Optimizing quantum encodings for analog simulation through dynamical algebra reachability
Abstract
Analog quantum computers provides direct access to continuous many-body dynamics, but their native control Hamiltonians generate only a restricted operator space. Consequently, the fidelity with which they can reproduce a target Hamiltonian's dynamics depends not only on spectral agreement but on whether the physical controls can actually generate the required evolution. We introduce a geometry-independent framework for diagnosing and optimizing this compatibility between the spectral algebra generated by a target Hamiltonian H and a Krylov-type operator space generated from the device's independently tunable control Hamiltonians and a fixed initial state. The encoding problem can be formulated as an optimization over the unitary orbit of the target Hamiltonian. We maximize a smooth subspace-overlap functional using Riemannian gradient descent on U(d), thereby selecting a spectrally equivalent representation whose target algebra is better aligned with the native controls. We apply this framework to the deuteron Hamiltonian encoded on a Rydberg-atom analog processor. The standard binary encoding is strongly misaligned with this space for small system sizes, while principal-angle optimization substantially improves the algebraic compatibility of the encoding. Moreover, using a single geometry-independent optimized encoding substantially reduces the sensitivity of state-preparation fidelity to the atomic geometry. These results establish algebraic reachability as a useful preprocessing criterion for analog encoding design: it identifies representation-level incompatibilities before device-specific geometry and pulse optimization, while the distinction between algebra-level and state-level reachability clarifies when full encoding optimization is necessary and when geometry-dependent control resources can compensate for incomplete algebraic alignment.
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BibTeX
@misc{manginbrinet2026optimizing,
title = {{Optimizing quantum encodings for analog simulation through dynamical algebra reachability}},
author = {Mariane Mangin-Brinet},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11351},
eprint = {2609.11351},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05759396v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimizing quantum encodings for analog simulation through dynamical algebra reachability
AU - Mariane Mangin-Brinet
PY - 2026
DA - 2026/09/10
PB - HAL
DO - 10.48550/arxiv.2609.11351
UR - https://hal.science/hal-05759396v1
AB - Analog quantum computers provides direct access to continuous many-body dynamics, but their native control Hamiltonians generate only a restricted operator space. Consequently, the fidelity with which they can reproduce a target Hamiltonian's dynamics depends not only on spectral agreement but on whether the physical controls can actually generate the required evolution. We introduce a geometry-independent framework for diagnosing and optimizing this compatibility between the spectral algebra generated by a target Hamiltonian H and a Krylov-type operator space generated from the device's independently tunable control Hamiltonians and a fixed initial state. The encoding problem can be formulated as an optimization over the unitary orbit of the target Hamiltonian. We maximize a smooth subspace-overlap functional using Riemannian gradient descent on U(d), thereby selecting a spectrally equivalent representation whose target algebra is better aligned with the native controls. We apply this framework to the deuteron Hamiltonian encoded on a Rydberg-atom analog processor. The standard binary encoding is strongly misaligned with this space for small system sizes, while principal-angle optimization substantially improves the algebraic compatibility of the encoding. Moreover, using a single geometry-independent optimized encoding substantially reduces the sensitivity of state-preparation fidelity to the atomic geometry. These results establish algebraic reachability as a useful preprocessing criterion for analog encoding design: it identifies representation-level incompatibilities before device-specific geometry and pulse optimization, while the distinction between algebra-level and state-level reachability clarifies when full encoding optimization is necessary and when geometry-dependent control resources can compensate for incomplete algebraic alignment.
ER -