Spectral Core-Tail Architecture for Locally Certified Gibbs-State Preparation
Abstract
Preparing a quantum Gibbs state requires reproducing both its thermal distribution and the associated many-body eigenspaces. In this work, we formalize the spectral core-tail architecture (SCTA) as a framework comprising a structured thermal core, a geometrically characterized unitary tail, and an exact residual measuring the remaining core-frame Hamiltonian mismatch. We derive a local Gibbs-state error bound separating core-preparation, tail-implementation, and modeling errors. The modeling contribution is volume uniform when its Kubo-Mori response meets the shell summability condition and the relevant local data remain uniform. We then highlight three anchor Hamiltonian classes which admit exact core-tail constructions with zero residuals. For small deformations of an exact anchor, we employ a Schrieffer-Wolff reduction procedure to construct a corrected core-tail pair that formally removes the deformation order by order. Under uniform locality and solvability assumptions, we show that the first-order reduction yields a residual that remains bounded and is quadratic in the deformation strength. Furthermore, we numerically test the first-order reduction on deformed graph-stabilizer Hamiltonians. The numerical results show approximately quadratic suppression of both the Hamiltonian-level mismatch and the local Gibbs-state error in the perturbative regime. We also find that the constructed correction circuit structure remains useful as a variational ansatz beyond perturbative control, often improving on both the bare and prescribed first-order states.
Related
- Adiabatic tracking and geometric schedules for classical and quantum Gibbs-state preparation
- Gibbs state preparation through quantum decoding
- Quantum Gibbs State Preparation via Relative Decoding: From Fast-Mixing Sources to Broader Target Classes
- Spectral Analysis Beyond the Spectral Gap: Rapid Mixing of Quantum Gibbs Samplers in One Dimension
- Modular-Annihilator Parent Hamiltonians for Purified Gibbs States: Spectral Design and Controlled Approximation
BibTeX
@misc{li2026spectral,
title = {{Spectral Core-Tail Architecture for Locally Certified Gibbs-State Preparation}},
author = {Rui-Hao Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09291},
eprint = {2609.09291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09291},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral Core-Tail Architecture for Locally Certified Gibbs-State Preparation
AU - Rui-Hao Li
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09291
UR - https://arxiv.org/abs/2609.09291
AB - Preparing a quantum Gibbs state requires reproducing both its thermal distribution and the associated many-body eigenspaces. In this work, we formalize the spectral core-tail architecture (SCTA) as a framework comprising a structured thermal core, a geometrically characterized unitary tail, and an exact residual measuring the remaining core-frame Hamiltonian mismatch. We derive a local Gibbs-state error bound separating core-preparation, tail-implementation, and modeling errors. The modeling contribution is volume uniform when its Kubo-Mori response meets the shell summability condition and the relevant local data remain uniform. We then highlight three anchor Hamiltonian classes which admit exact core-tail constructions with zero residuals. For small deformations of an exact anchor, we employ a Schrieffer-Wolff reduction procedure to construct a corrected core-tail pair that formally removes the deformation order by order. Under uniform locality and solvability assumptions, we show that the first-order reduction yields a residual that remains bounded and is quadratic in the deformation strength. Furthermore, we numerically test the first-order reduction on deformed graph-stabilizer Hamiltonians. The numerical results show approximately quadratic suppression of both the Hamiltonian-level mismatch and the local Gibbs-state error in the perturbative regime. We also find that the constructed correction circuit structure remains useful as a variational ansatz beyond perturbative control, often improving on both the bare and prescribed first-order states.
ER -