ArXiv Preprint Introduces O(sqrt(m)) Approximation for Time-Optimal Hamiltonian Engineering via Cut Polytopes

The work shows that only commutation relations between control pulses and the native Hamiltonian are needed to cast pulse design as a linear program. By relaxing the NP-complete polytope to the elliptope and adding O(m) uniformly sampled pulses, the algorithm produces feasible pulse sequences whose quantum run times stay within a provable factor of the optimum and saturate with lattice size in the fermionic case. Benchmarks indicate near-optimal durations wherever the exact optimum is computable and clear outperformance of prior heuristics with the same pulse budget. This bridges discrete optimization geometry with analog quantum control, offering a route to automatic programming of simulators that avoids exhaustive search over exponentially many pulse combinations. Connections to earlier results on quantum gate compilation and open-system control become visible once the polytope lens is applied: the same rounding technique that yields good cut approximations also stabilizes pulse sequences against the decoherence channels that dominate near-term devices.