Hamiltonian engineering via pulses: beyond group averaging
Abstract
We develop a geometric framework for Hamiltonian engineering in finite-dimensional quantum systems using ideal control pulses. Starting from a bilinear Schrödinger equation with unbounded control amplitudes, we construct the closed pulse group and use extensions of control systems and Filippov's relaxation theorem to obtain a family of effective Hamiltonians given by the convex hull of the drift's adjoint orbit plus the Lie algebra of the pulse group. The geometry of this orbitope describes possibilities beyond group averaging. Using the isotypic decomposition of the adjoint representation, we characterize its affine hull and show that the group average lies in its interior. This yields locally accessible families of effective Hamiltonians around the invariant part of the drift. We apply the framework to recover the necessary and sufficient condition for dynamical decoupling from arbitrary interactions with a finite-dimensional bath. For connected abelian pulse groups, we describe the relevant representation decomposition through restricted roots. Finally, for qubit networks with identical pairwise couplings, we give a qualitative characterization and quantitative estimation of effective Hamiltonians that can be generated using our framework.
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BibTeX
@misc{beschastnyi2026hamiltonian,
title = {{Hamiltonian engineering via pulses: beyond group averaging}},
author = {Ivan Beschastnyi and Lucah Patel and David Tinoco},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18911},
eprint = {2609.18911},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05795355v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Hamiltonian engineering via pulses: beyond group averaging
AU - Ivan Beschastnyi
AU - Lucah Patel
AU - David Tinoco
PY - 2026
DA - 2026/09/16
PB - HAL
DO - 10.48550/arxiv.2609.18911
UR - https://hal.science/hal-05795355v1
AB - We develop a geometric framework for Hamiltonian engineering in finite-dimensional quantum systems using ideal control pulses. Starting from a bilinear Schrödinger equation with unbounded control amplitudes, we construct the closed pulse group and use extensions of control systems and Filippov's relaxation theorem to obtain a family of effective Hamiltonians given by the convex hull of the drift's adjoint orbit plus the Lie algebra of the pulse group. The geometry of this orbitope describes possibilities beyond group averaging. Using the isotypic decomposition of the adjoint representation, we characterize its affine hull and show that the group average lies in its interior. This yields locally accessible families of effective Hamiltonians around the invariant part of the drift. We apply the framework to recover the necessary and sufficient condition for dynamical decoupling from arbitrary interactions with a finite-dimensional bath. For connected abelian pulse groups, we describe the relevant representation decomposition through restricted roots. Finally, for qubit networks with identical pairwise couplings, we give a qualitative characterization and quantitative estimation of effective Hamiltonians that can be generated using our framework.
ER -