Emergent Prethermal Symmetries for Scalable Hamiltonian Learning
Abstract
Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order 1/ε to attain ε precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with 1/ε. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a d-dimensional lattice of n qubits, this enables learning every coefficient to accuracy ε, with failure probability at most δ, using total evolution time 𝒪(logd(1/ε)log2(n/δ)/ε). Thus, our learning protocol attains the information-theoretically optimal 1/ε dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.
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BibTeX
@misc{shin2026emergent,
title = {{Emergent Prethermal Symmetries for Scalable Hamiltonian Learning}},
author = {Myeongjin Shin and Junseo Lee and Iman Marvian and Yu Tong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27181},
eprint = {2609.27181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27181},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergent Prethermal Symmetries for Scalable Hamiltonian Learning
AU - Myeongjin Shin
AU - Junseo Lee
AU - Iman Marvian
AU - Yu Tong
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27181
UR - https://arxiv.org/abs/2609.27181
AB - Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order 1/ε to attain ε precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with 1/ε. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a d-dimensional lattice of n qubits, this enables learning every coefficient to accuracy ε, with failure probability at most δ, using total evolution time 𝒪(log^d(1/ε)log^2(n/δ)/ε). Thus, our learning protocol attains the information-theoretically optimal 1/ε dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.
ER -