Fast Hamiltonian engineering from cut polytope geometry
Abstract
Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific commutation relations between the control pulses and the system Hamiltonian, we provide a unified framework for broad classes of $2$-local qubit, qudit, and fermionic systems. We reformulate time-optimal HE as a complex k-cut polytope problem, with k the number of distinct phases in these commutation relations, and prove it NP-complete for every finite k. We therefore relax the polytope to the elliptope and apply a Krivine-type rounding, yielding pulses informed by the system and target Hamiltonians, which we then use in a linear program. We derive how many informed pulses are necessary and sufficient for the linear program to be reliably feasible. Additionally mixing in uniformly sampled pulses guarantees a solution close to the relaxation value from O(m) pulses, with m the number of interaction terms. Together with upper and lower bounds on the optimal quantum run time, this yields an O(√m) approximation ratio. In benchmarks on a fully connected Ising model, a chiral clock model for qudits, and the fermionic Harper-Hofstadter model, our approach attains near-optimal quantum run times wherever the optimum is computable, reaches run times that saturate with the lattice size in the fermionic case, and outperforms state-of-the-art methods with O(m) pulses. This establishes a unified approach with provable guarantees to the automatic programming of analog quantum simulators.
Related
- Robust Hamiltonian engineering with subensemble control
- Hamiltonian engineering via pulses: beyond group averaging
- Hamiltonian Learning and Certification via Eigenphase Engineering
- Poisson Pencils, Lie Symmetries and Hamiltonian Reductions of a Coupled Nonlinear Wave System:Tangent KdV Geometry and Elliptic Moduli
- Fermionic Hamiltonian engineering with local control
BibTeX
@misc{friese2026fast,
title = {{Fast Hamiltonian engineering from cut polytope geometry}},
author = {Thomas Joachim Friese and Özgün Kum and Aram W. Harrow and Martin Kliesch},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36006},
eprint = {2609.36006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36006},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fast Hamiltonian engineering from cut polytope geometry
AU - Thomas Joachim Friese
AU - Özgün Kum
AU - Aram W. Harrow
AU - Martin Kliesch
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36006
UR - https://arxiv.org/abs/2609.36006
AB - Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific commutation relations between the control pulses and the system Hamiltonian, we provide a unified framework for broad classes of $2$-local qubit, qudit, and fermionic systems. We reformulate time-optimal HE as a complex k-cut polytope problem, with k the number of distinct phases in these commutation relations, and prove it NP-complete for every finite k. We therefore relax the polytope to the elliptope and apply a Krivine-type rounding, yielding pulses informed by the system and target Hamiltonians, which we then use in a linear program. We derive how many informed pulses are necessary and sufficient for the linear program to be reliably feasible. Additionally mixing in uniformly sampled pulses guarantees a solution close to the relaxation value from O(m) pulses, with m the number of interaction terms. Together with upper and lower bounds on the optimal quantum run time, this yields an O(√m) approximation ratio. In benchmarks on a fully connected Ising model, a chiral clock model for qudits, and the fermionic Harper-Hofstadter model, our approach attains near-optimal quantum run times wherever the optimum is computable, reaches run times that saturate with the lattice size in the fermionic case, and outperforms state-of-the-art methods with O(m) pulses. This establishes a unified approach with provable guarantees to the automatic programming of analog quantum simulators.
ER -