Fermionic Hamiltonian engineering with local control
Abstract
Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible Hamiltonians beyond the fixed system Hamiltonian provided by the hardware. We introduce a framework for fermionic Hamiltonian engineering based on interleaving free evolution under the system Hamiltonian with a sequence of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently through a linear program, enabling effective time evolution under a broad class of target Hamiltonians. In particular, our method realizes arbitrary complex tunnelling coefficients, constrained only by the connectivity of the underlying system Hamiltonian. We further show that symmetries of the Hamiltonian engineering task can be exploited to drastically reduce the cost of computing the control parameters, and that errors arising from finite pulse times can be compensated within the same framework through a simple modification of the linear program. To our knowledge, this is the first automated method to realize locally tunable artificial gauge fields in interacting fermionic lattice models using only site-resolved energy shifts as control. We demonstrate the method by engineering the dynamics of interacting Fermi-Hubbard chains with complex tunnelling coefficients and of the Harper-Hofstadter model on a 1088-mode lattice. For the latter, we exploit the translation symmetry of the model to determine a provably optimal six-pulse sequence that produces the desired dynamics independent of the lattice size.
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BibTeX
@misc{kum2026fermionic,
title = {{Fermionic Hamiltonian engineering with local control}},
author = {Özgün Kum and Matthias Zipper and Ludwig Mathey and Martin Kliesch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.17158},
eprint = {2606.17158},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17158},
}
RIS
TY - UNPB
TI - Fermionic Hamiltonian engineering with local control
AU - Özgün Kum
AU - Matthias Zipper
AU - Ludwig Mathey
AU - Martin Kliesch
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2606.17158
UR - https://arxiv.org/abs/2606.17158
AB - Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible Hamiltonians beyond the fixed system Hamiltonian provided by the hardware. We introduce a framework for fermionic Hamiltonian engineering based on interleaving free evolution under the system Hamiltonian with a sequence of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently through a linear program, enabling effective time evolution under a broad class of target Hamiltonians. In particular, our method realizes arbitrary complex tunnelling coefficients, constrained only by the connectivity of the underlying system Hamiltonian. We further show that symmetries of the Hamiltonian engineering task can be exploited to drastically reduce the cost of computing the control parameters, and that errors arising from finite pulse times can be compensated within the same framework through a simple modification of the linear program. To our knowledge, this is the first automated method to realize locally tunable artificial gauge fields in interacting fermionic lattice models using only site-resolved energy shifts as control. We demonstrate the method by engineering the dynamics of interacting Fermi-Hubbard chains with complex tunnelling coefficients and of the Harper-Hofstadter model on a 1088-mode lattice. For the latter, we exploit the translation symmetry of the model to determine a provably optimal six-pulse sequence that produces the desired dynamics independent of the lattice size.
ER -