local dissipation? We address this question for free-fermion Hamiltonians, using a quadratic Lindbladian with linear jump operators for the dissipative ground-state preparation. For translation-invariant targets, Fourier correspondence relates spatial locality to momentum-space analyticity, allowing us to derive a complete spectral criterion for the existence of exponentially local linear jump operators that prepare the ground state. This criterion leads to a no-go theorem that, sign-changing Fermi-level crossings exclude exponentially local linear jump operators for preparing the ground state. While these crossings are the complete obstruction in one dimension, additional obstructions generally arise in higher dimensions. We illustrate these additional obstructions using two quadratic-band-touching models with algebraically decaying ground-state correlations. We further show that short-range ground-state correlations, although not necessary, are sufficient for local dissipative preparation even without translation invariance. Our results establish how the spectral structure of the target Hamiltonian governs the locality of dissipative ground-state preparation.
Abstract:Can the ground state of a local Hamiltonian be prepared by local dissipation? We address this question for free-fermion Hamiltonians, using a quadratic Lindbladian with linear jump operators for the dissipative ground-state preparation. For translation-invariant targets, Fourier correspondence relates spatial locality to momentum-space analyticity, allowing us to derive a complete spectral criterion for the existence of exponentially local linear jump operators that prepare the ground state. This criterion leads to a no-go theorem that, sign-changing Fermi-level crossings exclude exponentially local linear jump operators for preparing the ground state. While these crossings are the complete obstruction in one dimension, additional obstructions generally arise in higher dimensions. We illustrate these additional obstructions using two quadratic-band-touching models with algebraically decaying ground-state correlations. We further show that short-range ground-state correlations, although not necessary, are sufficient for local dissipative preparation even without translation invariance. Our results establish how the spectral structure of the target Hamiltonian governs the locality of dissipative ground-state preparation.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2610.40628 [quant-ph]
(or arXiv:2610.40628v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.40628 Focus to learn more arXiv-issued DOI via DataCite
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