Quantum control as renormalization group flow
Abstract
The Renormalization Group (RG) establishes relations between effective descriptions of physical systems at different scales; in Hamiltonian RG, these relations induce a flow in the space of Hamiltonians. In direct correspondence, we design an RG framework for quantum control by constructing a flow in the space of time-dependent Hamiltonians. A prescribed control subspace, selected to contain only experimentally accessible terms, forms the fixed-point manifold, while the flow preserves the target unitary and monotonically reduces the Hamiltonian weight outside this subspace. Exploiting the freedom in constructing the flow, we introduce flow-equation engineering to enhance the versatility of the framework for diverse control problems, including time-periodic and open-interval smooth protocols with prescribed endpoints. We provide two disparate applications to exhibit the utility of our approach: (i) Nonperturbative Floquet engineering beyond the regime of validity of high-frequency expansions, which we demonstrate by constructing an implementable time-periodic protocol for the Haldane model; (ii) Accessible fast-forward driving from unit-fidelity counterdiabatic evolution, which we showcase for large transverse-field Ising chains away from the adiabatic regime by compressing the long-range multibody adiabatic gauge potential into the original time-dependent Ising control schedules. Our control RG framework reveals a unifying perspective on Hamiltonian engineering and unitary quantum control, and can serve as an organizing principle behind seemingly disparate nonequilibrium quantum dynamics.
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BibTeX
@misc{wang2026quantum,
title = {{Quantum control as renormalization group flow}},
author = {Zuo Wang and Paul M. Schindler and Modesto Orozco-Ruiz and Nguyen H. Le and Florian Mintert and Marin Bukov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26154},
eprint = {2610.26154},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26154},
}
RIS
TY - UNPB
TI - Quantum control as renormalization group flow
AU - Zuo Wang
AU - Paul M. Schindler
AU - Modesto Orozco-Ruiz
AU - Nguyen H. Le
AU - Florian Mintert
AU - Marin Bukov
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26154
UR - https://arxiv.org/abs/2610.26154
AB - The Renormalization Group (RG) establishes relations between effective descriptions of physical systems at different scales; in Hamiltonian RG, these relations induce a flow in the space of Hamiltonians. In direct correspondence, we design an RG framework for quantum control by constructing a flow in the space of time-dependent Hamiltonians. A prescribed control subspace, selected to contain only experimentally accessible terms, forms the fixed-point manifold, while the flow preserves the target unitary and monotonically reduces the Hamiltonian weight outside this subspace. Exploiting the freedom in constructing the flow, we introduce flow-equation engineering to enhance the versatility of the framework for diverse control problems, including time-periodic and open-interval smooth protocols with prescribed endpoints. We provide two disparate applications to exhibit the utility of our approach: (i) Nonperturbative Floquet engineering beyond the regime of validity of high-frequency expansions, which we demonstrate by constructing an implementable time-periodic protocol for the Haldane model; (ii) Accessible fast-forward driving from unit-fidelity counterdiabatic evolution, which we showcase for large transverse-field Ising chains away from the adiabatic regime by compressing the long-range multibody adiabatic gauge potential into the original time-dependent Ising control schedules. Our control RG framework reveals a unifying perspective on Hamiltonian engineering and unitary quantum control, and can serve as an organizing principle behind seemingly disparate nonequilibrium quantum dynamics.
ER -